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Common Core: 5th Grade Math : Number & Operations in Base Ten

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 #521 : Number & Operations In Base Ten

Round 729.487 to the nearest tenth.

Possible Answers:

729.4

730

729.5

729.49

729.3

Correct answer:

729.5

Explanation:

When we round a number to the nearest tenth we look to the hundredths place to tell us if we round up or down.

$729.4{\color{Blue} 8}7$

If the number in our hundredths place is or greater, we round up. If the number in the hundredths place is or less, we round down. When we round up, the number in the hundredths place increases by and all the other numbers to the right become . When we round down, the number in the hundredths place stays the same and all the other numbers to the right become .

In this case, is greater than so our rounded number is 729.500 or 729.5

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Example Question #82 : Round Decimals: Ccss.Math.Content.5.Nbt.A.4

Round 444.376 to the nearest tenth.

Possible Answers:

444.4

444.38

444.37

444.3

440

Correct answer:

444.4

Explanation:

When we round a number to the nearest tenth we look to the hundredths place to tell us if we round up or down.

$444.3{\color{Blue} 7}6$

In this case, is greater than so our rounded number is 444.400 or 444.4

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Example Question #522 : Number & Operations In Base Ten

$45\times 5=$

$36\times 3=$

Possible Answers:

$45\times5=220,\ 36\times3=118$

$45\times5=215,\ 36\times3=109$

$45\times5=215,\ 36\times3=108$

$45\times5=225,\ 36\times3=108$

$45\times5=225,\ 36\times3=208$

Correct answer:

$45\times5=225,\ 36\times3=108$

Explanation:

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Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

$\frac{\begin{array}[b]{r}1 3\\ \times\ 11\end{array}}{\ \ \ \ }$

Possible Answers:

113

164

133

143

130

Correct answer:

143

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 3}\\ \times\ {1\color{Red} 1}\end{array}}{\ \ \ \ \ 3}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}3\\ \times\ {1\color{Red} 1}\end{array}}{\ \ \ 13}$

Now, we multiply the digit in the tens place of the multiplier by each digit of the multiplicand. In order to do this, we need to start a new line in our math problem and put a as a place holder in the ones position.

$\frac{\begin{array}[b]{r}1 3\\ \times\ 11\end{array}}{\ \ \ 13 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}1 {\color{Red} 3}\\ \times\ {\color{Red} 1}1\end{array}}{\ \ \ 13 }\\ {\ \ \ \ \ \ \ \ \ 30}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1} {\color{Black} 3}\\ \times\ {\color{Red} 1}1\end{array}}{\ \ \ 13 }\\ {\ \ \ \ \ \ \ \ 1 30}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}13\\ \times \ \ \ 11\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 13}\\ \ +\ {\color{Red} 130} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 143}$

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Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

$\frac{\begin{array}[b]{r}21\\ \times\ 17\end{array}}{\ \ \ \ }$

Possible Answers:

147

210

432

357

257

Correct answer:

357

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}2{\color{Red} 1}\\ \times\ {1\color{Red} 7}\end{array}}{\ \ \ \ \ 7}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 2}1\\ \times\ {1\color{Red} 7}\end{array}}{\ \ 147}$

$\frac{\begin{array}[b]{r}21\\ \times\ 17\end{array}}{\ \ 147 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}2 {\color{Red} 1}\\ \times\ {\color{Red} 1}7\end{array}}{\ \ 147 }\\ {\ \ \ \ \ \ \ \ \ \ 10}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 2} {\color{Black} 1}\\ \times\ {\color{Red} 1}7\end{array}}{\ \ 147 }\\ {\ \ \ \ \ \ \ \ 210}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}21\\ \times \ \ \ 17\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 147}\\ \ +\ {\color{Red} 210} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 357}$

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Example Question #3 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

$\frac{\begin{array}[b]{r}3 6\\ \times\ 12\end{array}}{\ \ \ \ }$

Possible Answers:

486

660

256

512

432

Correct answer:

432

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}^13{\color{Red} 6}\\ \times\ {1\color{Red} 2}\end{array}}{\ \ \ \ \ 2}$

