Exercise 22 Page 348

Practice makes perfect

When adding or subtracting fractions, they should have the same denominator. In this exercise, we are given two fractions with different denominators. - 4/5 +7/12 To add fractions, their denominators need to be the same. Since 60 is the product of 5 and 12, we can multiply both the numerator and denominator of - 45 by 12 and 712 by 5 to create a common denominator. Let's start with the first fraction.

- 4/5

ExpandFrac

a/b=a * 12/b * 12

- 4* 12/5* 12

Multiply

- 48/60

Let's continue with the second fraction.

7/12

ExpandFrac

a/b=a * 5/b * 5

7* 5/12* 5

Multiply

35/60

Now that we have a common denominator, we can proceed to simplifying the expression.

- 48/60+35/60

MoveNegFracToNum

Put minus sign in numerator

- 48/60+35/60

AddFrac

Add fractions

- 48+35/60

AddTerms

Add terms

- 13/60

MoveNegNumToFrac

Put minus sign in front of fraction

- 13/60

We want to find the following sum. 5/9 +( - 1/4) To add fractions, their denominators need to be the same. Since 36 is the product of 9 and 4, we can multiply both the numerator and denominator of 59 by 4 and - 14 by 9 to create a common denominator. Let's start with the first fraction.

5/9

ExpandFrac

a/b=a * 4/b * 4

5* 4/9* 4

Multiply

20/36

Let's continue with the second fraction.

- 1/4

ExpandFrac

a/b=a * 9/b * 9

- 1* 9/4* 9

Multiply

- 9/36

Now that we have a common denominator, we can proceed to simplifying the expression.

20/36 +( - 9/36)

AddNeg

a+(- b)=a-b

20/36 - 9/36

SubFrac

Subtract fractions

20-9/36

SubTerm

Subtract term

11/36

To multiply the given fractions, remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.

- 3/7 * 11/12

MultFrac

Multiply fractions

- 3* 11/7* 12

Multiply

- 33/84

ReduceFrac

a/b=.a /3./.b /3.

- 33÷ 3/84÷ 3

CalcQuot

Calculate quotient

- 11/28

Before we evaluate the given expression, let's first rewrite the expression so that all of the numbers are fractions.

- 1 23 * 4/5

MixedToFrac

a bc=a* c+b/c

- 1* 3+2/3 * 4/5

IdPropMult

Identity Property of Multiplication

- 3+2/3 * 4/5

AddTerms

Add terms

- 5/3 * 4/5

When multiplying fractions, remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.

- 5/3 * 4/5

MultFrac

Multiply fractions

- 5* 4/3* 5

CancelCommonFac

Cancel out common factors

- 5* 4/3* 5

SimpQuot

Simplify quotient

- 4/3