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

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

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

Learn to multiply fractions, mixed numbers, and decimals.

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.

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 (–) • (+) = (–)

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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

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

= = 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

– – 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.