Multiplying and dividing fractions

The area of Galveston County is 378 square miles. If the county was divided into equal sections of 1/6 square mile, how many sections would there be?

• 63 sections

• 1/63 sections

• 2,268 sections

• 1/2,268 sections

Answer explanation

You are dividing the county into 1/6 sections. Whatever is being divided goes first in the equation.

378 divided by 1/6 sections =

Put 378 over 1 to make it a "visible" fraction.

(**invisible math - the one is always there, just invisible**).

Then flip the 2nd number (1/6 to 6/1) and multiply straight across.

378/1 x 6/1 = 2,268/1

Simplify 2,268/1 = 2,268

Nancy has a gallon-sized container in which she collects rainwater.

** Last weeks’ rain filled 1/9 of the container.

** Nancy wants to water 5 of her plants with this rainwater.

** Each plant will be watered with the same amount of rainwater.

What amount of rainwater will each plant receive?

Answer explanation

You are dividing the amount of rain collected (1/9) by the 5 plants.

1/9 divided by 5 = 1/45

Put the 5 over one to make a visible fraction.

(**invisible math: the one is always there, you just can't see it.)

1/9 divided 5/1=

Flip the second number and multiply straight across.

1/9 x 1/5 = 1/45

• 6

• 150

Answer explanation

Put 30 over one to make it a visible fraction.

1/5 divided by 30/1

Flip the second number and multiply straight across.

1/5 x 1/30 = 1/150

Answer explanation

Dividing

3 cups divided by 1/2 cup each day.

Put a one under the 3 to make it a visible fraction.

3/1 divided by 1/2 = 6

Flip the second number and multiply straight across.

3/1 x 2/1 = 6/1

Simplify 6/1 = 6

• 18

• 144

• 12

• 8

Answer explanation

Divide

18 cups divided by 1/8 cup

Put 1 under 18 to make it a visible fraction.

18/1 divided by 1/8 = 144

Flip the second number and multiply straight across.

18/1 x 8/1 = 144/1 = 144

The question asked how many dozen. Your answer gave you how many cookies.

Divide 144 by 12 to get how many dozen because there are 12 in a dozen.

144 divided by 12 = 12

So, 12 dozen cookies can be made from 18 cups of dough if each cookie is 1/8 cup.

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Answer explanation

Multiply

7 boxes and each box has 3/4 in it.

Count all the 3/4 and put them together in boxes with a total of 4 parts.

Your answer is 5 wholes and 1/4

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Answer explanation

You have 15 bars in 5 groups of 3.

3 of the 5 groups are shaded in.

Anna is baking cookies. The recipe asks for  cup of flour per batch. Anna wants to bake 4 batches of cookies. She made a model to help her find the amount of flour, in cups, for 4 batches of cookies.

Answer explanation

3/4 x 4 = 12/4

the picture shows 4 groups of 3/4 and then those groups put together, making 3 whole groups.

12/4 is improper

To simplify you divide 4 into 12 and that = 3

Julissa was allowed to spend 3/4 of her allowance at the mall. Of that money, she spent 1/2 of it on a purse. What part of her allowance did she spend on a purse?

• 6/4

• 3/8

• 7/8

• 4/6

Answer explanation

Multiply:

Clue phrase:

1/2 OF it (it is the money)

Clue word OF

1/2 OF the money.

What do you know:

She is spending 3/4 of her allowance at

the mall.

She is spending 1/2 OF that 3/4 on a purse.

OF tells you to multiply

1/2 x 3/4 = 3/8

Answer explanation

Multiply:

What you know:

1 1/2 pizza left over

John's dad ate 3/4 OF the leftovers

Meaning he ate 3/4 OF 1 1/2

Clue words

OF

change 1 1/2 into an improper fraction.

(multiply 1x2 then add 1 and put the answer over 2) 3/2

3/2 x 3/4 = 9/8

simplify 9/8

8 divides into 9 one time (whole number) with one left over (numerator) 8 stays the denominator.

9/8 = 1 1/8