3 3 Multiplying Rational Numbers Learn to multiply

3 -3 Multiplying Rational Numbers Learn to multiply fractions, decimals, and mixed numbers. Pre-Algebra

3 -3 Multiplying Rational Numbers Olivia invited 36 people to a party. She needs to triple the recipe for a dip, or multiply the amount of each ingredient by 3. Remember that multiplication by a whole number can be written as repeated addition. Repeated addition 1 1 1 3 = + + 4 4 Multiplication 1 = 3 • 1= 3 3 4 4 4 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. Pre-Algebra

3 -3 Multiplying Rational Numbers 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 (–) • (+) = (–) Pre-Algebra

3 -3 Multiplying Rational Numbers Example 1 A: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. A. – 8 67 – 8 • 6 7 – 48 = Multiply 7 6 = – 6 Simplify 7 = Pre-Algebra Helpful Hint To write 12 5 as a mixed number, divide: 12 5 = 2 R 2 25 =2

3 -3 Multiplying Rational Numbers Example 1 B: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. B. 2 5 13 =2 = 16 3 32 3 = 10 Pre-Algebra 23 1 53 5(3) + 1 3 = Multiply Simplify = 16 3

3 -3 Multiplying Rational Numbers 35 • 2 3 A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators. 35 • • 23 = 6 15 = 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. Pre-Algebra

3 -3 Multiplying Rational Numbers To simplify the product, rearrange the six green squares into the first two columns. You can see that this is 25. = 6 15 = 25 Helpful Hint A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Pre-Algebra

3 -3 Multiplying Rational Numbers Example 2 A: Multiplying Fractions Multiply. Write the answer in simplest form. A. 1 6 8 7 1(6) = 8(7) = = Pre-Algebra 6 3 28 56 Multiply numerators. Multiply denominators. Look for common factors: 2. Simplest form

3 -3 Multiplying Rational Numbers Example 2 B: Multiplying Fractions Multiply. Write the answer in simplest form. B. 2 9 – 3 2 – 2(9) = 3(2) – 18 = = – 3 Pre-Algebra 6 Multiply numerators. Multiply denominators. Simplify

3 -3 Multiplying Rational Numbers Example 2 C: Multiplying Fractions Multiply. Write the answer in simplest form. 3 4 7 C. 43 7 1 2 1 = 31 1 2 7 2 31(1) = 7(2) 31 3 14 = or 2 14 Pre-Algebra Write as an improper fraction. Multiply numerators. Multiply denominators. Simplify

3 -3 Multiplying Rational Numbers 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 (–) • (+) = (–) Pre-Algebra

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

3 -3 Multiplying Rational Numbers Try This: Example 2 B Multiply. Write the answer in simplest form. B. – 7 4 8 7 – 7(4) = 8(7) – 1 1 – 7(4) = 8(7) 2 =– Pre-Algebra 12 Multiply numerators. Multiply denominators. Look for common factors: 4, 7. 1 Simplest form

3 -3 Multiplying Rational Numbers Example 3: Multiplying Decimals Multiply. A. 2(– 0. 51) 2 • (– 0. 51) = – 1. 02 Product is negative with 2 decimal places. B. (– 0. 4)(– 3. 75) Product is positive (– 0. 4) • (– 3. 75) = 1. 500 with 3 decimal places. = 1. 500 You can drop the zeros after the decimal point. Pre-Algebra

3 -3 Multiplying Rational Numbers Try This: Example 3 Multiply. A. 3. 1 (0. 28) 3. 1 • (0. 28) = 0. 868 Product is positive with 3 decimal places. B. (– 0. 4)(– 2. 53) (– 0. 4) • (– 2. 53) = 1. 012 Product is positive with 3 decimal places. Pre-Algebra

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

3 -3 Multiplying Rational Numbers Example 4 B: Evaluating Expressions with Rational Numbers Continued 18 Evaluate – 3 x for the value of x. B. x = 2 7 – 3 18 x = – 3 = – 25 27 8 =– =– Pre-Algebra 18 27 50 56 25 28 Substitute 27 for x. Write as an improper fraction. Look for common factors: 2.

3 -3 Multiplying Rational Numbers Try This: Example 4 A 35 Evaluate – 5 y for the value of y. A. y = 67 – 5 35 y = – 5 = 35 67 – 4– 28 • 6 = 5 • 71 Pre-Algebra 24 5 , 67 for x. Write as an improper fraction. – 28 67 5 =– Substitute Look for common factors: 7. or – 4 45

3 -3 Multiplying Rational Numbers Try This: Example 4 B 35 Evaluate – 5 y for the value of y. B. y = 3 – 5 35 y = – 5 35(3) Substitute 3 for y. = – 28 5 = – 84 5 (3) Write as an improper = – 16 Pre-Algebra fraction. 4 5 – 84 ÷ 5 = – 16 R 4