5th Grade Math - Solve Word Problems Involving Division of Whole Numbers Leading to Answers in the Form of Fractions or Mixed Numbers: CCSS.Math.Content.5.NF.B.3

1

Identify the division problem that equals the following:

$\frac{1}{4}$

$1\div4$

$4\div1$

$2\div4$

$4\div2$

Explanation

The fraction line means divided by; therefore, we can read $\frac{1}{4}$ as divided by , or $1\div4$

2

Identify the division problem that equals the following:

$\frac{2}{4}$

$2\div4$

$4\div2$

$3\div4$

$4\div3$

Explanation

The fraction line means divided by; therefore, we can read $\frac{2}{4}$ as divided by , or $2\div4$

3

A baker has cakes to make this weekend. If he has $64\textup{ pounds}$ of sugar, how much sugar does can he put in each cake, assuming each cake's recipe calls for an equal amount of sugar? Select the answer that contains the pair of numbers that the answer falls between.

and

Explanation

We can think of this problem as an improper fraction and solve for the mixed number by placing the amount of sugar over the number of cakes to be made. We get the following:

$\small \frac{64\textup{ pounds of sugar}}{9\textup{ cakes}}$

can go into only times. In other words, we are looking for the number that when multiplied by the denominator gets us as close to the numerator as possible, without going over the value of the numerator.

Simple multiplication reveals the following:

$9\times 7=63$

In order to find out what is left over, we must subtract this number from the numerator.

The difference will always be less than the denominator from the original improper fraction. If it is not, then check your work in the previous step because this means that the denominator could have been divided into the numerator at least one more time.

Then, we put the difference over the denominator:

$\frac{1}{9}$

Let's solve for the entire improper fraction by putting these values together and forming a mixed number:

$\small \frac{64}{9}=7\frac{1}{9}$

Last, we know that $7\frac{1}{9}$ is between the numbers and ; therefore, the correct answer is:

and

4

The cafe has $136\textup { liters}$ of coffee to last days. How many liters of coffee does the cafe have per day, assuming that each day has an equal amount of coffee? Select the answer that contains the pair of numbers that the answer falls between.

and

Explanation

We can think of this problem as an improper fraction and solve for the mixed number by placing the amount of coffee over the number of days. We get the following:

$\small \frac{136\textup{ liters of coffee}}{10\textup{ days}}$

can go into only times. In other words, we are looking for the number that when multiplied by the denominator gets us as close to the numerator as possible, without going over the value of the numerator.

Simple multiplication reveals the following:

$10\times 13=130$

In order to find out what is left over, we must subtract this number from the numerator.

The difference will always be less than the denominator from the original improper fraction. If it is not, then check your work in the previous step because this means that the denominator could have been divided into the numerator at least one more time.

Then, we put the difference over the denominator:

$\frac{6}{10}$

Let's solve for the entire improper fraction by putting these values together and forming a mixed number:

$\small \frac{136}{10}=13\frac{6}{10}$

Last, we know that $13\frac{6}{10}$ is between the numbers and ; therefore, the correct answer is:

and

5

The cafe has $134\textup { liters}$ of coffee to last days. How many liters of coffee does the cafe have per day, assuming that each day has an equal amount of coffee? Select the answer that contains the pair of numbers that the answer falls between.

and

Explanation

We can think of this problem as an improper fraction and solve for the mixed number by placing the amount of coffee over the number of days. We get the following:

$\small \frac{134\textup{ liters of coffee}}{7\textup{ days}}$

can go into only times. In other words, we are looking for the number that when multiplied by the denominator gets us as close to the numerator as possible, without going over the value of the numerator.

Simple multiplication reveals the following:

$7\times 17=133$

In order to find out what is left over, we must subtract this number from the numerator.

The difference will always be less than the denominator from the original improper fraction. If it is not, then check your work in the previous step because this means that the denominator could have been divided into the numerator at least one more time.

Then, we put the difference over the denominator:

$\frac{1}{7}$

Let's solve for the entire improper fraction by putting these values together and forming a mixed number:

$\small \frac{134}{7}=19\frac{1}{7}$

Last, we know that $19\frac{1}{7}$ is between the numbers and ; therefore, the correct answer is:

and

6

The cafe has $375\textup { liters}$ of coffee to last days. How many liters of coffee does the cafe have per day, assuming that each day has an equal amount of coffee? Select the answer that contains the pair of numbers that the answer falls between.

and

Explanation

We can think of this problem as an improper fraction and solve for the mixed number by placing the amount of coffee over the number of days. We get the following:

$\small \frac{375\textup{ liters of coffee}}{13\textup{ days}}$

can go into only times. In other words, we are looking for the number that when multiplied by the denominator gets us as close to the numerator as possible, without going over the value of the numerator.

Simple multiplication reveals the following:

$13\times 28=364$

In order to find out what is left over, we must subtract this number from the numerator.

The difference will always be less than the denominator from the original improper fraction. If it is not, then check your work in the previous step because this means that the denominator could have been divided into the numerator at least one more time.

Then, we put the difference over the denominator:

$\frac{11}{13}$

Let's solve for the entire improper fraction by putting these values together and forming a mixed number:

$\small \frac{375}{13}=28\frac{11}{13}$

Last, we know that $28\frac{11}{13}$ is between the numbers and ; therefore, the correct answer is:

and

7

Ashley has pieces of candy that she wants to divide amongst her friends. How many pieces of candy will each friend get, assuming that each friend gets the same amount? Select the answer that contains the pair of numbers that the answer falls between.

and

Explanation

We can think of this problem as an improper fraction and solve for the mixed number by placing the amount of candy over the number of Ashley's friends. We get the following:

$\small \frac{100\textup{ pieces of candy}}{8\textup{ friends}}$

can go into only times. In other words, we are looking for the number that when multiplied by the denominator gets us as close to the numerator as possible, without going over the value of the numerator.

Simple multiplication reveals the following:

$8\times 12=96$

In order to find out what is left over, we must subtract this number from the numerator.

The difference will always be less than the denominator from the original improper fraction. If it is not, then check your work in the previous step because this means that the denominator could have been divided into the numerator at least one more time.

Then, we put the difference over the denominator:

$\frac{4}{8}$