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### Multiplying Rational Numbers

• To multiply fractions, multiply the numerators then multiply the denominators; lastly simplify if possible.
• You can use cross simplification to make multiplying fractions and simplifying products of fractions a lot easier.
• To raise a fraction to a power, pay careful attention to the location of the exponent. Sometimes you will be repeatedly multiplying both the numerator and denominator. Sometimes you will only be multiplying the numerator or denominator. Finally, sometimes you may not be repeatedly multiplying the negative sign.

## ([5/7])2 =

• [(52)/(72)] =

## ( − [6/11])2 =

• [(( − 6)2)/(112)] =

## −([4/9])3 =

• − [(43)/(93)] =

• − [45/36] =
• − [5/4] =

## Compare (−[2/5])3 to (−[2/5])3.

• −([2/5])3 = − [(23)/(53)] =
• −[(2 ·2 ·2)/(5 ·5 ·5)] =
• −[8/125]
• − ([2/5])3 = [(− 23)/(53)] =
• [(( − 2) ·( − 2) ·( − 2))/(5 ·5 ·5)] =
• − [8/125]

## Michelle has 9.4 pounds of paint. [1/6] of that paint is red. How many pounds of paint is not red?

• If [1/6] of the paint is red, then 1 − [1/6] of the paint is not red.
• 1− [1/6] = [5/6] of the paint is not red.
• 9.4 ×[5/6] =
• 9[4/10] ×[5/6] =
• [94/10] ×[5/6] =
• [470/60] =
• [47/6] =

## Tiffany spends [1/5] of her income on taxes, [2/7] of her income on rent, and [1/9] of her income on groceries. Tiffany makes \$ 5500 per month. How much of her income is spent on taxes, rent, and groceries per month?

• Amount spent on taxes: \$ 5500 ×[1/5] =
• \$ [5500/5] =
• \$ 1100
• Amount spent on rent: \$ 5500 ×[2/7] =
• \$ [11,000/7] =
• \$ 1571.43
• Amount spent on groceries: \$ 5500 ×[1/9] =
• \$ [5500/9] =

### \$ 611.11

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.