Math Lesson 67 Solving fractions and Equations: Multiplication and Division

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?

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.

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?

36 beads. 18 ÷ 2/1 = 36

Solving Fraction Equations: Multiplication and Division

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.

reciprocal

One of two numbers whose product is 1; it is also called multiplicative inverse. * 6/7 recip 7/6

Explain how to solve an equation where the variable is multiplied by a fraction.

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.

Find the quotient. Simplify. 7 1/2 ÷ 2 a. 3 3/4 b. 4/15 c. 9 1/2 d. 15

a. 3 3/4

Solve. 5/7a = 8 a. 56/5 b. a = 5/56 c. a = 40/7 d. a = 7/40

a. 56/5

Solve. 14a = 1/4 a. a = 1/56 b. a = 56 c. a = 2/7 d. a = 7/2

a. a = 1/56

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

a. n = 6

Solve t/5 + 3 = 3 a. t = 0 b. t = 6/5 c. t = 6 d. t = 30

a. t = 0

Solve. 2/9z = 5 a. z = 45/2 b. z = 2/45 c. z = 9/10 d. z = 10/9

a. z = 45/2

Evaluate x ÷ 20 for x = 2/3. a. 30 b. 1/30 c. 3/40 d. 13 1/3

b. 1/30

Solve. 2/3y = 10 a. 7 b. 15 c. 30 d. 20

b. 15

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

b. 2/3 inch

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

b. 36/95

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

b. 5/6

Solve. 6h = 5/7 a. h = 42/5 b. h = 5/42 c. h = 30/7 d. h = 7/30

b. h = 5/42

Solve. 1/6k = 2 a. k = 3 b. k = 12 c. k = 1/3 d. k = 1/12

b. k = 12

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

b. n = 2

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

c. 9 buckets

Solve. 5/8 f = 9 a. f = 45/8 b. f = 8/45 c. f = 72/5 d. f = 5/72

c. f = 72/5

Solve 3n - 6 = 9 a. n = 1 b. n = 3 c. n = 5 d. n = 9

c. n = 5

Solve x/2 + 4 = 10 a. x = 3 b. x = 7 c. x = 12 d. x = 28

c. x = 12

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

d. 1 1/2 cup

Solve. 2/3x = 9 a. 6 b. 9 2/3 c. 12 d. 13 1/2

d. 13 1/2

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

d. 20

Solve - 4k - 2 = 10. a. k = 2 b. k = -2 c. k = 3 d. k = -3

d. k = -3

A number n is multiplied by 1/3 and the product is 12. Write and solve the equation.

n x 1/3 = 12; n = 36