Section 4.2 Part 1: Simplifying and Multiplying Fractions

Multiply and simplify: −17/52⋅8/68

-1/26 To multiply fractions, multiply the numerators and multiply the denominators and then simplify by removing common factors. Notice that since the signs are different, the product is negative. −17/52⋅8/68=−17⋅8/52⋅68 =−1⋅17⋅2⋅2⋅2/26⋅2⋅2⋅2⋅17 =−1⋅17⋅2⋅2⋅2/26⋅2⋅2⋅2⋅17= =−1/26

Simplify: −108/63. Write your answer as an improper fraction.

-12/7 Since 108=9⋅12 and 63=9⋅7, we can rewrite the numerator and denominator to show the common factors. −9⋅12/9⋅7 Using the Equivalent Fractions Property, we can simplify to get −9⋅12/9⋅7 After canceling the common factors, we are left with the simplified form. −108/63= −12/7

Simplify: −104/48. Enter your answer as an improper fraction if necessary.

-13/6 Since 104=8⋅13 and 48=8⋅6, we can rewrite the numerator and denominator to show the common factors. −8⋅13/8⋅6 Using the Equivalent Fractions Property, we can simplify to get −8⋅13/8⋅6 After canceling the common factors, we are left with the simplified form. −104/48= −13/6

Simplify: −3x/12y.

-x/4y Since 12=3⋅4, we can rewrite the numerator and denominator to show the common factors. −3⋅x/3⋅4⋅y Using the Equivalent Fractions Property, we can simplify to get −3⋅x/3⋅4⋅y After canceling the common factors, we are left with the simplified form. −3x/12y =−x/4y

Simplify: 4/24.

1/6 Since 24=6⋅4, we can rewrite the numerator and denominator to show the common factors. 4/6⋅4 Using the Equivalent Fractions Property, we can simplify to get 4/6⋅4 After canceling the common factors, we are left with the simplified form. 4/24=1/6

Simplify: 182/294.

13/21 Since 182=2⋅7⋅13 and 294=2⋅3⋅7⋅7, we can rewrite the numerator and denominator to show the common factors. 2⋅7⋅13/2⋅3⋅7⋅7 Using the Equivalent Fractions Property, we can simplify to get 2⋅7⋅13/2⋅3⋅7⋅7 After canceling the common factors, we are left with the simplified form. 182/294=13/3⋅7 =13/21

Multiply: (4/20)(13). Note: Make sure to simplify your answer.

13/5 To multiply fractions, multiply the numerators and multiply the denominators and then simplify by removing common factors. Notice that since the signs are the same, the product is positive.

Multiply: (−19/29)(11y).

209y/29 To multiply fractions, multiply the numerators and multiply the denominators and then simplify by removing common factors. In this case, there are no common factors to remove. Notice that since the signs are different, the product is negative. −19/29⋅11y= −19⋅11y/29⋅1= −209y/29

Simplify: 14x^2/21y.

2x^2/3y Since 14=2⋅7 and 21=3⋅7, we can rewrite the numerator and denominator to show the common factors. 2⋅7⋅x^2/3⋅7⋅y Using the Equivalent Fractions Property, we can simplify to get2⋅7⋅x^2/3⋅7⋅y After canceling the common factors, we are left with the simplified form. 14x^2/21y =2x^2/3y

Simplify: 6/10.

3/5 Since 6=2⋅3 and 10=2⋅5, we can rewrite the numerator and denominator to show the common factors. 2⋅3/2⋅5 Using the Equivalent Fractions Property, we can simplify to get 2⋅3/2⋅5 After canceling the common factors, we are left with the simplified form. 6/10=3/5

Multiply: 9/2⋅20s/54. *****Enter a simplified improper fraction.*****

5s/3 To multiply fractions, multiply the numerators and multiply the denominators and then simplify by removing common factors. Notice that since the signs are the same, the product is positive. 9/2⋅20s54=9⋅20s/2⋅54 =3⋅3⋅5s⋅2⋅2/2⋅2⋅3⋅3⋅3 =3⋅3⋅5s⋅2⋅2/2⋅2⋅3⋅3⋅3 =5s/3

Multiply: (−14/36)(−6s/112)

s/48 To multiply fractions, multiply the numerators and multiply the denominators and then simplify by removing common factors. Notice that since the signs are the same, the product is positive.

Multiply: (−18/54)(−3x/90).

x/90 To multiply fractions, multiply the numerators and multiply the denominators and then simplify by removing common factors. Notice that since the signs are the same, the product is positive.