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Numbers, fractions and percents exercises · Physics Playground

Numbers, fractions and percents

458 problems with worked solutions, from Prealgebra and Elementary Algebra.

Start with a random one

Learn it first: Fractions, Ratios & Percentages, Direct, Inverse & Square Proportion

Prealgebra1.1 Introduction to Whole Numbers

Example 1.1Which of the following are ⓐ counting numbers? ⓑ whole numbers? 0,1/4,3,5.2,15,105Plus a twin to try
Example 1.2Use place value notation to find the value of the number modeled by the base-10 blocks shown.With a figurePlus a twin to try
Example 1.3In the number 63,407,218; find the place value of each of the following digits: ⓐ 7 ⓑ 0 ⓒ 1 ⓓ 6 ⓔ 3Plus a twin to try
Example 1.4Name the number 8,165,432,098,710 in words.Plus a twin to try
Example 1.5A student conducted research and found that the number of mobile phone users in the United States during one month in 2014 was 327,577,529. Name that number in words.Plus a twin to try
Example 1.6Write the following numbers using digits. ⓐ fifty-three million, four hundred one thousand, seven hundred forty-two ⓑ nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-ninePlus a twin to try
Example 1.7A state budget was about $77 billion. Write the budget in standard form.Plus a twin to try
Example 1.8Round 843 to the nearest ten.Plus a twin to try
Example 1.9Round each number to the nearest hundred: ⓐ 23,658 ⓑ 3,978Plus a twin to try
Example 1.10Round each number to the nearest thousand: ⓐ 147,032 ⓑ 29,504Plus a twin to try

Prealgebra1.2 Add Whole Numbers

Example 1.11Translate from math notation to words: ⓐ 7+1ⓑ 12+14Plus a twin to try
Example 1.12Model the addition 2+6.Plus a twin to try
Example 1.13Model the addition 5+8.Plus a twin to try
Example 1.14Model the addition: 17+26.Plus a twin to try
Example 1.15Find each sum: ⓐ 0+11ⓑ 42+0Plus a twin to try
Example 1.16Add: ⓐ 8+7ⓑ 7+8Plus a twin to try
Example 1.17Add: 28+61.Plus a twin to try
Example 1.18Add: 43+69.Plus a twin to try
Example 1.19Add: 324+586.Plus a twin to try
Example 1.20Add: 1,683+479.Plus a twin to try
Example 1.21Add: 21,357+861+8,596.Plus a twin to try
Example 1.22Translate and simplify: the sum of 19 and 23.Plus a twin to try
Example 1.23Translate and simplify: 28 increased by 31.Plus a twin to try
Example 1.24Hao earned grades of 87,93,68,95,and89 on the five tests of the semester. What is the total number of points he earned on the five tests?Plus a twin to try
Example 1.25Find the perimeter of the patio shown.With a figurePlus a twin to try

Prealgebra1.3 Subtract Whole Numbers

Example 1.26Translate from math notation to words: ⓐ 8−1 ⓑ 26−14.Plus a twin to try
Example 1.27Model the subtraction: 8−2.Plus a twin to try
Example 1.28Model the subtraction: 13−8.Plus a twin to try
Example 1.29Model the subtraction: 43−26.Plus a twin to try
Example 1.30Subtract and then check by adding: ⓐ 9−7ⓑ 8−3.Plus a twin to try
Example 1.31Subtract and then check by adding: 89−61.Plus a twin to try
Example 1.32Subtract: 43−26.Plus a twin to try
Example 1.33Subtract and then check by adding: 207−64.Plus a twin to try
Example 1.34Subtract and then check by adding: 910−586.Plus a twin to try
Example 1.35Subtract and then check by adding: 2,162−479.Plus a twin to try
Example 1.36Translate and then simplify: ⓐ the difference of 13 and 8 ⓑ subtract 24 from 43Plus a twin to try
Example 1.37The temperature in Chicago one morning was 73 degrees Fahrenheit. A cold front arrived and by noon the temperature was 27 degrees Fahrenheit. What was the difference between the temperature in the morning and the…Plus a twin to try
Example 1.38A washing machine is on sale for $399. Its regular price is $588. What is the difference between the regular price and the sale price?Plus a twin to try

Prealgebra1.4 Multiply Whole Numbers

Example 1.39Translate from math notation to words: ⓐ 7×6 ⓑ 12·14 ⓒ 6(13)Plus a twin to try
Example 1.40Model: 3×8.Plus a twin to try
Example 1.41Multiply: ⓐ 0·11ⓑ (42)0Plus a twin to try
Example 1.42Multiply: ⓐ (11)1ⓑ 1·42Plus a twin to try
Example 1.43Multiply: ⓐ 8·7ⓑ 7·8Plus a twin to try
Example 1.44Multiply: 15·4.Plus a twin to try
Example 1.45Multiply: 286·5.Plus a twin to try
Example 1.46Multiply: 62(87).Plus a twin to try
Example 1.47Multiply: ⓐ 47·10ⓑ 47·100.Plus a twin to try
Example 1.48Multiply: (354)(438).Plus a twin to try
Example 1.49Multiply: (896)201.Plus a twin to try
Example 1.50Translate and simplify: the product of 12 and 27.Plus a twin to try
Example 1.51Translate and simplify: twice two hundred eleven.Plus a twin to try
Example 1.52Humberto bought 4 sheets of stamps. Each sheet had 20 stamps. How many stamps did Humberto buy?Plus a twin to try
Example 1.53When Rena cooks rice, she uses twice as much water as rice. How much water does she need to cook 4 cups of rice?Plus a twin to try
Example 1.54Van is planning to build a patio. He will have 8 rows of tiles, with 14 tiles in each row. How many tiles does he need for the patio?Plus a twin to try
Example 1.55Jen’s kitchen ceiling is a rectangle that measures 9 feet long by 12 feet wide. What is the area of Jen’s kitchen ceiling?Plus a twin to try

Prealgebra1.5 Divide Whole Numbers

Example 1.56Translate from math notation to words. ⓐ 64÷8 ⓑ (42)/7 ⓒ 428Plus a twin to try
Example 1.57Model the division: 24÷8.Plus a twin to try
Example 1.58Divide. Then check by multiplying. ⓐ 42÷6 ⓑ (72)/9 ⓒ 763Plus a twin to try
Example 1.59Divide. Then check by multiplying: ⓐ 11÷11 ⓑ (19)/1 ⓒ 17Plus a twin to try
Example 1.60Divide. Check by multiplying: ⓐ 0÷3 ⓑ 10/0.Plus a twin to try
Example 1.61Divide 2,596÷4. Check by multiplying:Plus a twin to try
Example 1.62Divide 4,506÷6. Check by multiplying:Plus a twin to try
Example 1.63Divide 7,263÷9. Check by multiplying.Plus a twin to try
Example 1.64Divide 1,439÷4. Check by multiplying.Plus a twin to try
Example 1.65Divide and then check by multiplying: 1,461÷13.Plus a twin to try
Example 1.66Divide and check by multiplying: 74,521÷241.Plus a twin to try
Example 1.67Translate and simplify: the quotient of 51 and 17.Plus a twin to try
Example 1.68Cecelia bought a 160-ounce box of oatmeal at the big box store. She wants to divide the 160 ounces of oatmeal into 8-ounce servings. She will put each serving into a plastic bag so she can take one bag to work each…Plus a twin to try

