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**Multiplying Rational Numbers**

2-4 Multiplying Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

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Warm Up Write each number as an improper fraction. 1 7 3 7 15 8 2 17 5 1. 2 2. 1 3. 3 3 8 5 2 20 3 3 43 8 4. 6 5. 5 3 8

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Problem of the Day The sum of three consecutive integers is 168. What are the three integers? 55, 56, and 57

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**Learn to multiply fractions, mixed numbers, and decimals.**

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**1 4 3 4 3 4 3 • 1 1 + = Repeated addition = Multiplication**

Notice that multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator.

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**RULES FOR MULTIPLYING TWO RATIONAL NUMBERS**

If the signs of the factors are the same, the product is positive. (+) • (+) = (+) or (–) • (–) = (+) If the signs of the factors are different, the product is negative. (+) • (–) = (–) or (–) • (+) = (–)

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**Additional Example 1A: Multiplying a Fraction and an Integer**

Multiply. Write the answer in simplest form. 6 7 To write as a mixed number, divide: Helpful Hint –48 7 –48 7 = –6 R6 6 7 = –6 –8 –8 • 6 7 = –48 7 = Multiply. –6 6 7 = Simplify.

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**Additional Example 1B: Multiplying a Fraction and an Integer**

Multiply. Write the answer in simplest form. 1 3 2 5 16 3 = 2 5(3) + 1 3 = 1 3 5 16 3 32 3 = Multiply. 10 2 3 = Simplify.

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**5 8 –3 –3 • 5 8 = –15 8 = –1 7 8 = Multiply. Simplify.**

Check It Out: Example 1A Multiply. Write the answer in simplest form. 5 8 –3 –3 • 5 8 = –15 8 = Multiply. –1 7 8 = Simplify.

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Check It Out: Example 1B Multiply. Write the answer in simplest form. 2 5 4 9 47 5 = 4 9(5) = 2 5 9 47 5 188 5 = Multiply. 37 3 5 = Simplify.

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A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Caution!

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**Additional Example 2A: Multiplying Fractions**

Multiply. Write the answer in simplest form. 1 8 6 7 = 1(6) 8(7) Multiply numerators. Multiply denominators. 3 4 1(6) 8(7) = Look for common factors: 2. 3 28 = Simplify.

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**Additional Example 2B: Multiplying Fractions**

Multiply. Write the answer in simplest form. 2 3 9 2 – = –2(9) 3(2) Multiply numerators. Multiply denominators. 1 –1 3 1 –2(9) 3(2) = Look for common factors: 2, 3. –3 = Simplify.

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**3 5 5 8 3(5) 5(8) = 3(5) 5(8) = 3 8 = Multiply numerators.**

Check It Out: Example 2A Multiply. Write the answer in simplest form. 3 5 5 8 = 3(5) 5(8) Multiply numerators. Multiply denominators. 1 3(5) 5(8) = Look for common factors: 5. 3 8 = Simplify.

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**7 8 4 7 – = –7(4) 8(7) –1 –7(4) 8(7) = 1 2 = – Multiply numerators.**

Check It Out: Example 2B Multiply. Write the answer in simplest form. 7 8 4 7 – = –7(4) 8(7) Multiply numerators. Multiply denominators. 1 –1 1 2 –7(4) 8(7) = Look for common factors: 4, 7. 1 2 = – Simplify.

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**Additional Example 3: Multiplying Decimals**

Product is negative with 2 decimal places. 2 • (–0.51) = –1.02 B. (–0.4)(–3.75) Product is positive with 3 decimal places. (–0.4) • (–3.75) = 1.500 = 1.5 00 You can drop the zeros after the decimal point.

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Check It Out: Example 3 Multiply. A. 3.1 (0.28) Product is positive with 3 decimal places. 3.1 • (0.28) = 0.868 B. (–0.4)(–2.53) Product is positive with 3 decimal places. (–0.4) • (–2.53) = 1.012

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**Additional Example 4: Application**

Joy completes of her painting each day. How much of her painting does she complete in a 7 day week? 1 20 1 20 1 20 71 (7) = Write as an improper fraction. 1 • 7 20 • 1 = Multiply. 7 20 = Joy completes of her painting in a 7-day week. 7 20

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**= = Check It Out: Example 4 1 7**

1 7 Mark runs mile each day. What is the total distance Mark runs in a 5-day week? 1 7 1 7 51 (5) = Write as an improper fraction. 1 • 5 I7 • 1 = Multiply. 5 7 = Mark runs mile in a 7-day week. 5 7

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**– – Lesson Quiz Multiply. 1 7 1 2 7 1. 9 2 3 5 8 5 12 2. 3. –0.47(2.2)**

–1.034 1 2 45 4. Evaluate 2 (x) for x = . 2 6 miles 2 9 8 9 Edgar runs mile each day. What is the total distance that Edgar runs in a 7-day week? 5.

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