Common Core: 5th Grade Math : Number & Operations with Fractions

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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Example Questions

Example Question #151 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #152 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #153 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #154 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #155 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #156 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #157 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #158 : Number & Operations With Fractions

The cafe has  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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #159 : Number & Operations With Fractions

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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

Example Question #160 : Number & Operations With Fractions

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. 

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 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:

 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:

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:

 

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

Last, we know that  is between the numbers  and ; therefore, the correct answer is:

 and 

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