Prealgebra3.1 Introduction to Integers

Example 3.1Plot the numbers on a number line: ⓐ3 ⓑ−3 ⓒ−2Plus a twin to try
Example 3.2Order each of the following pairs of numbers using < or >: ⓐ14___6 ⓑ−1___9 ⓒ−1___−4 ⓓ2___−20Plus a twin to try
Example 3.3Find the opposite of each number: ⓐ7 ⓑ−10Plus a twin to try
Example 3.4Simplify: −(−6).Plus a twin to try
Example 3.5Evaluate −x: ⓐ when x=8 ⓑ when x=−8.Plus a twin to try
Example 3.6Simplify: ⓐ |3| ⓑ |−44| ⓒ |0|Plus a twin to try
Example 3.7Evaluate: ⓐ|x|whenx=−35 ⓑ|−y|wheny=−20 ⓒ −|u|whenu=12 ⓓ −|p|whenp=−14Plus a twin to try
Example 3.8Fill in <,>,or= for each of the following: ⓐ|−5|___−|−5| ⓑ8___−|−8| ⓒ−9___−|−9| ⓓ−|−7|___−7Plus a twin to try
Example 3.9Simplify: ⓐ|9−3| ⓑ4|−2|Plus a twin to try
Example 3.10Simplify: |8+7|−|5+6|.Plus a twin to try
Example 3.11Simplify: 24−|19−3(6−2)|.Plus a twin to try
Example 3.12Translate each phrase into an expression with integers: ⓐ the opposite of positive fourteen ⓑ the opposite of −11 ⓒ negative sixteen ⓓ two minus negative sevenPlus a twin to try
Example 3.13Translate into an expression with integers: ⓐ The temperature is 12degrees Fahrenheit below zero. ⓑ The football team had a gain of 3yards. ⓒ The elevation of the Dead Sea is 1,302feet below sea level. ⓓ A checking…Plus a twin to try

Prealgebra3.2 Add Integers

Example 3.14Model: 5+3.Plus a twin to try
Example 3.18ⓐ 4 + 2 ⓑ −3 + 6 ⓒ 4 + (−5) ⓓ -2 + (−3)Plus a twin to try
Example 3.19Simplify: ⓐ19+(−47) ⓑ−32+40Plus a twin to try
Example 3.20Simplify: −14+(−36).Plus a twin to try
Example 3.21Simplify: −5+3(−2+7).Plus a twin to try
Example 3.22Evaluate x+7when ⓐx=−2 ⓑx=−11.Plus a twin to try
Example 3.23When n=−5, evaluate ⓐn+1 ⓑ−n+1.Plus a twin to try
Example 3.24Evaluate 3a+b when a=12 and b=−30.Plus a twin to try
Example 3.25Evaluate (x+y)^2 when x=−18 and y=24.Plus a twin to try
Example 3.26Translate and simplify: the sum of −9 and 5.Plus a twin to try
Example 3.27Translate and simplify: the sum of 8 and −12, increased by 3.Plus a twin to try
Example 3.28The temperature in Buffalo, NY, one morning started at 7degrees below zero Fahrenheit. By noon, it had warmed up 12degrees. What was the temperature at noon?Plus a twin to try
Example 3.29A football team took possession of the football on their 42-yard line. In the next three plays, they lost 6 yards, gained 4 yards, and then lost 8 yards. On what yard line was the ball at the end of those three plays?Plus a twin to try

Prealgebra3.3 Subtract Integers

Example 3.34Model each subtraction. ⓐ 8 − 2 ⓑ −5 − 4 ⓒ 6 − (−6) ⓓ −8 − (−3)Plus a twin to try
Example 3.35Model each subtraction expression: ⓐ 2−8 ⓑ−3−(−8)Plus a twin to try
Example 3.36Simplify: ⓐ13−8and13+(−8) ⓑ−17−9and−17+(−9)Plus a twin to try
Example 3.37Simplify: ⓐ9−(−15)and9+15 ⓑ−7−(−4)and−7+4Plus a twin to try
Example 3.38Simplify: −74−(−58).Plus a twin to try
Example 3.39Simplify: 7−(−4−3)−9.Plus a twin to try
Example 3.40Simplify: 3·7−4·7−5·8.Plus a twin to try
Example 3.41Evaluate x−4when ⓐx=3 ⓑx=−6.Plus a twin to try
Example 3.42Evaluate 20−zwhen ⓐz=12 ⓑz=−12Plus a twin to try
Example 3.43Translate and then simplify: ⓐ the difference of 13 and −21 ⓑ subtract 24 from −19Plus a twin to try
Example 3.44The temperature in Urbana, Illinois one morning was 11 degrees Fahrenheit. By mid-afternoon, the temperature had dropped to −9 degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?Plus a twin to try
Example 3.45Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is 14,497 feet above sea level and the elevation of Death Valley is 282 feet below sea…Plus a twin to try
Example 3.46Leslie has $25 in her checking account and she writes a check for $8. ⓐ What is the balance after she writes the check? ⓑ She writes a second check for $20. What is the new balance after this check? ⓒ Leslie’s friend…Plus a twin to try

Prealgebra3.4 Multiply and Divide Integers

Example 3.47Multiply each of the following: ⓐ−9·3 ⓑ−2(−5) ⓒ4(−8) ⓓ7·6Plus a twin to try
Example 3.48Multiply each of the following: ⓐ−1·7 ⓑ−1(−11)Plus a twin to try
Example 3.49Divide each of the following: ⓐ−27÷3 ⓑ−100÷(−4)Plus a twin to try
Example 3.50Divide each of the following: ⓐ16÷(−1) ⓑ−20÷(−1)Plus a twin to try
Example 3.51Simplify:7(−2)+4(−7)−6.Plus a twin to try
Example 3.52Simplify: ⓐ (−2)^4 ⓑ −2^4Plus a twin to try
Example 3.53Simplify:12−3(9−12).Plus a twin to try
Example 3.54Simplify: 8(−9)÷(−2)^3.Plus a twin to try
Example 3.55Simplify:−30÷2+(−3)(−7).Plus a twin to try
Example 3.57Evaluate3x+4y−6whenx=−1andy=2.Plus a twin to try
Example 3.58Translate to an algebraic expression and simplify if possible: the product of −2 and 14.Plus a twin to try
Example 3.59Translate to an algebraic expression and simplify if possible: the quotient of −56 and −7.Plus a twin to try

