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ISEE Lower Level Quantitative : Operations with fractions and whole numbers

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

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1955 : Numbers And Operations

T.J. lives $\frac{4}{7}$ $\displaystyle \frac{4}{7}$ of a mile away from his friend's house. He walked $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$\frac{8}{28}\textup { of a mile}$ $\displaystyle \frac{8}{28}\textup { of a mile}$

$6\textup { miles}$ $\displaystyle 6\textup { miles}$

$8\textup { miles}$ $\displaystyle 8\textup { miles}$

$28\textup { miles}$ $\displaystyle 28\textup { miles}$

$\frac{6}{28}\textup { of a mile}$ $\displaystyle \frac{6}{28}\textup { of a mile}$

Correct answer:

$\frac{8}{28}\textup { of a mile}$ $\displaystyle \frac{8}{28}\textup { of a mile}$

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". $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{4}{7}$ $\displaystyle \frac{4}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{2}{4}\times\frac{4}{7}$ $\displaystyle \frac{2}{4}\times\frac{4}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 2$ and over $\displaystyle 4$, 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).

$\frac{2}{4}\times\frac{4}{7}=\frac{8}{28}$ $\displaystyle \frac{2}{4}\times\frac{4}{7}=\frac{8}{28}$

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Example Question #1956 : Numbers And Operations

Dan lives $\frac{4}{7}$ $\displaystyle \frac{4}{7}$ of a mile away from his friend's house. He walked $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$\frac{4}{28}\textup { of a mile}$ $\displaystyle \frac{4}{28}\textup { of a mile}$

$\frac{3}{28}\textup { of a mile}$ $\displaystyle \frac{3}{28}\textup { of a mile}$

$\frac{5}{28}\textup { of a mile}$ $\displaystyle \frac{5}{28}\textup { of a mile}$

$3\textup { miles}$ $\displaystyle 3\textup { miles}$

$5\textup { miles}$ $\displaystyle 5\textup { miles}$

Correct answer:

$\frac{4}{28}\textup { of a mile}$ $\displaystyle \frac{4}{28}\textup { of a mile}$

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". $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{4}{7}$ $\displaystyle \frac{4}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{1}{4}\times\frac{4}{7}$ $\displaystyle \frac{1}{4}\times\frac{4}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 1$ and over $\displaystyle 4$, 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).

$\frac{1}{4}\times\frac{4}{7}=\frac{4}{28}$ $\displaystyle \frac{1}{4}\times\frac{4}{7}=\frac{4}{28}$

Report an Error

Example Question #321 : Number & Operations With Fractions

Chris lives $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ of a mile away from his friend's house. He walked $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$\frac{4}{28}\textup { of a mile}$ $\displaystyle \frac{4}{28}\textup { of a mile}$

$\frac{2}{28}\textup { of a mile}$ $\displaystyle \frac{2}{28}\textup { of a mile}$

$\frac{3}{28}\textup { of a mile}$ $\displaystyle \frac{3}{28}\textup { of a mile}$

$28\textup { miles}$ $\displaystyle 28\textup { miles}$

$4\textup { miles}$ $\displaystyle 4\textup { miles}$

Correct answer:

$\frac{3}{28}\textup { of a mile}$ $\displaystyle \frac{3}{28}\textup { of a mile}$

Explanation:

We know that his friend lives $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{1}{4}\times\frac{3}{7}$ $\displaystyle \frac{1}{4}\times\frac{3}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 1$ and over $\displaystyle 3$, 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).

$\frac{1}{4}\times\frac{3}{7}=\frac{3}{28}$ $\displaystyle \frac{1}{4}\times\frac{3}{7}=\frac{3}{28}$

Report an Error

Example Question #1958 : Numbers And Operations

Todd lives $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ of a mile away from his friend's house. He walked $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$\frac{6}{28}\textup { of a mile}$ $\displaystyle \frac{6}{28}\textup { of a mile}$

$6\textup { miles}$ $\displaystyle 6\textup { miles}$

$\frac{5}{28}\textup { of a mile}$ $\displaystyle \frac{5}{28}\textup { of a mile}$

$5\textup { miles}$ $\displaystyle 5\textup { miles}$

$\frac{1}{28}\textup { of a mile}$ $\displaystyle \frac{1}{28}\textup { of a mile}$

Correct answer:

$\frac{6}{28}\textup { of a mile}$ $\displaystyle \frac{6}{28}\textup { of a mile}$

Explanation:

We know that his friend lives $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{2}{4}\times\frac{3}{7}$ $\displaystyle \frac{2}{4}\times\frac{3}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 2$ and over $\displaystyle 3$, 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).

