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ISEE Lower Level Quantitative : ISEE Lower Level (grades 5-6) Quantitative Reasoning

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 #1151 : Common Core Math: Grade 5

Linda made $\displaystyle 9$ gallons of punch. $\frac{1}{10}$ $\displaystyle \frac{1}{10}$ of the punch was water. How much water did she use to make the punch?

Possible Answers:

$\frac{10}{10}$ $\displaystyle \frac{10}{10}$

$\frac{9}{10}$ $\displaystyle \frac{9}{10}$

$\displaystyle 10$

$\displaystyle 9$

$\frac{1}{10}$ $\displaystyle \frac{1}{10}$

Correct answer:

$\frac{9}{10}$ $\displaystyle \frac{9}{10}$

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". $\frac{1}{10}$ $\displaystyle \frac{1}{10}$ of the punch is water.

We know that we have $\displaystyle 9$ gallons of punch so we can set up our multiplication problem.

$\frac{1}{10}\times9$ $\displaystyle \frac{1}{10}\times9$

9 10

$\frac{1}{10}\times9$ $\displaystyle \frac{1}{10}\times9$ which means $\frac{1}{10}$ $\displaystyle \frac{1}{10}$ of each group of $9=\frac{9}{10}$ $\displaystyle 9=\frac{9}{10}$

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Example Question #2981 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Malinda lives $\frac{8}{9}$ $\displaystyle \frac{8}{9}$ 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:

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

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

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

$7\textup { miles}$ $\displaystyle 7\textup { miles}$

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

Correct answer:

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

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

$\frac{1}{3}\times\frac{8}{9}$ $\displaystyle \frac{1}{3}\times\frac{8}{9}$

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.

8 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 $\displaystyle 8$, 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).

$\frac{1}{3}\times\frac{8}{9}=\frac{8}{27}$ $\displaystyle \frac{1}{3}\times\frac{8}{9}=\frac{8}{27}$

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Example Question #301 : Fractions

Eric lives $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ 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 tie his shoe. How far did Eric travel before he stopped to tie his shoe?

Possible Answers:

$1\textup { mile}$ $\displaystyle 1\textup { mile}$

$\frac{1}{12}\textup { of a mile}$ $\displaystyle \frac{1}{12}\textup { of a mile}$

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

$\frac{3}{12}\textup { of a mile}$ $\displaystyle \frac{3}{12}\textup { of a mile}$

$\frac{2}{12}\textup { of a mile}$ $\displaystyle \frac{2}{12}\textup { of a mile}$

Correct answer:

$\frac{2}{12}\textup { of a mile}$ $\displaystyle \frac{2}{12}\textup { of a mile}$

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 $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of a mile away from him so we can set up our multiplication problem.

$\frac{1}{4}\times\frac{2}{3}$ $\displaystyle \frac{1}{4}\times\frac{2}{3}$

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 $\displaystyle 3$ 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).

$\frac{1}{4}\times\frac{2}{3}=\frac{2}{12}$ $\displaystyle \frac{1}{4}\times\frac{2}{3}=\frac{2}{12}$

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Example Question #302 : Fractions

Aaron lives $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ 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 tie his shoe. How far did he travel before he stopped to tie his shoe?

Possible Answers:

$\frac{4}{12}\textup { of a mile}$ $\displaystyle \frac{4}{12}\textup { of a mile}$

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

$\frac{1}{12}\textup { of a mile}$ $\displaystyle \frac{1}{12}\textup { of a mile}$

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

$\frac{3}{12}\textup { of a mile}$ $\displaystyle \frac{3}{12}\textup { of a mile}$

Correct answer:

$\frac{4}{12}\textup { of a mile}$ $\displaystyle \frac{4}{12}\textup { of a mile}$

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 $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of a mile away from him so we can set up our multiplication problem.

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

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 $\displaystyle 3$ 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).

$\frac{2}{4}\times\frac{2}{3}=\frac{4}{12}$ $\displaystyle \frac{2}{4}\times\frac{2}{3}=\frac{4}{12}$

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Example Question #31 : 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 $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ 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 tie his shoe. How far did he travel before he stopped to tie his shoe?

Possible Answers:

$\frac{6}{12}\textup { of a mile}$ $\displaystyle \frac{6}{12}\textup { of a mile}$

$\frac{5}{12}\textup { of a mile}$ $\displaystyle \frac{5}{12}\textup { of a mile}$

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

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

$\frac{7}{12}\textup { of a mile}$ $\displaystyle \frac{7}{12}\textup { of a mile}$

Correct answer:

$\frac{6}{12}\textup { of a mile}$ $\displaystyle \frac{6}{12}\textup { of a mile}$

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 $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ of a mile away from him so we can set up our multiplication problem.

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

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 $\displaystyle 3$ by $\displaystyle 4$ because those are the denominators of our fractions. We shade up $\displaystyle 3$ 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).

$\frac{3}{4}\times\frac{2}{3}=\frac{6}{12}$ $\displaystyle \frac{3}{4}\times\frac{2}{3}=\frac{6}{12}$

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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 $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from his friend's house. He walked $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ 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:

$\frac{4}{20}\textup { of a mile}$ $\displaystyle \frac{4}{20}\textup { of a mile}$

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

$\frac{2}{20}\textup { of a mile}$ $\displaystyle \frac{2}{20}\textup { of a mile}$

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

$\frac{3}{20}\textup { of a mile}$ $\displaystyle \frac{3}{20}\textup { of a mile}$

Correct answer:

$\frac{3}{20}\textup { of a mile}$ $\displaystyle \frac{3}{20}\textup { of a mile}$

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". $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from him so we can set up our multiplication problem.

$\frac{1}{5}\times\frac{3}{4}$ $\displaystyle \frac{1}{5}\times\frac{3}{4}$

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 $\displaystyle 4$ by $\displaystyle 5$ 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).