Prealgebra3.5 Solve Equations Using Integers; The Division Property of Equality

Example 3.60Determine whether each of the following is a solution of 2x−5=−13: ⓐx=4 ⓑx=−4 ⓒx=−9.Plus a twin to try
Example 3.61Solve: y+9=5.Plus a twin to try
Example 3.62Solve: a−6=−8Plus a twin to try
Example 3.63Write an equation modeled by the envelopes and counters, and then solve it.With a figurePlus a twin to try
Example 3.64Solve:7x=−49.Plus a twin to try
Example 3.65Solve: −3y=63.Plus a twin to try
Example 3.66Translate and solve: five more than x is equal to −3.Plus a twin to try
Example 3.67Translate and solve: the difference of n and 6 is −10.Plus a twin to try
Example 3.68Translate and solve: the number 108 is the product of −9 and y.Plus a twin to try

Prealgebra4.1 Visualize Fractions

Example 4.1Name the fraction of the shape that is shaded in each of the figures.With a figurePlus a twin to try
Example 4.2Shade 3/4 of the circle.With a figurePlus a twin to try
Example 4.3Use fraction circles to make wholes using the following pieces: ⓐ 4 fourths ⓑ 5 fifths ⓒ 6 sixthsPlus a twin to try
Example 4.4Use fraction circles to make wholes using the following pieces: ⓐ 3 halves ⓑ 8 fifths ⓒ 7 thirdsPlus a twin to try
Example 4.5Name the improper fraction modeled. Then write the improper fraction as a mixed number.With a figurePlus a twin to try
Example 4.6Draw a figure to model (11)/8.Plus a twin to try
Example 4.7Use a model to rewrite the improper fraction (11)/6 as a mixed number.Plus a twin to try
Example 4.8Use a model to rewrite the mixed number 14/5 as an improper fraction.Plus a twin to try
Example 4.9Convert (11)/6 to a mixed number.Plus a twin to try
Example 4.10Convert the improper fraction (33)/8 to a mixed number.Plus a twin to try
Example 4.11Convert the mixed number 42/3 to an improper fraction.Plus a twin to try
Example 4.12Convert the mixed number 102/7 to an improper fraction.Plus a twin to try
Example 4.13Use fraction tiles to find equivalent fractions. Show your result with a figure. ⓐ How many eighths equal one-half? ⓑ How many tenths equal one-half? ⓒ How many twelfths equal one-half?Plus a twin to try
Example 4.14Find three fractions equivalent to 2/5.Plus a twin to try
Example 4.15Find a fraction with a denominator of 21 that is equivalent to 2/7.Plus a twin to try
Example 4.16Locate and label the following on a number line: 3/4,4/3,5/3,41/5, and 7/2.Plus a twin to try
Example 4.17Locate and label the following on the number line: 1/4,−1/4,11/3,−11/3,5/2, and −5/2.Plus a twin to try
Example 4.18Order each of the following pairs of numbers, using < or >: ⓐ−2/3____−1 ⓑ−31/2____−3 ⓒ−3/7____−3/8 ⓓ−2____(−16)/9Plus a twin to try

Prealgebra4.2 Multiply and Divide Fractions

Example 4.19Simplify: (10)/(15).Plus a twin to try
Example 4.20Simplify: −(18)/(24).Plus a twin to try
Example 4.21Simplify: −(56)/(32).Plus a twin to try
Example 4.22Simplify: (210)/(385).Plus a twin to try
Example 4.23Simplify: (5xy)/(15x).Plus a twin to try
Example 4.24Use a diagram to model 1/2·3/4.Plus a twin to try
Example 4.25Multiply, and write the answer in simplified form: 3/4·1/5.Plus a twin to try
Example 4.26Multiply, and write the answer in simplified form: −5/8(−2/3).Plus a twin to try
Example 4.27Multiply, and write the answer in simplified form: −(14)/(15)·(20)/(21).Plus a twin to try
Example 4.28Multiply, and write the answer in simplified form: ⓐ1/7·56 ⓑ(12)/5(−20x)Plus a twin to try
Example 4.29Find the reciprocal of each number. Then check that the product of each number and its reciprocal is 1. ⓐ4/9 ⓑ−1/6 ⓒ−(14)/5 ⓓ7Plus a twin to try
Example 4.30Fill in the chart for each fraction in the left column: Number Opposite Absolute Value Reciprocal −3/8 1/2 9/5 −5Plus a twin to try
Example 4.31Model: 1/4÷1/8.Plus a twin to try
Example 4.32Model: 2÷1/4.Plus a twin to try
Example 4.33Divide, and write the answer in simplified form: 2/5÷(−3/7).Plus a twin to try
Example 4.34Divide, and write the answer in simplified form: 2/3÷n/5.Plus a twin to try
Example 4.35Divide, and write the answer in simplified form: −3/4÷(−7/8).Plus a twin to try
Example 4.36Divide, and write the answer in simplified form: 7/(18)÷(14)/(27).Plus a twin to try

Prealgebra4.3 Multiply and Divide Mixed Numbers and Complex Fractions

Example 4.37Multiply: 31/3·5/8Plus a twin to try
Example 4.38Multiply, and write your answer in simplified form: 24/5(−17/8).Plus a twin to try
Example 4.39Divide, and write your answer in simplified form: 34/7÷5.Plus a twin to try
Example 4.40Divide: 21/2÷11/4.Plus a twin to try
Example 4.41Translate the phrase into an algebraic expression: “the quotient of 3x and 8.”Plus a twin to try
Example 4.42Translate the phrase into an algebraic expression: the quotient of the difference of m and n, and p.Plus a twin to try
Example 4.43Simplify: (3/4)/(5/8).Plus a twin to try
Example 4.44Simplify: (−6/7)/3.Plus a twin to try
Example 4.45Simplify: (x/2)/((xy)/6).Plus a twin to try
Example 4.46Simplify: (23/4)/(1/8).Plus a twin to try
Example 4.47Which of the following fractions are equivalent to 7/(−8)? (−7)/(−8),(−7)/8,7/8,−7/8Plus a twin to try
Example 4.48Simplify: (4+8)/(5−3).Plus a twin to try
Example 4.49Simplify: (4−2(3))/(2^2+2).Plus a twin to try
Example 4.50Simplify: ((8−4)^2)/(8^2−4^2).Plus a twin to try
Example 4.51Simplify: (4(−3)+6(−2))/(−3(2)−2).Plus a twin to try