$\frac{2}{4}\times\frac{3}{7}=\frac{6}{28}$ $\displaystyle \frac{2}{4}\times\frac{3}{7}=\frac{6}{28}$

Report an Error

Example Question #1959 : Numbers And Operations

Austin lives $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ of a mile away from his friend's house. He walked $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$9\textup { miles}$ $\displaystyle 9\textup { miles}$

$\frac{9}{28}\textup { of a mile}$ $\displaystyle \frac{9}{28}\textup { of a mile}$

$\frac{6}{28}\textup { of a mile}$ $\displaystyle \frac{6}{28}\textup { of a mile}$

$6\textup { miles}$ $\displaystyle 6\textup { miles}$

$28\textup { miles}$ $\displaystyle 28\textup { miles}$

Correct answer:

$\frac{9}{28}\textup { of a mile}$ $\displaystyle \frac{9}{28}\textup { of a mile}$

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". $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{3}{7}$ $\displaystyle \frac{3}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{3}{4}\times\frac{3}{7}$ $\displaystyle \frac{3}{4}\times\frac{3}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 3$ and over $\displaystyle 3$, 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).

$\frac{3}{4}\times\frac{3}{7}=\frac{9}{28}$ $\displaystyle \frac{3}{4}\times\frac{3}{7}=\frac{9}{28}$

Report an Error

Example Question #322 : Number & Operations With Fractions

Dylan lives $\frac{2}{7}$ $\displaystyle \frac{2}{7}$ of a mile away from his friend's house. He walked $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$3\textup { miles}$ $\displaystyle 3\textup { miles}$

$\frac{3}{28}\textup { of a mile}$ $\displaystyle \frac{3}{28}\textup { of a mile}$

$\frac{1}{28}\textup { of a mile}$ $\displaystyle \frac{1}{28}\textup { of a mile}$

$2\textup { miles}$ $\displaystyle 2\textup { miles}$

$\frac{2}{28}\textup { of a mile}$ $\displaystyle \frac{2}{28}\textup { of a mile}$

Correct answer:

$\frac{2}{28}\textup { of a mile}$ $\displaystyle \frac{2}{28}\textup { of a mile}$

Explanation:

We know that his friend lives $\frac{2}{7}$ $\displaystyle \frac{2}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{1}{4}\times\frac{2}{7}$ $\displaystyle \frac{1}{4}\times\frac{2}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 1$ and over $\displaystyle 2$, 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).

$\frac{1}{4}\times\frac{2}{7}=\frac{2}{28}$ $\displaystyle \frac{1}{4}\times\frac{2}{7}=\frac{2}{28}$

Report an Error

Example Question #321 : Fractions

Gerry lives $\frac{2}{7}$ $\displaystyle \frac{2}{7}$ of a mile away from his friend's house. He walked $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ of the way there and then stopped to pet a dog. How far did he travel before he stopped to pet the dog?

Possible Answers:

$\frac{6}{28}\textup { of a mile}$ $\displaystyle \frac{6}{28}\textup { of a mile}$

$\frac{9}{28}\textup { of a mile}$ $\displaystyle \frac{9}{28}\textup { of a mile}$

$9\textup { miles}$ $\displaystyle 9\textup { miles}$

$4\textup { miles}$ $\displaystyle 4\textup { miles}$

$\frac{4}{28}\textup { of a mile}$ $\displaystyle \frac{4}{28}\textup { of a mile}$

Correct answer:

$\frac{4}{28}\textup { of a mile}$ $\displaystyle \frac{4}{28}\textup { of a mile}$

Explanation:

We know that his friend lives $\frac{2}{7}$ $\displaystyle \frac{2}{7}$ of a mile away from him so we can set up our multiplication problem.

$\frac{2}{4}\times\frac{2}{7}$ $\displaystyle \frac{2}{4}\times\frac{2}{7}$

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 28

We make the area model $\displaystyle 7$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 2$ and over $\displaystyle 2$, 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).

$\frac{2}{4}\times\frac{2}{7}=\frac{4}{28}$ $\displaystyle \frac{2}{4}\times\frac{2}{7}=\frac{4}{28}$

Report an Error

Example Question #91 : Operations With Fractions And Whole Numbers

Julia lives $\frac{8}{9}$ $\displaystyle \frac{8}{9}$ of a mile away from her friend's house. She walked $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ 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:

$\frac{16}{27}\textup { of a mile}$ $\displaystyle \frac{16}{27}\textup { of a mile}$

$\frac{8}{27}\textup { of a mile}$ $\displaystyle \frac{8}{27}\textup { of a mile}$

$\frac{16}{28}\textup { of a mile}$ $\displaystyle \frac{16}{28}\textup { of a mile}$

$\frac{10}{27}\textup { of a mile}$ $\displaystyle \frac{10}{27}\textup { of a mile}$

$\frac{10}{28}\textup { of a mile}$ $\displaystyle \frac{10}{28}\textup { of a mile}$

Correct answer:

$\frac{16}{27}\textup { of a mile}$ $\displaystyle \frac{16}{27}\textup { of a mile}$

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". $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{8}{9}$ $\displaystyle \frac{8}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{2}{3}\times\frac{8}{9}$ $\displaystyle \frac{2}{3}\times\frac{8}{9}$

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.