$\frac{1}{5}\times\frac{3}{4}=\frac{3}{20}$ $\displaystyle \frac{1}{5}\times\frac{3}{4}=\frac{3}{20}$

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Example Question #2981 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Armen lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from his friend's house. He walked $\frac{2}{5}$ $\displaystyle \frac{2}{5}$ 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:

$\frac{7}{20}\textup { of a mile}$ $\displaystyle \frac{7}{20}\textup { of a mile}$

$\frac{6}{20}\textup { of a mile}$ $\displaystyle \frac{6}{20}\textup { of a mile}$

$1\textup { mile}$ $\displaystyle 1\textup { mile}$

$\frac{1}{20}\textup { of a mile}$ $\displaystyle \frac{1}{20}\textup { of a mile}$

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

Correct answer:

$\frac{6}{20}\textup { of a mile}$ $\displaystyle \frac{6}{20}\textup { of a mile}$

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". $\frac{2}{5}$ $\displaystyle \frac{2}{5}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from him so we can set up our multiplication problem.

$\frac{2}{5}\times\frac{3}{4}$ $\displaystyle \frac{2}{5}\times\frac{3}{4}$

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 $\displaystyle 4$ by $\displaystyle 5$ 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).

$\frac{2}{5}\times\frac{3}{4}=\frac{6}{20}$ $\displaystyle \frac{2}{5}\times\frac{3}{4}=\frac{6}{20}$

Report an Error

Example Question #1943 : Numbers And Operations

Brett lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from his friend's house. He walked $\frac{3}{5}$ $\displaystyle \frac{3}{5}$ 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:

$\frac{9}{20}\textup { of a mile}$ $\displaystyle \frac{9}{20}\textup { of a mile}$

$\frac{6}{20}\textup { of a mile}$ $\displaystyle \frac{6}{20}\textup { of a mile}$

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

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

$20\textup { miles}$ $\displaystyle 20\textup { miles}$

Correct answer:

$\frac{9}{20}\textup { of a mile}$ $\displaystyle \frac{9}{20}\textup { of a mile}$

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". $\frac{3}{5}$ $\displaystyle \frac{3}{5}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from him so we can set up our multiplication problem.

$\frac{3}{5}\times\frac{3}{4}$ $\displaystyle \frac{3}{5}\times\frac{3}{4}$

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 $\displaystyle 4$ by $\displaystyle 5$ 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).

$\frac{3}{5}\times\frac{3}{4}=\frac{9}{20}$ $\displaystyle \frac{3}{5}\times\frac{3}{4}=\frac{9}{20}$

Report an Error

Example Question #1944 : Numbers And Operations

Steve lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from his friend's house. He walked $\frac{4}{5}$ $\displaystyle \frac{4}{5}$ 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:

$\frac{7}{20}\textup { of a mile}$ $\displaystyle \frac{7}{20}\textup { of a mile}$

$7\textup { miles}$ $\displaystyle 7\textup { miles}$

$12\textup { miles}$ $\displaystyle 12\textup { miles}$

$\frac{12}{20}\textup { of a mile}$ $\displaystyle \frac{12}{20}\textup { of a mile}$

$\frac{13}{20}\textup { of a mile}$ $\displaystyle \frac{13}{20}\textup { of a mile}$

Correct answer:

$\frac{12}{20}\textup { of a mile}$ $\displaystyle \frac{12}{20}\textup { of a mile}$

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". $\frac{4}{5}$ $\displaystyle \frac{4}{5}$ of the way to his friends house he stopped.

We know that his friend lives $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a mile away from him so we can set up our multiplication problem.

$\frac{4}{5}\times\frac{3}{4}$ $\displaystyle \frac{4}{5}\times\frac{3}{4}$

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 $\displaystyle 4$ by $\displaystyle 5$ because those are the denominators of our fractions. We shade up $\displaystyle 4$ 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).

$\frac{4}{5}\times\frac{3}{4}=\frac{12}{20}$ $\displaystyle \frac{4}{5}\times\frac{3}{4}=\frac{12}{20}$

Report an Error

Example Question #1945 : Numbers And Operations

David lives $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ of a mile away from his friend's house. He walked $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ 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:

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

$\frac{3}{20}\textup { of a mile}$ $\displaystyle \frac{3}{20}\textup { of a mile}$

$\frac{5}{20}\textup { of a mile}$ $\displaystyle \frac{5}{20}\textup { of a mile}$

$\frac{2}{20}\textup { of a mile}$ $\displaystyle \frac{2}{20}\textup { of a mile}$

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

Correct answer:

$\frac{2}{20}\textup { of a mile}$ $\displaystyle \frac{2}{20}\textup { of a mile}$

Explanation:

We know that his friend lives $\frac{2}{4}$ $\displaystyle \frac{2}{4}$ of a mile away from him so we can set up our multiplication problem.

$\frac{1}{5}\times\frac{2}{4}$ $\displaystyle \frac{1}{5}\times\frac{2}{4}$

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.

We make the area model $\displaystyle 4$ by $\displaystyle 5$ 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).

$\frac{1}{5}\times\frac{2}{4}=\frac{2}{20}$ $\displaystyle \frac{1}{5}\times\frac{2}{4}=\frac{2}{20}$

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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 : ISEE Lower Level (grades 5-6) Quantitative Reasoning

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #1151 : Common Core Math: Grade 5

Example Question #2981 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Example Question #301 : Fractions

Example Question #302 : Fractions

Example Question #31 : 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

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

Example Question #2981 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

Example Question #1943 : Numbers And Operations

Example Question #1944 : Numbers And Operations

Example Question #1945 : Numbers And Operations

All ISEE Lower Level Quantitative Resources

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