Prealgebra4.4 Add and Subtract Fractions with Common Denominators

Example 4.52Use a model to find the sum 3/8+2/8.Plus a twin to try
Example 4.53Find the sum: 3/5+1/5.Plus a twin to try
Example 4.54Find the sum: x/3+2/3.Plus a twin to try
Example 4.55Find the sum: −9/d+3/d.Plus a twin to try
Example 4.56Find the sum: (2n)/(11)+(5n)/(11).Plus a twin to try
Example 4.57Find the sum: −3/(12)+(−5/(12)).Plus a twin to try
Example 4.58Use fraction circles to find the difference: 4/5−1/5.Plus a twin to try
Example 4.59Find the difference: (23)/(24)−(14)/(24).Plus a twin to try
Example 4.60Find the difference: y/6−1/6.Plus a twin to try
Example 4.61Find the difference: −(10)/x−4/x.Plus a twin to try
Example 4.62Simplify: 3/8+(−5/8)−1/8.Plus a twin to try

Prealgebra4.5 Add and Subtract Fractions with Different Denominators

Example 4.63Find the LCD for the fractions 7/(12) and 5/(18).Plus a twin to try
Example 4.64Find the least common denominator for the fractions 8/(15) and (11)/(24).Plus a twin to try
Example 4.65Convert 1/4and1/6 to equivalent fractions with denominator 12, their LCD.Plus a twin to try
Example 4.66Convert 8/(15) and (11)/(24) to equivalent fractions with denominator 120, their LCD.Plus a twin to try
Example 4.67Add: 1/2+1/3.Plus a twin to try
Example 4.68Subtract: 1/2−(−1/4).Plus a twin to try
Example 4.69Add: 7/(12)+5/(18).Plus a twin to try
Example 4.70Subtract: 7/(15)−(19)/(24).Plus a twin to try
Example 4.71Add: −(11)/(30)+(23)/(42).Plus a twin to try
Example 4.72Add: 3/5+x/8.Plus a twin to try
Example 4.73Simplify: ⓐ−1/4+1/6 ⓑ−1/4÷1/6Plus a twin to try
Example 4.74Simplify: ⓐ(5x)/6−3/(10) ⓑ(5x)/6·3/(10)Plus a twin to try
Example 4.75Simplify: ((1/2)^2)/(4+3^2).Plus a twin to try
Example 4.76Simplify: (1/2+2/3)/(3/4−1/6).Plus a twin to try
Example 4.77Evaluate x+1/3 when ⓐx=−1/3 ⓑx=−3/4.Plus a twin to try
Example 4.78Evaluate y−5/6 when y=−2/3.Plus a twin to try
Example 4.79Evaluate 2x^2y when x=1/4 and y=−2/3.Plus a twin to try
Example 4.80Evaluate (p+q)/r when p=−4,q=−2, and r=8.Plus a twin to try

Prealgebra4.6 Add and Subtract Mixed Numbers

Example 4.81Model 21/3+12/3 and give the sum.Plus a twin to try
Example 4.82Model 13/5+23/5 and give the sum as a mixed number.Plus a twin to try
Example 4.83Add: 34/9+22/9.Plus a twin to try
Example 4.84Find the sum: 95/9+57/9.Plus a twin to try
Example 4.85Add by converting the mixed numbers to improper fractions: 37/8+43/8.Plus a twin to try
Example 4.86Use a model to subtract: 1−1/3.Plus a twin to try
Example 4.87Use a model to subtract: 2−3/4.Plus a twin to try
Example 4.88Use a model to subtract: 2−12/5.Plus a twin to try
Example 4.89Use a model to subtract: 11/4−3/4Plus a twin to try
Example 4.90Find the difference: 53/5−24/5.Plus a twin to try
Example 4.91Find the difference by converting to improper fractions: 96/(11)−7(10)/(11).Plus a twin to try
Example 4.92Add: 21/2+52/3.Plus a twin to try
Example 4.93Subtract: 43/4−27/8.Plus a twin to try
Example 4.94Subtract: 35/(11)−43/4.Plus a twin to try

Prealgebra4.7 Solve Equations with Fractions

Example 4.95Determine whether each of the following is a solution of x−3/(10)=1/2. ⓐx=1 ⓑx=4/5 ⓒx=−4/5Plus a twin to try
Example 4.96Solve: y+9/(16)=5/(16).Plus a twin to try
Example 4.97Solve: a−5/9=−8/9.Plus a twin to try
Example 4.98Solve: 10q=44.Plus a twin to try
Example 4.99Solve: x/7=−9.Plus a twin to try
Example 4.100Solve: p/(−8)=−40.Plus a twin to try
Example 4.101Solve: −y=15.Plus a twin to try
Example 4.102Solve: 3/4x=24.Plus a twin to try
Example 4.103Solve: −3/8w=72.Plus a twin to try
Example 4.104Translate and solve: n divided by 6 is −24.Plus a twin to try
Example 4.105Translate and solve: The quotient of q and −5 is 70.Plus a twin to try
Example 4.106Translate and solve: Two-thirds of f is 18.Plus a twin to try
Example 4.107Translate and solve: The quotient of m and 5/6 is 3/4.Plus a twin to try
Example 4.108Translate and solve: The sum of three-eighths and x is three and one-half.Plus a twin to try

Prealgebra5.1 Decimals

Example 5.1Name each decimal: ⓐ4.3 ⓑ2.45 ⓒ0.009 ⓓ−15.571.Plus a twin to try
Example 5.2Write fourteen and thirty-seven hundredths as a decimal.Plus a twin to try
Example 5.3Write twenty-four thousandths as a decimal.Plus a twin to try
Example 5.4Write each of the following decimal numbers as a fraction or a mixed number: ⓐ4.09 ⓑ3.7 ⓒ−0.286Plus a twin to try
Example 5.5Locate 0.4 on a number line.Plus a twin to try
Example 5.6Locate −0.74 on a number line.Plus a twin to try
Example 5.7Order the following decimals using <or>: ⓐ0.64__0.6 ⓑ0.83__0.803Plus a twin to try
Example 5.8Use <or> to order. −0.1__−0.8.Plus a twin to try
Example 5.9Round 18.379 to the nearest hundredth.Plus a twin to try
Example 5.10Round 18.379 to the nearest ⓐ tenth ⓑ whole number.Plus a twin to try

