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ISEE Middle Level Quantitative : Numbers and Operations

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

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Number & Operations With Fractions

Ben washed $\frac{3}{8}$ $\displaystyle \frac{3}{8}$ of the windows and Jen washed $\frac{1}{4}$ $\displaystyle \frac{1}{4}$. How much of the windows have they washed?

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

$\frac{5}{7}$ $\displaystyle \frac{5}{7}$

$\frac{3}9{}$ $\displaystyle \frac{3}9{}$

$\frac{4}{12}$ $\displaystyle \frac{4}{12}$

Correct answer:

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

Explanation:

$\frac{3}{8}+\frac{1}{4}$ $\displaystyle \frac{3}{8}+\frac{1}{4}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$ $\displaystyle \frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{3}{8}+\frac{2}8{=\frac{5}{8}}$ $\displaystyle \frac{3}{8}+\frac{2}8{=\frac{5}{8}}$

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Example Question #5 : Number & Operations With Fractions

Jake ate $\frac{1}{7}$ $\displaystyle \frac{1}{7}$ of the popcorn and Dave ate $\small \frac{4}{14}$ $\displaystyle \small \frac{4}{14}$ of the popcorn. How much of the popcorn have they eaten?

Possible Answers:

$\small \frac{5}{21}$ $\displaystyle \small \frac{5}{21}$

$\small \frac{13}{21}$ $\displaystyle \small \frac{13}{21}$

$\small \frac{2}{3}$ $\displaystyle \small \frac{2}{3}$

$\small \frac{3}{7}$ $\displaystyle \small \frac{3}{7}$

$\small \frac{5}{7}$ $\displaystyle \small \frac{5}{7}$

Correct answer:

$\small \frac{3}{7}$ $\displaystyle \small \frac{3}{7}$

Explanation:

$\small \frac{1}{7}+\frac{4}{14}$ $\displaystyle \small \frac{1}{7}+\frac{4}{14}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{7}\times\frac{2}{2}=\frac{2}{14}$ $\displaystyle \frac{1}{7}\times\frac{2}{2}=\frac{2}{14}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\small \frac{2}{14}+\frac{4}{14}=\frac{6}{14}$ $\displaystyle \small \frac{2}{14}+\frac{4}{14}=\frac{6}{14}$

$\small \frac{6}{14}$ $\displaystyle \small \frac{6}{14}$ can be reduced by dividing $\small 2$ $\displaystyle \small 2$ by both sides.

$\small \frac{6}{14}\div\frac{2}{2}=\frac{3}{7}$ $\displaystyle \small \frac{6}{14}\div\frac{2}{2}=\frac{3}{7}$

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Example Question #6 : Number & Operations With Fractions

Jessica ate $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the cake and Megan ate $\frac{1}{2}$ $\displaystyle \frac{1}{2}$. How much of the cake have they eaten?

Possible Answers:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

$\frac{5}6{}$ $\displaystyle \frac{5}6{}$

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

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

Correct answer:

$\frac{5}6{}$ $\displaystyle \frac{5}6{}$

Explanation:

$\frac{1}{3}+\frac{1}2{}$ $\displaystyle \frac{1}{3}+\frac{1}2{}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}3{\times\frac{2}{2}=\frac{2}{6}}$ $\displaystyle \frac{1}3{\times\frac{2}{2}=\frac{2}{6}}$

$\frac{1}{2}\times\frac{3}{3}=\frac{3}{6}$ $\displaystyle \frac{1}{2}\times\frac{3}{3}=\frac{3}{6}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

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

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Example Question #7 : Number & Operations With Fractions

Tim mowed $\frac{1}{7}$ $\displaystyle \frac{1}{7}$ of the yard and Tom mowed $\frac{1}{3}$ $\displaystyle \frac{1}{3}$. How much of the yard have they mowed?

Possible Answers:

$\frac{2}{10}$ $\displaystyle \frac{2}{10}$

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

$\frac{9}{21}$ $\displaystyle \frac{9}{21}$

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

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

Correct answer:

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

Explanation:

$\frac{1}{7}+\frac{1}{3}$ $\displaystyle \frac{1}{7}+\frac{1}{3}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$ $\displaystyle \frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$

$\frac{1}{3}\times \frac{7}{7}=\frac{7}{21}$ $\displaystyle \frac{1}{3}\times \frac{7}{7}=\frac{7}{21}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{3}{21}+\frac{7}{21}=\frac{10}{21}$ $\displaystyle \frac{3}{21}+\frac{7}{21}=\frac{10}{21}$

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Example Question #81 : Numbers And Operations

Shannon has painted $\frac{5}{8}$ $\displaystyle \frac{5}{8}$ of the house and Dan has paided $\frac{1}4{}$ $\displaystyle \frac{1}4{}$ of the house. How much of the house is painted?

Possible Answers:

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

$\frac{7}{8}$ $\displaystyle \frac{7}{8}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

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

$\frac{6}{12}$ $\displaystyle \frac{6}{12}$

Correct answer:

$\frac{7}{8}$ $\displaystyle \frac{7}{8}$

Explanation:

$\frac{5}{8}+\frac{1}{4}$ $\displaystyle \frac{5}{8}+\frac{1}{4}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$ $\displaystyle \frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{5}{8}+\frac{2}{8}=\frac{7}{8}$ $\displaystyle \frac{5}{8}+\frac{2}{8}=\frac{7}{8}$

Report an Error

Example Question #82 : Numbers And Operations

David ate $\frac{3}{12}$ $\displaystyle \frac{3}{12}$ of the pizza and Alison ate $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the pizza. How much of the pizza did they eat?

