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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.

### Multiplying Rational Numbers

0.42 ×1.08 =
0.4536
− 0.07 ×2.13 =
− 0.1491
− 2.07 ×( − 0.002) =
0.00414
([5/7])2 =
• [(52)/(72)] =
[25/49]
( − [6/11])2 =
• [(( − 6)2)/(112)] =
[36/121]
−([4/9])3 =
• − [(43)/(93)] =
− [64/729]
[5/18] ×− [9/2] =
• − [45/36] =
• − [5/4] =
− 1[1/4]
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]
−([2/5])3 = ( − [2/5])3
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] =
7[5/6] pounds of paint is not red
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.

### Multiplying Rational Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:17
• Rational Number
• Exponent
• Power
• Multiplying Decimals 0:47
• Example 1: Multiplying Decimals
• Example 2: Multiplying Decimals
• Multiplying Rational Numbers in Word Problems 1:51
• Example: Length of Pipes
• Raising a Fraction to a Power 2:58
• Examples: Raising Fractions to Power
• Extra Example 1: Multiplying Fractions 4:45
• Extra Example 2: Compare Fractions 5:34
• Extra Example 3: Flour 7:28
• Extra Example 4: Income 8:50