Prealgebra5.2 Decimal Operations

Example 5.11Add: 3.7+12.4.Plus a twin to try
Example 5.12Add: 23.5+41.38.Plus a twin to try
Example 5.13Subtract: 20−14.65.Plus a twin to try
Example 5.14Subtract: 2.51−7.4.Plus a twin to try
Example 5.15Multiply: (3.9)(4.075).Plus a twin to try
Example 5.16Multiply: (−8.2)(5.19).Plus a twin to try
Example 5.17Multiply: (0.03)(0.045).Plus a twin to try
Example 5.18Multiply 5.63 by factors of ⓐ10 ⓑ100ⓒ1000.Plus a twin to try
Example 5.19Divide: 0.12÷3.Plus a twin to try
Example 5.20Divide: $3.99÷24.Plus a twin to try
Example 5.21Divide: −2.89÷(3.4).Plus a twin to try
Example 5.22Divide: −25.65÷(−0.06).Plus a twin to try
Example 5.23Divide: 4÷0.05.Plus a twin to try
Example 5.24Paul received $50 for his birthday. He spent $31.64 on a video game. How much of Paul’s birthday money was left?Plus a twin to try
Example 5.25Jessie put 8 gallons of gas in her car. One gallon of gas costs $3.529. How much does Jessie owe for the gas? (Round the answer to the nearest cent.)Plus a twin to try
Example 5.26Four friends went out for dinner. They shared a large pizza and a pitcher of soda. The total cost of their dinner was $31.76. If they divide the cost equally, how much should each friend pay?Plus a twin to try
Example 5.27Marla buys 6 bananas that cost $0.22 each and 4 oranges that cost $0.49 each. How much is the total cost of the fruit?Plus a twin to try

Prealgebra5.3 Decimals and Fractions

Example 5.28Write the fraction 3/4 as a decimal.Plus a twin to try
Example 5.29Write the fraction −7/2 as a decimal.Plus a twin to try
Example 5.30Write (43)/(22) as a decimal.Plus a twin to try
Example 5.31Simplify: 7/8+6.4.Plus a twin to try
Example 5.32Order 3/8__0.4 using < or >.Plus a twin to try
Example 5.33Order −0.5___−3/4 using < or >.Plus a twin to try
Example 5.34Write the numbers (13)/(20),0.61,(11)/(16) in order from smallest to largest.Plus a twin to try
Example 5.35Simplify the expressions: ⓐ7(18.3−21.7) ⓑ2/3(8.3−3.8)Plus a twin to try
Example 5.36Simplify each expression: ⓐ6÷0.6+(0.2)4−(0.1)^2 ⓑ(1/(10))^2+(3.5)(0.9)Plus a twin to try
Example 5.37A circle has radius 10 centimeters. Approximate its ⓐ circumference and ⓑ area.Plus a twin to try
Example 5.38A circle has radius 42.5 centimeters. Approximate its ⓐ circumference and ⓑ area.Plus a twin to try
Example 5.39A circle has radius (14)/(15) meter. Approximate its ⓐ circumference and ⓑ area.Plus a twin to try

Prealgebra5.4 Solve Equations with Decimals

Example 5.40Determine whether each of the following is a solution of x−0.7=1.5: ⓐx=1ⓑx=−0.8ⓒx=2.2Plus a twin to try
Example 5.41Solve: y+2.3=−4.7.Plus a twin to try
Example 5.42Solve: a−4.75=−1.39.Plus a twin to try
Example 5.43Solve: −4.8=0.8n.Plus a twin to try
Example 5.44Solve: p/(−1.8)=−6.5.Plus a twin to try
Example 5.45Translate and solve: The difference of n and 4.3 is 2.1.Plus a twin to try
Example 5.46Translate and solve: The product of −3.1 and x is 5.27.Plus a twin to try
Example 5.47Translate and solve: The quotient of p and −2.4 is 6.5.Plus a twin to try
Example 5.48Translate and solve: The sum of n and 2.9 is 1.7.Plus a twin to try

Prealgebra5.5 Averages and Probability

Example 5.49Find the mean of the numbers 8,12,15,9,and6.Plus a twin to try
Example 5.50The ages of the members of a family who got together for a birthday celebration were 16,26,53,56,65,70,93,and97 years. Find the mean age.Plus a twin to try
Example 5.51For the past four months, Daisy’s cell phone bills were $42.75,$50.12,$41.54,$48.15. Find the mean cost of Daisy’s cell phone bills.Plus a twin to try
Example 5.52Find the median of 12,13,19,9,11,15,and18.Plus a twin to try
Example 5.53Kristen received the following scores on her weekly math quizzes: 83,79,85,86,92,100,76,90,88,and64. Find her median score.Plus a twin to try
Example 5.54The ages of students in a college math class are listed below. Identify the mode. 18,18,18,18,19,19,19,20,20,20,20,20,20,20,21,21,22,22,22,22,22,23,24,24,25,29,30,40,44Plus a twin to try
Example 5.55The data lists the heights (in inches) of students in a statistics class. Identify the mode. 56 61 63 64 65 66 67 67 60 62 63 64 65 66 67 70 60 63 63 64 66 66 67 74 61 63 64 65 66 67 67Plus a twin to try
Example 5.56The ski club is holding a raffle to raise money. They sold 100 tickets. All of the tickets are placed in a jar. One ticket will be pulled out of the jar at random, and the winner will receive a prize. Cherie bought…Plus a twin to try
Example 5.57Three women and five men interviewed for a job. One of the candidates will be offered the job. ⓐ Find the probability the job is offered to a woman. ⓑ Convert the fraction to a decimal.Plus a twin to try

Prealgebra5.6 Ratios and Rate

Example 5.58Write each ratio as a fraction: ⓐ15to27ⓑ45to18.Plus a twin to try
Example 5.59Write each ratio as a fraction of whole numbers: ⓐ4.8to11.2 ⓑ2.7to0.54Plus a twin to try
Example 5.60Write the ratio of 11/4to23/8 as a fraction.Plus a twin to try
Example 5.61Hector's total cholesterol is 249 mg/dl and his HDL cholesterol is 39 mg/dl. ⓐ Find the ratio of his total cholesterol to his HDL cholesterol. ⓑ Assuming that a ratio less than 5 to 1 is considered good, what would…Plus a twin to try
Example 5.62The Americans with Disabilities Act (ADA) Guidelines for wheel chair ramps require a maximum vertical rise of 1 inch for every 1 foot of horizontal run. What is the ratio of the rise to the run?Plus a twin to try
Example 5.63Bob drove his car 525 miles in 9 hours. Write this rate as a fraction.Plus a twin to try
Example 5.64Anita was paid $384 last week for working 32 hours. What is Anita’s hourly pay rate?Plus a twin to try
Example 5.65Sven drives his car 455 miles, using 14 gallons of gasoline. How many miles per gallon does his car get?Plus a twin to try
Example 5.66The grocery store charges $3.99 for a case of 24 bottles of water. What is the unit price?Plus a twin to try
Example 5.67Paul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at $14.99 for 64 loads of laundry and the same brand of powder detergent is priced at $15.99 for 80 loads. Which is the…Plus a twin to try
Example 5.68Translate the word phrase into an algebraic expression: ⓐ427 miles per h hours ⓑx students to 3 teachers ⓒy dollars for 18 hoursPlus a twin to try

