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

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. (+) (+) = (+) (–) (–) = (+) (+) (–) = (–) (–) (+) = (–)

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

Multiply Simplify (3) = = Multiply. Write the answer in simplest form. B.

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

Multiply Simplify (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 = = 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 = = 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 Simplest form 3 28 = 1818 = 1(6) 8(7) Multiply numerators. Multiply denominators. Look for common factors: Additional Example 2A: Multiplying Fractions A.

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

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

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

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

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

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

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

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

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

4. Evaluate 2 (x) for x =. 1. Lesson Quiz: Part 1 Multiply. – – –0.47(2.2) –

Assignment Pg even and even