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ISEE Lower Level Quantitative : Numbers and Operations

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 #331 : Fractions

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

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

$\frac{6}{26}\textup{ of a mile}$

$\frac{1}{27}\textup{ of a mile}$

$\frac{5}{27}\textup{ of a mile}$

$\frac{5}{26}\textup{ of a mile}$

Correct answer:

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

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

We know that her friend lives $\frac{3}{9}$ of a mile away from her so we can set up our multiplication problem.

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

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.

6 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).

$\frac{2}{3}\times\frac{3}{9}=\frac{6}{27}$

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Example Question #332 : Fractions

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

$\frac{4}{26}\text{ of a mile}$

$\frac{4}{27}\text{ of a mile}$

$\frac{5}{26}\text{ of a mile}$

$\frac{3}{26}\text{ of a mile}$

$\frac{3}{27}\text{ of a mile}$

Correct answer:

$\frac{3}{27}\text{ of a mile}$

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

We know that her friend lives $\frac{3}{9}$ of a mile away from her so we can set up our multiplication problem.

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

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.

3 27

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

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Example Question #1 : Adding Mixed Numbers

$4\frac{1}{5}+1\frac{1}{5}$

Possible Answers:

$5\frac{2}{5}$

$5\frac{1}{5}$

$5\frac{2}{10}$

$5\frac{1}{10}$

$5\frac{3}{10}$

Correct answer:

$5\frac{2}{5}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

4+1=5

$\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

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Example Question #2 : Adding Mixed Numbers

$2\frac{5}{10}+5\frac{3}{10}$

Possible Answers:

$7\frac{9}{10}$

$7\frac{3}{5}$

$7\frac{7}{10}$

$7\frac{4}{5}$

$7\frac{3}6{}$

Correct answer:

$7\frac{4}{5}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

2+5=7

$\frac{5}{10}+\frac{3}{10}=\frac{8}{10}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

$\frac{8}{10}$ can be reduced by dividing to both sides.

$\frac{8}{10}\div\frac{2}{2}=\frac{4}{5}$

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Example Question #3 : Adding Mixed Numbers

$3\frac{1}{5}+8\frac{2}{5}$

Possible Answers:

$11\frac{3}{5}$

$11\frac{4}{10}$

$11\frac{3}{10}$

$11\frac{4}{5}$

Correct answer:

$11\frac{3}{5}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

3+8=11

$\frac{1}{5}+\frac{2}{5}=\frac{3}{5}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

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Example Question #4 : Adding Mixed Numbers

Solve:

$6\frac{4}{10}+5\frac{5}{10}$

Possible Answers:

$11\frac{4}{5}$

$11\frac{8}{20}$

$11\frac{9}{20}$

$11\frac{8}{10}$

$11\frac{9}{10}$

Correct answer:

$11\frac{9}{10}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

6+5=11

$\frac{4}{10}+\frac{5}{10}=\frac{9}{10}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

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Example Question #5 : Add And Subtract Mixed Numbers With Like Denominators: Ccss.Math.Content.4.Nf.B.3c

$2\frac{3}{7}+9\frac{1}{7}$

Possible Answers:

$11\frac{4}{7}$

$11\frac{3}{14}$

$11\frac{3}{7}$

$11\frac{4}{14}$

Correct answer:

$11\frac{4}{7}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

2+9=11

$\frac{3}{7}+\frac{1}{7}=\frac{4}{7}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

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Example Question #5 : Adding Mixed Numbers

$5\frac{3}{6}+8\frac{2}{6}$

Possible Answers:

$13\frac{5}{12}$

$13\frac{5}{6}$

$13\frac{1}{2}$

$13\frac{3}{6}$

Correct answer:

$13\frac{5}{6}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

5+8=13

$\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

Report an Error

Example Question #6 : Adding Mixed Numbers

$6\frac{1}{7}+6\frac{1}{7}$

Possible Answers:

$12\frac{2}{7}$

$6\frac{2}{14}$

$12\frac{2}{14}$

$6\frac{2}{7}$

Correct answer:

$12\frac{2}{7}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

6+6=12

$\frac{1}{7}+\frac{1}{7}=\frac{2}{7}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

Report an Error

Example Question #7 : Adding Mixed Numbers

$7\frac{1}{8}+5\frac{2}{8}$

Possible Answers:

$12\frac{3}{16}$

$12\frac{4}{16}$

$12\frac{4}{8}$

$12\frac{5}{8}$

$12\frac{3}{8}$

Correct answer:

$12\frac{3}{8}$

Explanation:

When we add mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

7+5=12

$\frac{1}{8}+\frac{2}{8}=\frac{3}{8}$

Remember, when we are adding fractions we must have common denominators and we only add the numerators.

Report an Error

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Numbers and Operations

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #331 : Fractions

Example Question #332 : Fractions

Example Question #1 : Adding Mixed Numbers

Example Question #2 : Adding Mixed Numbers

Example Question #3 : Adding Mixed Numbers

Example Question #4 : Adding Mixed Numbers

Example Question #5 : Add And Subtract Mixed Numbers With Like Denominators: Ccss.Math.Content.4.Nf.B.3c

Example Question #5 : Adding Mixed Numbers

Example Question #6 : Adding Mixed Numbers

Example Question #7 : Adding Mixed Numbers

All ISEE Lower Level Quantitative Resources

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