Exercise 5 Page 285

Rewrite the expression so that all of the numbers are fractions. Then, multiply both the numerators and the denominators.

Practice makes perfect

In the given expression, we have two mixed numbers. 3 34 * 2 25 Before we evaluate such expressions, we should rewrite the expression so that all of the numbers are fractions. We can rewrite any mixed number into a fraction using the following method.

a bc

WriteSum

Write as a sum

a+b/c

NumberToFrac

a = c* a/c

c* a/c+b/c

CommutativePropMult

Commutative Property of Multiplication

a* c/c+b/c

AddFrac

Add fractions

a* c+b/c

Let's first rewrite our expression so that all of the numbers are fractions!

3 34 * 2 25

MixedToFrac

a bc=a* c+b/c

3* 4+3/4 * 2* 5+2/5

Multiply

12+3/4 * 10+2/5

AddTerms

Add terms

15/4 * 12/5

When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

15/4 * 12/5

MultFrac

Multiply fractions

15* 12/4* 5

Rewrite

Rewrite 15 as 3* 5

3* 5* 12/4* 5

Rewrite

Rewrite 12 as 3* 4

3* 5* 3* 4/4* 5

CancelCommonFac

Cancel out common factors