11/30/09 Multiply & Divide Fractions #1

11/30/09 Multiply & Divide Fractions #1 LT: I will learn to multiply and divide mixed numbers and fractions. Fraction, Decimal, Percent Wheels • Circle all fractions that are in lowest terms. • Review the conversions & decorate your wheel. Today’s Plan: -Fraction, Decimal, Percent Wheel game -Lesson -Assignment Learning Target: I will learn to multiply and divide mixed numbers and fractions.

11/30/09 Multiply & Divide Fractions #1 LT: I will learn to multiply and divide mixed numbers and fractions. Fraction, Decimal, Percent Wheels Today’s Plan: -Fraction, Decimal, Percent Wheel game -Lesson -Assignment Learning Target: I will learn to multiply and divide mixed numbers and fractions.

11/30/09 Multiply & Divide Fractions #1 LT: I will learn to multiply and divide mixed numbers and fractions. Warm-up Katie made a bookshelf that is 5 feet long. The first 6 books she put on it took up 8 inches of shelf space. About how many books should fit on the shelf? 45 books Today’s Plan: -Fraction, Decimal, Percent Wheel game -Lesson -Assignment Learning Target: I will learn to multiply and divide mixed numbers and fractions.

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. (+)•(–)=(–) (–)•(+)=(–)

–8 • 6 7 –48 7 6 7 –6 Multiply. Write the answer in simplest form. 6 7 A. –8 Multiply Simplify

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

1(6) 8(7) = 3 1(6) 8(7) = 4 3 28 = Additional Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. 6 7 1 8 A. Multiply numerators. Multiply denominators. Look for common factors: 2. Simplest form

–2(9) 3(2) = –1 –2(9) 3(2) 3 = 1 1 –3 = Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. 2 3 9 2 B. – Multiply numerators. Multiply denominators. Look for common factors: 2, 3. Simplest form

3(5) 5(8) = 1 3(5) 5(8) = 1 3 8 = Try This: Example 2A Multiply. Write the answer in simplest form. 5 8 3 5 A. Multiply numerators. Multiply denominators. Look for common factors: 5. Simplest form

–7(4) 8(7) = –1 –7(4) 8(7) 1 = 1 2 1 2 = – Try This: Example 2B Multiply. Write the answer in simplest form. 4 7 7 8 B. – Multiply numerators. Multiply denominators. Look for common factors: 4, 7. Simplest form

13(7) 5(9) 91 45 1 45 = or 2 Try This: Example 2C Multiply. Write the answer in simplest form. 7 9 3 5 C. 2 Write as an improper fraction. 13 7 5 9 Multiply numerators. Multiply denominators. 91 ÷ 45 = 2 R 1

1 8 Evaluate –3 x for the value of x. 18 18 –3 x –3 (5) –25 8 = = (5) –125 8 = 5 8 = –15 Additional Example 4A: Evaluating Expressions with Rational Numbers A. x = 5 Substitute 5 for x. Write as an improper fraction. –125 ÷ 8 = –15 R5

1 8 Evaluate –3 x for the value of x. 18 –3 x 18 2 7 27 = –3 Substitute for x. 27 –25 8 = –25 • 2 = 8 • 7 25 28 = – Additional Example 4B: Evaluating Expressions with Rational Numbers Continued 2 B. x = 7 Write as an improper fraction. 1 Look for common factors: 2. 4

3 5 Evaluate –5 y for the value of y. 35 –5 y 6 7 Substitute for x. 67 35 = –5 67 –28 5 = –28 • 6 = 5 • 7 24 5 45 = – , or – 4 Try This: Example 4A 67 A. y = Write as an improper fraction. –4 Look for common factors: 7. 1

3 5 Evaluate –5 y for the value of y. 35 –5 y 35 = –5 (3) –28 5 (3) = –84 5 = 4 5 = –16 Try This: Example 4B B. y = 3 Substitute 3 for y. Write as an improper fraction. –84 ÷ 5 = –16 R4

A number and its reciprocalhave a product of 1. To find the reciprocal of a fraction, exchange the numerator and the denominator. Remember that an integer can be written as a fraction with a denominator of 1.

2 5 2 5 1 3 1 3 2 15 2 15 ÷ = = 5 2 1 3 2 15 2•515 •2 Multiplication and division are inverse operations. They undo each other. Notice that multiplying by the reciprocal gives the same result as dividing. = =

1 2 2 1 5 11 5 11 = ÷ • 2 1 5 11 = • 10 11 = Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. 1 2 5 11 A. ÷ Multiply by the reciprocal. No common factors. Simplest form

2 1 3 8 19 8 = ÷ ÷ 2 2 19 8 1 2 = 19 • 1 = 8 • 2 3 16 19 16 1 = = Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. 3 8 B. 2 2 ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors 19 ÷ 16 = 1 R 3

3 4 7 15 4 3 7 15 ÷ = • 7 • 4 = 28 45 15 • 3 = Try This: Example1A Divide. Write the answer in simplest form. 3 4 7 15 A. ÷ Multiply by the reciprocal. No common factors. Simplest form

22 5 3 1 2 5 4 ÷ 3 ÷ = 22 5 1 3 = 22 • 1 = 5 • 3 22 15 7 15 1 = or Try This: Example1B Divide. Write the answer in simplest form. 2 5 4 3 B. ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors. 22 ÷ 15 = 1 R 7

5 1 5 4 4 5 • = 1 4 254 = 5 • 5 6 = = 1 • 4 Additional Example 3B: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 4 5 B. k ÷ for k = 5 5÷

9 1 7 4 4 7 = ÷ 9 9 • 7 = 1 • 4 3 4 = 15 Try This: Example 3B Evaluate the expression for the given value of the variable. 4 7 B. u ÷ , for u = 9 Write as in improper fraction and multiply by the reciprocal. No common factors. 63 ÷ 4 = 15 R 3

Assignment Pg 124 5-12

11/30/09 Multiply & Divide Fractions #1