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

2. Course 3 2-4 Multiplying Rational Numbers Problem of the Day The sum of three consecutive integers is 168. What are the three integers? 55, 56, and 57

3. Course 3 2-4 Multiplying Rational Numbers Learn to multiply fractions, mixed numbers, and decimals. TB P. 76-79

4. Course 3 2-4 Multiplying Rational Numbers 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. 1414 3434 1414 ++ = Repeated addition 1414 3 3 4 = = Multiplication 3 1 4 1 4

5. Course 3 2-4 Multiplying Rational Numbers RULES FOR MULTIPLYING TWO RATIONAL NUMBERS If the signs of the factors are the same, the product is positive. If the signs of the factors are different, the product is negative. (+) (+) = (+) or (–) (–) = (+) (+) (–) = (–) or (–) (+) = (–)

6. Course 3 2-4 Multiplying Rational Numbers –8 6767 Multiply. Write the answer in simplest form. Multiply. Simplify. –48 7 = –6 6767 = –8 6 7 = To write as a mixed number, divide: Helpful Hint –48 7 –48 7 = –6 R6 6767 = –6 Additional Example 1A: Multiplying a Fraction and an Integer

7. Course 3 2-4 Multiplying Rational Numbers 2 1313 Multiply. Simplify. 10 2323 = 16 3 = 2 32 3 = 5 5(3) + 1 3 = = 1313 5 16 3 Multiply. Write the answer in simplest form. Additional Example 1B: Multiplying a Fraction and an Integer

8. Course 3 2-4 Multiplying Rational Numbers A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Caution!

9. Course 3 2-4 Multiplying Rational Numbers 1(6) 8(7) = Multiply. Write the answer in simplest form. 6767 Simplify. 3 28 = 1818 = 1(6) 8(7) Multiply numerators. Multiply denominators. Look for common factors: 2. 3 4 Additional Example 2A: Multiplying Fractions

10. Course 3 2-4 Multiplying Rational Numbers –2(9) 3(2) = = 3 1 Simplify. –3 = Multiply numerators. Multiply denominators. Look for common factors: 2, 3. 9292 2323 – 1 –1–1 Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form.

11. Course 3 2-4 Multiplying Rational Numbers Multiply. 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 You can drop the zeros after the decimal point. = 1.5 Additional Example 3: Multiplying Decimals A. 2(–0.51) 00

12. Course 3 2-4 Multiplying Rational Numbers Joy completes of her painting each day. How much of her painting does she complete in a 7 day week? Write as an improper fraction. 1 20 Additional Example 4: Application = (7) = 1 20 Multiply. 1 20 7171 1 7 20 1 = 7 20 Joy completes of her painting in a 7-day week. 7 20

13. Course 3 2-4 Multiplying Rational Numbers 4. Evaluate 2 (x) for x =. 1. Lesson Quiz Multiply. –1.034 2. 5858 2323 – 1717 9 3. –0.47(2.2) 1212 2 4545 – 5 12 1 2727 Edgar runs mile each day. What is the total distance that Edgar runs in a 7-day week? 5. 8989 6 miles 2929