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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 #11 : Subtract Fractions With Unlike Denominators

Solve:

$\frac{2}{3}-\frac{3}{5}$ $\displaystyle \frac{2}{3}-\frac{3}{5}$

Possible Answers:

$\frac{5}{15}$ $\displaystyle \frac{5}{15}$

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

$\frac{1}{30}$ $\displaystyle \frac{1}{30}$

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

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

Correct answer:

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

Explanation:

$\frac{2}{3}-\frac{3}{5}$ $\displaystyle \frac{2}{3}-\frac{3}{5}$

In order to solve this problem, we first have to find common denominators.

$\frac{2}{3}\times\frac{5}{5}=\frac{10}{15}$ $\displaystyle \frac{2}{3}\times\frac{5}{5}=\frac{10}{15}$

$\frac{3}{5}\times \frac{3}{3}=\frac{9}{15}$ $\displaystyle \frac{3}{5}\times \frac{3}{3}=\frac{9}{15}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{10}{15}-\frac{9}{15}=\frac{1}{15}$ $\displaystyle \frac{10}{15}-\frac{9}{15}=\frac{1}{15}$

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Example Question #61 : How To Subtract Fractions

Solve:

$\frac{7}{8}-\frac{3}{16}$ $\displaystyle \frac{7}{8}-\frac{3}{16}$

Possible Answers:

$\frac{4}{8}$ $\displaystyle \frac{4}{8}$

$\frac{11}{16}$ $\displaystyle \frac{11}{16}$

$\frac{13}{16}$ $\displaystyle \frac{13}{16}$

$\frac{4}{16}$ $\displaystyle \frac{4}{16}$

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

Correct answer:

$\frac{11}{16}$ $\displaystyle \frac{11}{16}$

Explanation:

$\frac{7}{8}-\frac{3}{16}$ $\displaystyle \frac{7}{8}-\frac{3}{16}$

In order to solve this problem, we first have to find common denominators.

$\frac{7}{8}\times\frac{2}{2}=\frac{14}{16}$ $\displaystyle \frac{7}{8}\times\frac{2}{2}=\frac{14}{16}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{14}{16}-\frac{3}{16}=\frac{11}{16}$ $\displaystyle \frac{14}{16}-\frac{3}{16}=\frac{11}{16}$

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Example Question #911 : 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 more of the pizza did Alison eat?

Possible Answers:

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

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

$\frac{9}{11}$ $\displaystyle \frac{9}{11}$

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

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

Correct answer:

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

Explanation:

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

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

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

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Example Question #111 : How To Subtract Fractions

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

Possible Answers:

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

$\frac{9}{11}$ $\displaystyle \frac{9}{11}$

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

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

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

Correct answer:

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

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

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Example Question #64 : How To Subtract 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 more of the yard did Tom mow?

Possible Answers:

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

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

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

$\frac{4}{21}$ $\displaystyle \frac{4}{21}$

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

Correct answer:

$\frac{4}{21}$ $\displaystyle \frac{4}{21}$

Explanation:

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

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{7}{21}-\frac{3}{21}=\frac{4}{21}$ $\displaystyle \frac{7}{21}-\frac{3}{21}=\frac{4}{21}$

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Example Question #11 : 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 more of the cake did Megan eat?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

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

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Example Question #12 : Number & Operations With Fractions

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 more of the bag of chips did Kara eat?

Possible Answers:

$\frac{9}{13}$ $\displaystyle \frac{9}{13}$

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

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

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

$\frac{5}{18}$ $\displaystyle \frac{5}{18}$

Correct answer:

$\frac{5}{18}$ $\displaystyle \frac{5}{18}$

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{7}{18}-\frac{2}{18}=\frac{5}{18}$ $\displaystyle \frac{7}{18}-\frac{2}{18}=\frac{5}{18}$

Report an Error

Example Question #67 : How To Subtract Fractions

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 more of the ice cream did Drew eat?

Possible Answers:

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

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

$\frac{1}{21}$ $\displaystyle \frac{1}{21}$

$\frac{9}{11}$ $\displaystyle \frac{9}{11}$

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

Correct answer:

$\frac{1}{21}$ $\displaystyle \frac{1}{21}$

Explanation:

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

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{7}{21}-\frac{6}{21}=\frac{1}{21}$ $\displaystyle \frac{7}{21}-\frac{6}{21}=\frac{1}{21}$

Report an Error

Example Question #13 : Number & Operations With Fractions

Joe paited $\frac{3}{10}$ $\displaystyle \frac{3}{10}$ of the fence an Sara painted $\frac{1}{2}$ $\displaystyle \frac{1}{2}$. How much more of the fence did Sara paint?

Possible Answers:

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

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

$\frac{7}{11}$ $\displaystyle \frac{7}{11}$

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

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

Correct answer:

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

Explanation:

$\frac{1}{2}-\frac{3}{10}$ $\displaystyle \frac{1}{2}-\frac{3}{10}$

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

$\frac{1}{2}\times\frac{5}{5}=\frac{5}{10}$ $\displaystyle \frac{1}{2}\times\frac{5}{5}=\frac{5}{10}$

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

$\frac{5}{10}-\frac{3}{10 }=\frac{2}{10}$ $\displaystyle \frac{5}{10}-\frac{3}{10 }=\frac{2}{10}$

$\frac{2}{10}$ $\displaystyle \frac{2}{10}$ can be reduced be dividing both sides by $\displaystyle 2$.

$\frac{2}{10} \div\frac{2}{2}=\frac{1}{5}$ $\displaystyle \frac{2}{10} \div\frac{2}{2}=\frac{1}{5}$

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Example Question #69 : How To Subtract Fractions

Ben washed $\frac{3}{8}$ $\displaystyle \frac{3}{8}$ of the windows and Jen washed $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of them. How much more of the windows did Ben wash?

Possible Answers:

$\frac{1}8{}$ $\displaystyle \frac{1}8{}$

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

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

$\frac{7}9{}$ $\displaystyle \frac{7}9{}$

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

Correct answer:

$\frac{1}8{}$ $\displaystyle \frac{1}8{}$

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 subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{3}{8}-\frac{2}8{=\frac{1}{8}}$ $\displaystyle \frac{3}{8}-\frac{2}8{=\frac{1}{8}}$

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All ISEE Middle Level Quantitative Resources

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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 #11 : Subtract Fractions With Unlike Denominators

Example Question #61 : How To Subtract Fractions

Example Question #911 : Numbers And Operations

Example Question #111 : How To Subtract Fractions

Example Question #64 : How To Subtract Fractions

Example Question #11 : Number & Operations With Fractions

Example Question #12 : Number & Operations With Fractions

Example Question #67 : How To Subtract Fractions

Example Question #13 : Number & Operations With Fractions

Example Question #69 : How To Subtract Fractions

All ISEE Middle Level Quantitative Resources

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