Math Lesson 67 Solving fractions and Equations: Multiplication and Division
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reciprocal
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One of two numbers whose product is 1; it is also called multiplicative inverse. * 6/7 recip 7/6
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Solving Fraction Equations: Multiplication and Division
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Dividing by a number is the same as multiplying by its reciprocal. To solve equations we must get the variable alone by multiplying and dividing.
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dexter makes dog biscuits for the animal shelter. He makes 3/4 of a recipe and uses 15 cups of powdered milk. How many cups of powdered milk are in the recipe?
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1. Understand the Problem. -The answer will be the number of cups of powdered milk in the recipe. -List the important information: *He makes 3/4 of the recipe. *He uses 15 cups of powdered sugar. 2. Make a Plan. -You can write and solve an equation. Let x represent the number of cups in the recipe. -He uses 15 cups, which is three-fourths of the amount in the recipe. 3. Solve.
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Explain how to solve an equation where the variable is multiplied by a fraction.
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So if you had the problem 15 = 3/4 • x you would multiply the 3/4 but the reciprocal, so it would be 4/3. Then you do it to the other side so you have 4/3 x 15/1 then you can reduce. So your problem is now 4/1 x 5/1 = 20/1 so then your answer is 20.
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Solve x/2 + 4 = 10 a. x = 3 b. x = 7 c. x = 12 d. x = 28
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c. x = 12
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Solve - 4k - 2 = 10. a. k = 2 b. k = -2 c. k = 3 d. k = -3
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d. k = -3
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Solve t/5 + 3 = 3 a. t = 0 b. t = 6/5 c. t = 6 d. t = 30
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a. t = 0
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Solve 3n - 6 = 9 a. n = 1 b. n = 3 c. n = 5 d. n = 9
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c. n = 5
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Each square on the graph paper has an area of 4/9 square inch. What is the length and width of each square? a. 1/9 inch b. 2/3 inch c. 2/9 inch d. 1/3 inch
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b. 2/3 inch
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A number n is multiplied by 1/3 and the product is 12. Write and solve the equation.
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n x 1/3 = 12; n = 36
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Amy has some beads that are each 1/2 inch long. How many beads will she need to make a necklace that is 18 inches long?
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36 beads. 18 ÷ 2/1 = 36
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Solve. 5/7a = 8 a. 56/5 b. a = 5/56 c. a = 40/7 d. a = 7/40
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a. 56/5
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Solve. 2/9z = 5 a. z = 45/2 b. z = 2/45 c. z = 9/10 d. z = 10/9
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a. z = 45/2
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A number n is multiplied by 1 1/2 and the product is 9. Solve for n. a. n = 6 b. n = 12 c. n = 13 1/2 d. n = 10 1/2
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a. n = 6
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in a fish tank, 3/4 of the fish have a red stripe on them. If 15 of the fish have that stripe, how many total fish are in the tank? a. 26 b. 24 c. 23 d. 20
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d. 20
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A recipe for a loaf of bread calls for 3/4 cup of oatmeal. How much oatmeal do you need if you double the recipe? a. 3/8 cup b. 1/2 cup c. 2/3 cup d. 1 1/2 cup
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d. 1 1/2 cup
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Solve. 2/3x = 9 a. 6 b. 9 2/3 c. 12 d. 13 1/2
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d. 13 1/2
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Solve. 14a = 1/4 a. a = 1/56 b. a = 56 c. a = 2/7 d. a = 7/2
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a. a = 1/56
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Solve. 1/6k = 2 a. k = 3 b. k = 12 c. k = 1/3 d. k = 1/12
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b. k = 12
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Solve. 2/3y = 10 a. 7 b. 15 c. 30 d. 20
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b. 15
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It takes 3 buckets of water to fill 1/3 of a fish tank. how many buckets does it take to fill the whole tank? a. 3 1/3 buckets b. 6 2/3 buckets c. 9 buckets d. 12 buckets
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c. 9 buckets
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A fraction divided by 2/3 is equal to 1 1/4. What is that fraction? a. 1/3 b. 5/6 c. 1/4 d. 1/2
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b. 5/6
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A number n is divided by 4 and the quotient is 1/2. Solve for n. a. n = 1/2 b. n = 2 c. n = 3/4 d. n = 8
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b. n = 2
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Solve. 5/8 f = 9 a. f = 45/8 b. f = 8/45 c. f = 72/5 d. f = 5/72
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c. f = 72/5
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Solve. 6h = 5/7 a. h = 42/5 b. h = 5/42 c. h = 30/7 d. h = 7/30
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b. h = 5/42
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Find the quotient. Simplify. 2 2/5 ÷ 6 1/3 a. 2 23/36 b. 36/95 c. 15 1/5 d. 8 11/15
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b. 36/95
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Find the quotient. Simplify. 7 1/2 ÷ 2 a. 3 3/4 b. 4/15 c. 9 1/2 d. 15
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a. 3 3/4
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Evaluate x ÷ 20 for x = 2/3. a. 30 b. 1/30 c. 3/40 d. 13 1/3
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b. 1/30
