 # 11/18-19 Multiply Fractions & Decimals #42 LT: I will learn to multiply mixed numbers, fractions, and decimals. Today’s Plan: -Warm up & correct homework.

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11/18-19 Multiply Fractions & Decimals #42 LT: I will learn to multiply mixed numbers, fractions, and decimals. Today’s Plan: -Warm up & correct homework -Lesson -Assignment Learning Target: I will learn to multiply mixed numbers, fractions, and decimals. 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

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 6767 Multiply. Write the answer in simplest form. Multiply Simplify –48 7 –6 6767 –8 6 7 A.

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. B.

–3 5858 Multiply. Write the answer in simplest form. Multiply Simplify –15 8 –1 7878 –3 5 8 A.

4 2525 Multiply Simplify 37 3535 47 5 4 188 5 9 9(5) + 2 5 = = 2525 9 47 5 Try This: Example 1B B. Multiply. Write the answer in simplest form.

A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators. 3535 2323 3535 = = 6 15 2323 If you place the first rectangle on top of the second, the number of green squares represents the numerator, and the number of total squares represents the denominator.

To simplify the product, rearrange the six green squares into the first two columns. You can see that this is. 2525 = = 2525 6 15 A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Helpful Hint

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

–2(9) 3(2) = = 3 1 Simplest form –3 = Multiply numerators. Multiply denominators. Look for common factors: 2, 3. 9292 2323 – 1 –1–1 Additional Example 2B: Multiplying Fractions B. Multiply. Write the answer in simplest form.

Multiply numerators. Multiply denominators. 1212 3737 4 Write as an improper fraction. = 31(1) 7(2) 31 ÷ 14 = 2 R3 = or 2 31 14 3 14 Additional Example 2C: Multiplying Fractions C. Multiply. Write the answer in simplest form. 1212 3737 4 = 31 1 7 2

3(5) 5(8) = Multiply. Write the answer in simplest form. 5858 Simplest form 3838 = 3535 = 3(5) 5(8) Multiply numerators. Multiply denominators. Look for common factors: 5. 1 1 Try This: Example 2A A.

–7(4) 8(7) = = 1 2 Simplest form Multiply numerators. Multiply denominators. Look for common factors: 4, 7. 4747 7878 – 1 –1–1 1212 = – B. Multiply. Write the answer in simplest form. Try This: Example 2B

7979 3535 2 C. Multiply. Write the answer in simplest form. Try This: Example 2C Multiply numerators. Multiply denominators. Write as an improper fraction. = 13(7) 5(9) 91 ÷ 45 = 2 R 1 = or 2 91 45 1 45 7979 3535 2 = 13 7 5 9

2(–0.51) Multiply. Product is negative with 2 decimal places. 2 (–0.51) = –1.02 ( –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. B. 00

3.1 (0.28) Multiply. Product is positive with 3 decimal places. 3.1 (0.28) = 0.868 ( –0.4)(–2.53) Product is positive with 3 decimal places. ( –0.4) (–2.53) = 1.012 Try This: Example 3 A. B.

A. x = 5 Evaluate –3 x for the value of x. 1818 Substitute 5 for x. –3 x 1818 –125 8 = = –15 5858 –125 ÷ 8 = –15 R5 Additional Example 4A: Evaluating Expressions with Rational Numbers –25 8 = (5) –3 (5) 1818 = Write as an improper fraction.

–25 2 8 7 = = – 25 28 2 7 Write as an improper fraction. Substitute for x. 2727 1 4 2727 Additional Example 4B: Evaluating Expressions with Rational Numbers Continued B. x = –3 x 1818 2727 –25 8 = –3 = 1818 Look for common factors: 2. Evaluate –3 x for the value of x. 1818

A.y = –28 6 5 7 = 6767 Write as an improper fraction. 1 –4 –28 5 = 6767 3535 –5 = 6767 –5 y 3535 Try This: Example 4A Look for common factors: 7. = – 24 5, or – 4 4545 Evaluate –5 y for the value of y. 3535 Substitute for x. 6767

B. y = 3 Substitute 3 for y. –5 y 3535 –84 5 = = –16 4545 –84 ÷ 5 = –16 R4 –28 5 = (3) Try This: Example 4B Evaluate –5 y for the value of y. 3535 Write as an improper fraction. 3535 –5 (3) =

4. Evaluate 2 (x) for x =. 1. Lesson Quiz: Part 1 Multiply. –1.034 2. 5858 2323 – 1717 9 3. –0.47(2.2) 1212 2 4545 – 5 12 1 2727

Assignment Pg 124 18-24 even and 36-56 even

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