Bell Work: What number is ½ of ¾?
Answer: 3/8
Lesson 23: Multiplying and Dividing Mixed Numbers
To multiply or divide mixed numbers we first write each mixed number (or whole number) as a fraction. A mixed number can be converted into a fraction. 2 ¼ = 4/4 + 4/4 + ¼ = 9/4
Another way to perform the conversion is to multiply the whole number by the denominator and add the numerator to find the numerator of the new fraction. 4 x = 9 2 ¼ = 9/4
If the answer is an improper fraction we might choose to convert the improper fraction to a mixed number. We do so by dividing the numerator by the denominator. 9/4 = 2 ¼ The remainder becomes the numerator of the fraction part of the mixed number.
Example: Simplify 2 1/3 x 1 1/2
Answer: 2 1/3 x 1 ½ = 7/3 x 3/2 = 21/6 = 3 3/6 = 3 1/2
Example: Simplify 1 2/3 ÷ 2 1/2
Answer: 1 2/3 ÷ 2 ½ = 5/3 ÷ 5/2 = 5/3 x 2/5 = 10/15 = 2/3
Both of the previous problems could have been reduced before multiplying. We may reduce (or cancel) to eliminate the need to reduce after multiplying.
Example: A carpenter is nailing horizontal boards to the outside surface of a building. The exposed portion of each board is 6 ¾ inches. How many rows of boards are needed to reach to the top of an 8 foot wall?
Answer: First convert 8 feet to 96 inches. 96 ÷ 6 ¾ = 96 ÷ 27/4 = 96/1 x 4/27 = 32/1 x 4/9 = 128/9 = 14 2/9 Fourteen boards is not enough. To reach to the top of the wall the carpenter will need 15 rows of boards.
Multiplying and Dividing Fractions and Mixed Numbers 1. Write whole numbers or mixed numbers as fractions 2. Multiplying Multiply numerators Multiply denominators Dividing Instead of dividing, multiply by the reciprocal of the divisor 3. Simplify the answer by reducing if possible. Improper fractions may be expressed as whole or mixed numbers
Example: What is the area of a rectangle 2 ½ inches long and 1 ½ inches wide?
Answer: 3 ¾ inches 2
Example: A recipe calls for 1 ¾ cups of milk. How many cups of milk are needed if the recipe is doubled?
Answer: 3 ½ cups
HW: Lesson 23 #1-30 Due Next time