16 27

We make the area model $\displaystyle 9$ by $\displaystyle 3$ because those are the denominators of our fractions. We shade up $\displaystyle 2$ and over $\displaystyle 8$, 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).

$\frac{2}{3}\times\frac{8}{9}=\frac{16}{27}$ $\displaystyle \frac{2}{3}\times\frac{8}{9}=\frac{16}{27}$

Report an Error

Example Question #1962 : Numbers And Operations

Jessie lives $\frac{7}{9}$ $\displaystyle \frac{7}{9}$ of a mile away from her friend's house. She walked $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ 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:

$\frac{14}{27}\textup { of a mile}$ $\displaystyle \frac{14}{27}\textup { of a mile}$

$\frac{10}{27}\textup { of a mile}$ $\displaystyle \frac{10}{27}\textup { of a mile}$

$\frac{10}{26}\textup { of a mile}$ $\displaystyle \frac{10}{26}\textup { of a mile}$

$\frac{14}{26}\textup { of a mile}$ $\displaystyle \frac{14}{26}\textup { of a mile}$

$\frac{9}{27}\textup { of a mile}$ $\displaystyle \frac{9}{27}\textup { of a mile}$

Correct answer:

$\frac{14}{27}\textup { of a mile}$ $\displaystyle \frac{14}{27}\textup { of a mile}$

Explanation:

We know that her friend lives $\frac{7}{9}$ $\displaystyle \frac{7}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{2}{3}\times\frac{7}{9}$ $\displaystyle \frac{2}{3}\times\frac{7}{9}$

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.

14 27

We make the area model $\displaystyle 9$ by $\displaystyle 3$ because those are the denominators of our fractions. We shade up $\displaystyle 2$ and over $\displaystyle 7$, 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).

$\frac{2}{3}\times\frac{7}{9}=\frac{14}{27}$ $\displaystyle \frac{2}{3}\times\frac{7}{9}=\frac{14}{27}$

Report an Error

Example Question #1963 : Numbers And Operations

Erica lives $\frac{7}{9}$ $\displaystyle \frac{7}{9}$ of a mile away from her friend's house. She walked $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ 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:

$\frac{8}{27}\textup { of a mile}$ $\displaystyle \frac{8}{27}\textup { of a mile}$

$\frac{6}{27}\textup { of a mile}$ $\displaystyle \frac{6}{27}\textup { of a mile}$

$\frac{6}{28}\textup { of a mile}$ $\displaystyle \frac{6}{28}\textup { of a mile}$

$\frac{8}{28}\textup { of a mile}$ $\displaystyle \frac{8}{28}\textup { of a mile}$

$\frac{7}{27}\textup { of a mile}$ $\displaystyle \frac{7}{27}\textup { of a mile}$

Correct answer:

$\frac{7}{27}\textup { of a mile}$ $\displaystyle \frac{7}{27}\textup { of a mile}$

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". $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{7}{9}$ $\displaystyle \frac{7}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{1}{3}\times\frac{7}{9}$ $\displaystyle \frac{1}{3}\times\frac{7}{9}$

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.

7 27

We make the area model $\displaystyle 9$ by $\displaystyle 3$ because those are the denominators of our fractions. We shade up $\displaystyle 1$ and over $\displaystyle 7$, 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).

$\frac{1}{3}\times\frac{7}{9}=\frac{7}{27}$ $\displaystyle \frac{1}{3}\times\frac{7}{9}=\frac{7}{27}$

Report an Error

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

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ISEE Lower Level Quantitative : Operations with fractions and whole numbers

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #1955 : Numbers And Operations

Example Question #1956 : Numbers And Operations

Example Question #321 : Number & Operations With Fractions

Example Question #1958 : Numbers And Operations

Example Question #1959 : Numbers And Operations

Example Question #322 : Number & Operations With Fractions

Example Question #321 : Fractions

Example Question #91 : Operations With Fractions And Whole Numbers

Example Question #1962 : Numbers And Operations

Example Question #1963 : Numbers And Operations

All ISEE Lower Level Quantitative Resources

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