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Exercises Numbers, fractions and percents

Example 4.74 from Prealgebra, 4.5 Add and Subtract Fractions with Different Denominators

Add and Subtract Fractions with Different Denominators: example 4.74

Simplify:

ⓐ $\frac{5 x}{6} - \frac{3}{10}$
ⓑ $\frac{5 x}{6} \cdot \frac{3}{10}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1

Solution

ⓐ The operation is subtraction. The fractions do not have a common denominator.

	$\frac{5 x}{6} - \frac{3}{10}$
Rewrite each fraction as an equivalent fraction with the LCD, 30.	$\frac{5 x \cdot 5}{6 \cdot 5} - \frac{3 \cdot 3}{10 \cdot 3}$
	$\frac{25 x}{30} - \frac{9}{30}$
Subtract the numerators and place the difference over the common denominator.	$\frac{25 x - 9}{30}$

ⓑ The operation is multiplication; no need for a common denominator.

	$\frac{5 x}{6} \cdot \frac{3}{10}$
To multiply fractions, multiply the numerators and multiply the denominators.	$\frac{5 x \cdot 3}{6 \cdot 10}$
Rewrite, showing common factors.	$\frac{5 \cdot x \cdot 3}{2 \cdot 3 \cdot 2 \cdot 5}$
Remove common factors to simplify.	$\frac{x}{4}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify:

ⓐ $\frac{3 a}{4} - \frac{8}{9}$
ⓑ $\frac{3 a}{4} \cdot \frac{8}{9}$

How did it go?

PreviousAdd and Subtract Fractions with Different Denominators: example 4.73 Next Add and Subtract Fractions with Different Denominators: example 4.75

From Prealgebra (1st edition) by OpenStax (Rice University), section 4.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.