ISEE Lower Level Quantitative : Operations with fractions and whole numbers

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

Example Question #35 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Lindsey made  gallons of punch.  of the punch was water. How much water did she use to make the punch? 

 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the punch is water. 

We know that we have  gallons of punch so we can set up our multiplication problem.

 

 8 10

  which means  of each group of 

Example Question #36 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Linda made  gallons of punch.  of the punch was water. How much water did she use to make the punch? 

 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the punch is water. 

We know that we have  gallons of punch so we can set up our multiplication problem.

 

 9 10

  which means  of each group of 

Example Question #37 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Malinda lives  of a mile away from her friend's house. She walked  of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream? 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to her friends house she stopped. 

We know that her friend lives  of a mile away from her so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

8 27

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #38 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Eric lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did Eric travel before he stopped to tie his shoe? 

 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

2 12

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #39 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Aaron lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did he travel before he stopped to tie his shoe? 

 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

4 12

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #40 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Joe lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did he travel before he stopped to tie his shoe? 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

6 12

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #41 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Drew lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did he travel before he stopped to tie his shoe? 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

3 20

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #42 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Armen lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did he travel before he stopped to tie his shoe? 

 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

6 20

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #42 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Brett lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did he travel before he stopped to tie his shoe? 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

9 20

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

Example Question #43 : Interpret The Product (A/B) × Q As A Part Of A Partition Of Q Into B Equal Parts: Ccss.Math.Content.5.Nf.B.4a

Steve lives  of a mile away from his friend's house. He walked  of the way there and then stopped to tie his shoe. How far did he travel before he stopped to tie his shoe? 

 

Possible Answers:

Correct answer:

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of".  of the way to his friends house he stopped. 

We know that his friend lives  of a mile away from him so we can set up our multiplication problem. 

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.


12 20

We make the area model  by  because those are the denominators of our fractions. We shade up  and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).  

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