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Common Core: 5th Grade Math : Common Core Math: Grade 5

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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All Common Core: 5th Grade Math Resources

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

Example Questions

Example Question #851 : Common Core Math: Grade 5

Solve:

$30{\overline{\smash{)}600}}$

Possible Answers:

Correct answer:

Explanation:

Before we begin, let's review the pieces of a division problem:

${\begin{array}[b]{r} \ \textup{ quotient}\\ \textup{ divisor}{\overline{\smash{)}\ \textup{dividend}}}\\\end{array}}{ \ \ \ \space}$

The quotient is the answer to the division problem. The dividend is the number that gets divided by the divisor.

One way to solve a division problem is to create an area model. The divisor equals the number of squares that make up the base of the area model. The dividend equals the number of total squares used. Fill the squares up from the base until you've used the correct number of squares. The height of the area model will be the quotient:

$30\times$ __________ =600

Another way to solve a division problem is to think of it as a multiplication problem. What number times the divisor equals the dividend?

$\frac{\begin{array}[b]{r}30\\ \times \ \ \ 20\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 00}\\ \ +\ {\color{Red} 600} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 600}$

This means that $13\times {\color{Red} 20}=600$ ; thus, ${\begin{array}[b]{r} \ \textup{ {\color{Red} 20}}\\ \textup{ 30}{\overline{\smash{)}\ \textup{600}}}\\\end{array}}{ \ \ \ \space}$

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Example Question #1 : Add, Subtract, Multiply, And Divide Decimals To Hundredths: Ccss.Math.Content.5.Nbt.B.7

$3.04+6.02\times 3-0.16=$

Possible Answers:

27.4

18.3

6.98

20.94

Correct answer:

20.94

Explanation:

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Example Question #1 : Number & Operations With Fractions

$\frac{1}{7}+\frac{3}{14}=$

Possible Answers:

$\frac{5}{14}$

$\frac{4}{14}$

$\frac{9}{14}$

$\frac{2}{7}$

$\frac{5}{7}$

Correct answer:

$\frac{5}{14}$

Explanation:

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Example Question #1 : Number & Operations With Fractions

Mary has a bag of marbles. She gives half of the marbles to her brother and a third of the marbles to her sister. What fraction of the original marbles does Mary have left?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{6}$

Explanation:

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Example Question #74 : How To Add Fractions

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

Possible Answers:

$\frac{4}{12}$

$\frac{3}{7}$

$\frac{4}{5}$

$\frac{9}{10}$

$\frac{7}{10}$

Correct answer:

$\frac{4}{5}$

Explanation:

$\frac{3}{10}+\frac{1}{2}$

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

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

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.

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

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

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

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Example Question #81 : How To Add Fractions

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:

$\frac{5}{9}$

$\frac{1}{3}$

$\frac{12}{21}$

$\frac{11}{24}$

$\frac{2}{11}$

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 #82 : 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:

$\frac{3}9{}$

$\frac{5}{8}$

$\frac{1}{2}$

$\frac{4}{12}$

$\frac{5}{7}$

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 #83 : How To Add Fractions

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:

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

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

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

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

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

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 #84 : How To Add Fractions

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

Possible Answers:

$\frac{5}{8}$

$\frac{2}{5}$

$\frac{2}{3}$

$\frac{5}{12}$

$\frac{5}6{}$

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 #85 : How To Add Fractions

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

Possible Answers:

$\frac{2}{10}$

$\frac{1}{5}$

$\frac{10}{21}$

$\frac{9}{21}$

$\frac{2}{3}$

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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Common Core: 5th Grade Math : Common Core Math: Grade 5

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #851 : Common Core Math: Grade 5

Example Question #1 : Add, Subtract, Multiply, And Divide Decimals To Hundredths: Ccss.Math.Content.5.Nbt.B.7

Example Question #1 : Number & Operations With Fractions

Example Question #1 : Number & Operations With Fractions

Example Question #74 : How To Add Fractions

Example Question #81 : How To Add Fractions

Example Question #82 : How To Add Fractions

Example Question #83 : How To Add Fractions

Example Question #84 : How To Add Fractions

Example Question #85 : How To Add Fractions

All Common Core: 5th Grade Math Resources

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