Prealgebra5.7 Simplify and Use Square Roots

Example 5.69Simplify: ⓐ√(25)ⓑ√(121).Plus a twin to try
Example 5.70Simplify. ⓐ−√9ⓑ−√(144.)Plus a twin to try
Example 5.71Simplify: ⓐ√(−169)ⓑ−√(121).Plus a twin to try
Example 5.72Simplify: ⓐ√(25)+√(144)ⓑ√(25+144).Plus a twin to try
Example 5.73Estimate √(60) between two consecutive whole numbers.Plus a twin to try
Example 5.74Round √(17) to two decimal places using a calculator.Plus a twin to try
Example 5.75Simplify: √(x^2).Plus a twin to try
Example 5.76Simplify: √(16x^2).Plus a twin to try
Example 5.77Simplify: −√(81y^2).Plus a twin to try
Example 5.78Simplify: √(36x^2y^2).Plus a twin to try
Example 5.79Mike and Lychelle want to make a square patio. They have enough concrete for an area of 200 square feet. To the nearest tenth of a foot, how long can a side of their square patio be?Plus a twin to try
Example 5.80Christy dropped her sunglasses from a bridge 400 feet above a river. How many seconds does it take for the sunglasses to reach the river?Plus a twin to try
Example 5.81After a car accident, the skid marks for one car measured 190 feet. To the nearest tenth, what was the speed of the car (in mph) before the brakes were applied?Plus a twin to try

Prealgebra6.1 Understand Percent

Example 6.1According to the Public Policy Institute of California (2010),44% of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.Plus a twin to try
Example 6.2In 2007, according to a U.S. Department of Education report, 21 out of every 100 first-time freshmen college students at 4-year public institutions took at least one remedial course. Write this as a ratio and then as…Plus a twin to try
Example 6.3Convert each percent to a fraction: ⓐ36% ⓑ125%Plus a twin to try
Example 6.4Convert each percent to a fraction: ⓐ24.5% ⓑ331/3%Plus a twin to try
Example 6.5Convert each percent to a decimal: ⓐ6% ⓑ78%Plus a twin to try
Example 6.6Convert each percent to a decimal: ⓐ135% ⓑ12.5%Plus a twin to try
Example 6.7Among a group of business leaders, 77% believe that poor math and science education in the U.S. will lead to higher unemployment rates. Convert the percent to: ⓐ a fraction ⓑ a decimalPlus a twin to try
Example 6.8There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is 25%. Convert the percent to: ⓐ a fraction ⓑ a…With a figurePlus a twin to try
Example 6.9Convert each decimal to a percent: ⓐ0.05 ⓑ0.83Plus a twin to try
Example 6.10Convert each decimal to a percent: ⓐ1.05 ⓑ0.075Plus a twin to try
Example 6.11Convert each fraction or mixed number to a percent: ⓐ3/4 ⓑ(11)/8 ⓒ21/5Plus a twin to try
Example 6.12Convert 5/7 to a percent.Plus a twin to try
Example 6.13An article in a medical journal claimed that approximately 1/3 of American adults are obese. Convert the fraction 1/3 to a percent.Plus a twin to try

Prealgebra6.2 Solve General Applications of Percent

Example 6.14What number is 35% of 90?Plus a twin to try
Example 6.15125% of 28 is what number?Plus a twin to try
Example 6.16Translate and solve: 36 is 75% of what number?Plus a twin to try
Example 6.176.5% of what number is $1.17?Plus a twin to try
Example 6.18What percent of 36 is 9?Plus a twin to try
Example 6.19144 is what percent of 96?Plus a twin to try
Example 6.20Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was $68.50. They want to leave an 18% tip. If the tip will be 18% of the total bill, how much should the tip be?Plus a twin to try
Example 6.21The label on Masao's breakfast cereal said that one serving of cereal provides 85 milligrams (mg) of potassium, which is 2% of the recommended daily amount. What is the total recommended daily amount of potassium?With a figurePlus a twin to try
Example 6.22Mitzi received some gourmet brownies as a gift. The wrapper said each brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat?Plus a twin to try
Example 6.23In 2011, the California governor proposed raising community college fees from $26 per unit to $36 per unit. Find the percent increase. (Round to the nearest tenth of a percent.)Plus a twin to try
Example 6.24The average price of a gallon of gas in one city in June 2014 was $3.71. The average price in that city in July was $3.64. Find the percent decrease.Plus a twin to try

Prealgebra6.3 Solve Sales Tax, Commission, and Discount Applications

Example 6.25Cathy bought a bicycle in Washington, where the sales tax rate was 6.5% of the purchase price. What was ⓐ the sales tax and ⓑ the total cost of a bicycle if the purchase price of the bicycle was $392?Plus a twin to try
Example 6.26Evelyn bought a new smartphone for $499 plus tax. She was surprised when she got the receipt and saw that the tax was $42.42. What was the sales tax rate for this purchase?Plus a twin to try
Example 6.27Helene is a realtor. She receives 3% commission when she sells a house. How much commission will she receive for selling a house that costs $260,000?Plus a twin to try
Example 6.28Rikki earned $87 commission when she sold a $1,450 stove. What rate of commission did she get?Plus a twin to try
Example 6.29Jason bought a pair of sunglasses that were on sale for $10 off. The original price of the sunglasses was $39. What was the sale price of the sunglasses?Plus a twin to try
Example 6.30Elise bought a dress that was discounted 35% off of the original price of $140. What was ⓐ the amount of discount and ⓑ the sale price of the dress?Plus a twin to try
Example 6.31Jeannette bought a swimsuit at a sale price of $13.95. The original price of the swimsuit was $31. Find the ⓐ amount of discount and ⓑ discount rate.Plus a twin to try
Example 6.32Adam's art gallery bought a photograph at the wholesale price of $250. Adam marked the price up 40%. Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.Plus a twin to try