Possible Answers:

$\frac{4}{15}$ $\displaystyle \frac{4}{15}$

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

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

$\frac{6}{12}$ $\displaystyle \frac{6}{12}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

Explanation:

$\frac{3}{12}+\frac{1}{3}$ $\displaystyle \frac{3}{12}+\frac{1}{3}$

In order to solve this problem, we first need to make common denominators.

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

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{3}{12}+\frac{4}{12}=\frac{7}{12}$ $\displaystyle \frac{3}{12}+\frac{4}{12}=\frac{7}{12}$

Report an Error

Example Question #2 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

Laura ate $\frac{2}{7}$ $\displaystyle \frac{2}{7}$ of the ice cream and Drew ate $\frac{1}{3}$ $\displaystyle \frac{1}{3}$. How much of the ice cream did they eat?

Possible Answers:

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

$\frac{9}{21}$ $\displaystyle \frac{9}{21}$

$\frac{13}{21}$ $\displaystyle \frac{13}{21}$

$\frac{11}{15}$ $\displaystyle \frac{11}{15}$

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

Correct answer:

$\frac{13}{21}$ $\displaystyle \frac{13}{21}$

Explanation:

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

In order to solve this problem, we first need to make common denominators.

$\frac{2}{7}\times\frac{3}{3}=\frac{6}{21}$ $\displaystyle \frac{2}{7}\times\frac{3}{3}=\frac{6}{21}$

$\frac{1}{3}\times\frac{7}{7}=\frac{7}{21}$ $\displaystyle \frac{1}{3}\times\frac{7}{7}=\frac{7}{21}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{6}{21}+\frac{7}{21}=\frac{13}{21}$ $\displaystyle \frac{6}{21}+\frac{7}{21}=\frac{13}{21}$

Report an Error

Example Question #83 : Numbers And Operations

Kara ate $\frac{7}{18}$ $\displaystyle \frac{7}{18}$ of the bag of chips and Andrew ate $\frac{1}{9}$ $\displaystyle \frac{1}{9}$. How much of the bag of chips did they eat?

Possible Answers:

$\frac{15}{21}$ $\displaystyle \frac{15}{21}$

$\frac{3}9{}$ $\displaystyle \frac{3}9{}$

$\frac{9}{18}$ $\displaystyle \frac{9}{18}$

$\frac{8}{27}$ $\displaystyle \frac{8}{27}$

$\frac{6}{10}$ $\displaystyle \frac{6}{10}$

Correct answer:

$\frac{9}{18}$ $\displaystyle \frac{9}{18}$

Explanation:

$\frac{7}{18}+\frac{1}{9}$ $\displaystyle \frac{7}{18}+\frac{1}{9}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{9}\times \frac{2}{2}=\frac{2}{18}$ $\displaystyle \frac{1}{9}\times \frac{2}{2}=\frac{2}{18}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{7}{18}+\frac{2}{18}=\frac{9}{18}$ $\displaystyle \frac{7}{18}+\frac{2}{18}=\frac{9}{18}$

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Example Question #84 : Numbers And Operations

Sally drank $\frac{1}{12}$ $\displaystyle \frac{1}{12}$ of the milk and Sam drank $\frac{2}{3}$ $\displaystyle \frac{2}{3}$. What fraction of the milk did they drink?

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{5}{7}$ $\displaystyle \frac{5}{7}$

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

$\frac{3}{15}$ $\displaystyle \frac{3}{15}$

$\frac{11}{15}$ $\displaystyle \frac{11}{15}$

Correct answer:

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

Explanation:

$\frac{1}{12}+\frac{2}{3}$ $\displaystyle \frac{1}{12}+\frac{2}{3}$

In order to solve this problem, we first need to make common denominators.

$\frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$ $\displaystyle \frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{1}{12}+\frac{8}{12}=\frac{9}{12}$ $\displaystyle \frac{1}{12}+\frac{8}{12}=\frac{9}{12}$

$\frac{9}{12}$ $\displaystyle \frac{9}{12}$ can be reduced by dividing $\displaystyle 3$ by both sides.

$\frac{9}{12}\div \frac{3}{3}=\frac{3}{4}$ $\displaystyle \frac{9}{12}\div \frac{3}{3}=\frac{3}{4}$

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Example Question #85 : Numbers And Operations

Lily pulled $\frac{1}{9}$ $\displaystyle \frac{1}{9}$ of the weeds and Rose pulled $\frac{1}{3}$ $\displaystyle \frac{1}{3}$. What fraction of the weeds have they pulled?

Possible Answers:

$\frac{2}{12}$ $\displaystyle \frac{2}{12}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{8}{15}$ $\displaystyle \frac{8}{15}$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

Correct answer:

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Explanation:

$\frac{1}{9}+\frac{1}{3}$ $\displaystyle \frac{1}{9}+\frac{1}{3}$

In order to solve this problem, we first need to make common denominators.

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

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{1}{9}+\frac{3}{9}=\frac{4}{9}$ $\displaystyle \frac{1}{9}+\frac{3}{9}=\frac{4}{9}$

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

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ISEE Middle Level Quantitative : Numbers and Operations

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #4 : Number & Operations With Fractions

Example Question #5 : Number & Operations With Fractions

Example Question #6 : Number & Operations With Fractions

Example Question #7 : Number & Operations With Fractions

Example Question #81 : Numbers And Operations

Example Question #82 : Numbers And Operations

Example Question #2 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

Example Question #83 : Numbers And Operations

Example Question #84 : Numbers And Operations

Example Question #85 : Numbers And Operations

All ISEE Middle Level Quantitative Resources

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