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SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

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All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

Zach cleaned $\frac{1}{8}$ of the house and Alex cleaned $\frac{1}{3}$ of the house. How much of the house did they clean?

Possible Answers:

$\frac{12}{21}$

$\frac{11}{24}$

$\frac{1}{3}$

$\frac{2}{11}$

$\frac{5}{9}$

Correct answer:

$\frac{11}{24}$

Explanation:

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

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

$\frac{1}{8}\times\frac{3}{3}=\frac{3}{24}$

$\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$

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.

$\frac{3}{24}+\frac{8}{24}=\frac{11}{24}$

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Example Question #61 : How To Add Fractions

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

Possible Answers:

$\frac{1}{2}$

$\frac{5}{7}$

$\frac{4}{12}$

$\frac{5}{8}$

$\frac{3}9{}$

Correct answer:

$\frac{5}{8}$

Explanation:

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

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

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

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.

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

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Example Question #4 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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.

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

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

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

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Example Question #1 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

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

Possible Answers:

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{5}6{}$

$\frac{5}{12}$

$\frac{5}{8}$

Correct answer:

$\frac{5}6{}$

Explanation:

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

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

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

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

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.

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

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

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

Possible Answers:

$\frac{2}{3}$

$\frac{2}{10}$

$\frac{9}{21}$

$\frac{1}{5}$

$\frac{10}{21}$

Correct answer:

$\frac{10}{21}$

Explanation:

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

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

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

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

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.

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

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Example Question #861 : Common Core Math: Grade 5

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

Possible Answers:

$\frac{1}{2}$

$\frac{2}{4}$

$\frac{7}{8}$

$\frac{3}{4}$

$\frac{6}{12}$

Correct answer:

$\frac{7}{8}$

Explanation:

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

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

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

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.

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

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Example Question #71 : How To Add Fractions

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

Possible Answers:

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{6}{12}$

$\frac{7}{12}$

$\frac{4}{15}$

Correct answer:

$\frac{7}{12}$

Explanation:

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

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

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

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.

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

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

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

Possible Answers:

$\frac{9}{21}$

$\frac{13}{21}$

$\frac{11}{15}$

$\frac{3}{4}$

$\frac{3}{10}$

Correct answer:

$\frac{13}{21}$

Explanation:

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

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

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

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

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.

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

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Example Question #81 : How To Add Fractions

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

Possible Answers:

$\frac{3}9{}$

$\frac{15}{21}$

$\frac{6}{10}$

$\frac{9}{18}$

$\frac{8}{27}$

Correct answer:

$\frac{9}{18}$

Explanation:

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

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

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

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.

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

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Example Question #1411 : Ssat Middle Level Quantitative (Math)

$\frac{6}{7}+\frac{3}{4}=$

Possible Answers:

$\frac{27}{28}$

$\frac{9}{28}$

$\frac{9}{11}$

$\frac{45}{28}$

$\frac{18}{28}$

Correct answer:

$\frac{45}{28}$

Explanation:

The first step is to find a common denominator between 4 and 7.

The common denominator that both 4 and 7 are mulitples of is 28. So the following procedure is applied to each fraction:

$\frac{6}{7}\times\frac{4}{4}+ \frac{3}{4}\times\frac{7}{7}=\frac{24}{28}+\frac{21}{28}= \frac{45}{28}$

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SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

Example Question #61 : How To Add Fractions

Example Question #4 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

Example Question #1 : Solve Word Problems Involving Addition And Subtraction Of Fractions: Ccss.Math.Content.5.Nf.A.2

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

Example Question #861 : Common Core Math: Grade 5

Example Question #71 : How To Add Fractions

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

Example Question #81 : How To Add Fractions

Example Question #1411 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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