Prealgebra6.4 Solve Simple Interest Applications

Example 6.33Find the simple interest earned after 3 years on $500 at an interest rate of 6%.Plus a twin to try
Example 6.34Find the principal invested if $178 interest was earned in 2 years at an interest rate of 4%.Plus a twin to try
Example 6.35Find the rate if a principal of $8,200 earned $3,772 interest in 4 years.Plus a twin to try
Example 6.36Nathaly deposited $12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years?Plus a twin to try
Example 6.37Loren lent his brother $3,000 to help him buy a car. In 4 years his brother paid him back the $3,000 plus $660 in interest. What was the rate of interest?Plus a twin to try
Example 6.38Eduardo noticed that his new car loan papers stated that with an interest rate of 7.5%, he would pay $6,596.25 in interest over 5 years. How much did he borrow to pay for his car?Plus a twin to try
Example 6.39Caroline got $900 as graduation gifts and invested it in a 10-month certificate of deposit that earned 2.1% interest. How much interest did this investment earn?Plus a twin to try

Prealgebra6.5 Solve Proportions and their Applications

Example 6.40Write each sentence as a proportion: ⓐ3 is to 7 as 15 is to 35. ⓑ5 hits in 8 at bats is the same as 30 hits in 48 at-bats. ⓒ$1.50 for 6 ounces is equivalent to $2.25 for 9 ounces.Plus a twin to try
Example 6.41Determine whether each equation is a proportion: ⓐ4/9=(12)/(28) ⓑ(17.5)/(37.5)=7/(15)Plus a twin to try
Example 6.42Solve: x/(63)=4/7.Plus a twin to try
Example 6.43Solve: (144)/a=9/4.Plus a twin to try
Example 6.44Solve: (52)/(91)=(−4)/y.Plus a twin to try
Example 6.45When pediatricians prescribe acetaminophen to children, they prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of the child’s weight. If Zoe weighs 80 pounds, how many milliliters of acetaminophen…Plus a twin to try
Example 6.46One brand of microwave popcorn has 120 calories per serving. A whole bag of this popcorn has 3.5 servings. How many calories are in a whole bag of this microwave popcorn?Plus a twin to try
Example 6.47Josiah went to Mexico for spring break and changed $325 dollars into Mexican pesos. At that time, the exchange rate had $1 U.S. is equal to 12.54 Mexican pesos. How many Mexican pesos did he get for his trip?Plus a twin to try
Example 6.48Translate to a proportion. What number is 75% of 90?Plus a twin to try
Example 6.49Translate to a proportion. 19 is 25% of what number?Plus a twin to try
Example 6.50Translate to a proportion. What percent of 27 is 9?Plus a twin to try
Example 6.51Translate and solve using proportions: What number is 45% of 80?Plus a twin to try
Example 6.52Translate and solve using proportions: 125% of 25 is what number?Plus a twin to try
Example 6.53Translate and solve: 6.5% of what number is $1.56?Plus a twin to try
Example 6.54Translate and solve using proportions: What percent of 72 is 9?Plus a twin to try

Elementary Algebra1.1 Introduction to Whole Numbers

Example 1.1In the number 63,407,218, find the place value of each digit: ⓐ 7 ⓑ 0 ⓒ 1 ⓓ 6 ⓔ 3Plus a twin to try
Example 1.2Name the number 8,165,432,098,710 using words.Plus a twin to try
Example 1.3Write nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine as a whole number using digits.Plus a twin to try
Example 1.4Round 23,658 to the nearest hundred.Plus a twin to try
Example 1.5Round 103,978 to the nearest: ⓐ hundred ⓑ thousand ⓒ ten thousandPlus a twin to try
Example 1.6Is 5,625 divisible by 2? By 3? By 5? By 6? By 10?Plus a twin to try
Example 1.7Factor 48.Plus a twin to try
Example 1.8Find the prime factorization of 252.Plus a twin to try
Example 1.9Find the least common multiple of 15 and 20 by listing multiples.Plus a twin to try
Example 1.10Find the Least Common Multiple (LCM) of 12 and 18 using the prime factors method.Plus a twin to try
Example 1.11Find the Least Common Multiple (LCM) of 24 and 36 using the prime factors method.Plus a twin to try

Elementary Algebra1.2 Use the Language of Algebra

Example 1.12Translate from algebra into English: ⓐ 17≤26 ⓑ 8≠17−3 ⓒ 12>27÷3 ⓓ y+7<19Plus a twin to try
Example 1.13Determine if each is an expression or an equation: ⓐ 2(x+3)=10 ⓑ 4(y−1)+1 ⓒ x÷25 ⓓ y+8=40Plus a twin to try
Example 1.15Simplify: ⓐ 4+3·7 ⓑ (4+3)·7.Plus a twin to try
Example 1.18Evaluate 7x−4, when ⓐ x=5 and ⓑ x=1.Plus a twin to try
Example 1.19Evaluate x=4, when ⓐ x^2 ⓑ 3^x.Plus a twin to try
Example 1.21Identify the coefficient of each term: ⓐ 14y ⓑ 15x^2 ⓒ a.Plus a twin to try
Example 1.22Identify the like terms: y^3, 7x^2, 14, 23, 4y^3, 9x, 5x^2.Plus a twin to try
Example 1.23Identify the terms in each expression. ⓐ 9x^2+7x+12 ⓑ 8x+3yPlus a twin to try
Example 1.24Simplify: 2x^2+3x+7+x^2+4x+5.Plus a twin to try
Example 1.25Translate each English phrase into an algebraic expression: ⓐ the difference of 17x and 5 ⓑ the quotient of 10x^2 and 7.Plus a twin to try
Example 1.26Translate the English phrase into an algebraic expression: ⓐ Seventeen more than y ⓑ Nine less than 9x^2.Plus a twin to try
Example 1.27Translate the English phrase into an algebraic expression: ⓐ five times the sum of m and n ⓑ the sum of five times m and n.Plus a twin to try
Example 1.28The length of a rectangle is 6 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.Plus a twin to try
Example 1.29June has dimes and quarters in her purse. The number of dimes is three less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.Plus a twin to try

Elementary Algebra1.3 Add and Subtract Integers

Example 1.31Find: ⓐ the opposite of 7 ⓑ the opposite of −10 ⓒ −(−6).Plus a twin to try
Example 1.32Evaluate ⓐ −x, when x=8 ⓑ −x, when x=−8.Plus a twin to try
Example 1.34Fill in <,>,or= for each of the following pairs of numbers: ⓐ |−5|___−|−5| ⓑ 8___−|−8| ⓒ −9___−|−9| ⓓ −(−16)___−|−16|Plus a twin to try
Example 1.37Add: ⓐ 1+4 ⓑ −1+(−4).Plus a twin to try
Example 1.38Add: ⓐ −1+5 ⓑ 1+(−5).Plus a twin to try
Example 1.39Simplify: ⓐ 19+(−47) ⓑ −14+(−36).Plus a twin to try
Example 1.41Subtract: ⓐ 7−5 ⓑ −7−(−5).Plus a twin to try
Example 1.42Subtract: ⓐ −3−1 ⓑ 3−(−1).Plus a twin to try

Elementary Algebra1.4 Multiply and Divide Integers

Example 1.46Multiply: ⓐ −9·3 ⓑ −2(−5) ⓒ 4(−8) ⓓ 7·6.Plus a twin to try
Example 1.47Multiply: ⓐ −1·7 ⓑ −1(−11).Plus a twin to try
Example 1.48Divide: ⓐ −27÷3 ⓑ −100÷(−4).Plus a twin to try
Example 1.56Evaluate 20−z when ⓐ z=12 and ⓑ z=−12.Plus a twin to try
Example 1.62The temperature in Urbana, Illinois one morning was 11 degrees. By mid-afternoon, the temperature had dropped to −9 degrees. What was the difference of the morning and afternoon temperatures?Plus a twin to try
Example 1.63The Mustangs football team received three penalties in the third quarter. Each penalty gave them a loss of fifteen yards. What is the number of yards lost?Plus a twin to try

Elementary Algebra1.5 Visualize Fractions

Example 1.65Simplify: −(32)/(56).Plus a twin to try
Example 1.67Simplify: (5x)/(5y).Plus a twin to try
Example 1.68Multiply: −(11)/(12)·5/7.Plus a twin to try
Example 1.69Multiply: −(12)/5(−20x).Plus a twin to try
Example 1.70Divide: −2/3÷n/5.Plus a twin to try
Example 1.71Find the quotient: −7/8÷(−(14)/(27)).Plus a twin to try
Example 1.76Translate the English phrase into an algebraic expression: the quotient of the difference of m and n, and p.Plus a twin to try

Elementary Algebra1.6 Add and Subtract Fractions

Example 1.78Find the difference: −(23)/(24)−(13)/(24).Plus a twin to try
Example 1.79Simplify: −(10)/x−4/x.Plus a twin to try
Example 1.88Evaluate −5/6−y when y=−2/3.Plus a twin to try

Elementary Algebra1.7 Decimals

Example 1.91Name the decimal 4.3.Plus a twin to try
Example 1.92Name the decimal: −15.571.Plus a twin to try
Example 1.93Write “fourteen and twenty-four thousandths” as a decimal.Plus a twin to try
Example 1.99Multiply 5.63 ⓐ by 10 ⓑ by 100 ⓒ by 1,000.Plus a twin to try
Example 1.100Divide: −25.56÷(−0.06).Plus a twin to try
Example 1.102Write 0.374 as a fraction.Plus a twin to try
Example 1.103Write −5/8 as a decimal.Plus a twin to try
Example 1.106Convert each percent to a decimal: ⓐ 62% ⓑ 135% ⓒ 35.7%.Plus a twin to try
Example 1.107Convert each decimal to a percent: ⓐ 0.51 ⓑ 1.25 ⓒ 0.093.Plus a twin to try

Elementary Algebra1.8 The Real Numbers

Example 1.110Write as the ratio of two integers: ⓐ −27 ⓑ 7.31.Plus a twin to try
Example 1.111Given the numbers 0.583–,0.47,3.605551275... list the ⓐ rational numbers ⓑ irrational numbers.Plus a twin to try
Example 1.112For each number given, identify whether it is rational or irrational: ⓐ √(36) ⓑ √(44).Plus a twin to try
Example 1.113For each number given, identify whether it is a real number or not a real number: ⓐ √(−169) ⓑ −√(64).Plus a twin to try
Example 1.114Given the numbers −7,(14)/5,8,√5,5.9,−√(64), list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers.Plus a twin to try
Example 1.115Locate and label the following on a number line: 4,3/4,−1/4,−3,6/5,−5/2,and7/3.Plus a twin to try
Example 1.116Order each of the following pairs of numbers, using < or >. It may be helpful to refer Figure 1.17. ⓐ −2/3___−1 ⓑ −31/2___−3 ⓒ −3/4___−1/4 ⓓ −2___−8/3 Figure 1.17With a figurePlus a twin to try
Example 1.117Locate 0.4 on the number line.Plus a twin to try
Example 1.118Locate −0.74 on the number line.Plus a twin to try
Example 1.119Order 0.64___0.6 using < or >.Plus a twin to try
Example 1.120Order 0.83___0.803 using < or >.Plus a twin to try

Elementary Algebra1.9 Properties of Real Numbers

Example 1.124Use the associative property to simplify 6(3x).Plus a twin to try
Example 1.125Find the additive inverse of ⓐ 5/8 ⓑ 0.6 ⓒ −8 ⓓ −4/3.Plus a twin to try
Example 1.126Find the multiplicative inverse of ⓐ 9 ⓑ −1/9 ⓒ 0.9.Plus a twin to try
Example 1.127Simplify: ⓐ −8·0 ⓑ 0/(−2) ⓒ (−32)/0.Plus a twin to try
Example 1.128Simplify: ⓐ 0/(n+5), where n≠−5 ⓑ (10−3p)/0, where 10−3p≠0.
Example 1.138Simplify: 8−2(x+3). Be sure to follow the order of operations. Multiplication comes before subtraction, so we will distribute the 2 first and then subtract.Plus a twin to try

Elementary Algebra1.10 Systems of Measurement

Example 1.140MaryAnne is 66 inches tall. Convert her height into feet.Plus a twin to try
Example 1.141Ndula, an elephant at the San Diego Safari Park, weighs almost 3.2 tons. Convert her weight to pounds.Plus a twin to try
Example 1.142Juliet is going with her family to their summer home. She will be away from her boyfriend for 9 weeks. Convert the time to minutes.Plus a twin to try
Example 1.143How many ounces are in 1 gallon?Plus a twin to try
Example 1.144Seymour bought three steaks for a barbecue. Their weights were 14 ounces, 1 pound 2 ounces and 1 pound 6 ounces. How many total pounds of steak did he buy?Plus a twin to try
Example 1.145Anthony bought four planks of wood that were each 6 feet 4 inches long. What is the total length of the wood he purchased?Plus a twin to try
Example 1.146Nick ran a 10K race. How many meters did he run?Plus a twin to try
Example 1.148Convert ⓐ 350 L to kiloliters ⓑ 4.1 L to milliliters.Plus a twin to try
Example 1.151Lee’s water bottle holds 500 mL of water. How many ounces are in the bottle? Round to the nearest tenth of an ounce.Plus a twin to try
Example 1.152Soleil was on a road trip and saw a sign that said the next rest stop was in 100 kilometers. How many miles until the next rest stop?Plus a twin to try
Example 1.153Convert 50° Fahrenheit into degrees Celsius.Plus a twin to try
Example 1.154While visiting Paris, Woody saw the temperature was 20° Celsius. Convert the temperature into degrees Fahrenheit.Plus a twin to try