Then, we multiply and and add the that was carried

$\frac{\begin{array}[b]{r}^{\color{Red} 1}{\color{Red} 3}6\\ \times\ {1\color{Red} 2}\end{array}}{\ \ \ \ 72}$

$\frac{\begin{array}[b]{r}3 6\\ \times\ 12\end{array}}{\ \ \ 72 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}3 {\color{Red} 6}\\ \times\ {\color{Red} 1}2\end{array}}{\ \ \ 72 }\\ {\ \ \ \ \ \ \ \ \ 60}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 3} {\color{Black} 6}\\ \times\ {\color{Red} 1}2\end{array}}{\ \ \ 72 }\\ {\ \ \ \ \ \ \ \ 360}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}36\\ \times \ \ \ 12\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 72}\\ \ +\ {\color{Red} 360} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 432}$

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Example Question #4 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

$\frac{\begin{array}[b]{r}3 3\\ \times\ 23\end{array}}{\ \ \ \ }$

Possible Answers:

554

627

834

759

960

Correct answer:

759

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}3{\color{Red} 3}\\ \times\ {2\color{Red} 3}\end{array}}{\ \ \ \ \ 9}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 3}3\\ \times\ {2\color{Red} 3}\end{array}}{\ \ \ 99}$

$\frac{\begin{array}[b]{r}3 3\\ \times\ 23\end{array}}{\ \ \ 99 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}3 {\color{Red} 3}\\ \times\ {\color{Red} 2}3\end{array}}{\ \ \ 99 }\\ {\ \ \ \ \ \ \ \ \ 60}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 3} {\color{Black} 3}\\ \times\ {\color{Red} 2}3\end{array}}{\ \ \ 99 }\\ {\ \ \ \ \ \ \ \ 660}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}33\\ \times \ \ \ 23\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 99}\\ \ +\ {\color{Red} 660} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 759}$

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Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

$\frac{\begin{array}[b]{r}14\\ \times\ 22\end{array}}{\ \ \ \ }$

Possible Answers:

432

226

396

308

476

Correct answer:

308

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 4}\\ \times\ {2\color{Red} 2}\end{array}}{\ \ \ \ \ 8}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}4\\ \times\ {2\color{Red} 2}\end{array}}{\ \ \ 28}$

$\frac{\begin{array}[b]{r}1 4\\ \times\ 22\end{array}}{\ \ \ 28 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}1 {\color{Red} 4}\\ \times\ {\color{Red} 2}2\end{array}}{\ \ \ 28 }\\ {\ \ \ \ \ \ \ \ \ 80}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1} {\color{Black} 4}\\ \times\ {\color{Red} 2}2\end{array}}{\ \ \ 28 }\\ {\ \ \ \ \ \ \ \ 280}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}14\\ \times \ \ \ 22\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 28}\\ \ +\ {\color{Red} 280} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 308}$

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Example Question #23 : How To Multiply

Solve:

$\frac{\begin{array}[b]{r}43\\ \times\ 35\end{array}}{\ \ \ \ }$

Possible Answers:

932

$1\textup,505$

804

876

985

Correct answer:

$1\textup,505$

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}^14{\color{Red} 3}\\ \times\ {3\color{Red} 5}\end{array}}{\ \ \ \ \ 5}$

Then, we multiply and and add the that was carried

$\frac{\begin{array}[b]{r}^{\color{Red} 1}{\color{Red} 4}3\\ \times\ {3\color{Red} 5}\end{array}}{\ \ \ 215}$

$\frac{\begin{array}[b]{r}43\\ \times\ 35\end{array}}{\ \ \ 215 }\\ {\ \ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}4 {\color{Red} 3}\\ \times\ {\color{Red} 3}5\end{array}}{\ \ \ 215 }\\ {\ \ \ \ \ \ \ \ \ \ 90}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 4} {\color{Black} 3}\\ \times\ {\color{Red} 3}5\end{array}}{\ \ \ 215 }\\ {\ \ \ \ \ \ \ 1290}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}43\\ \times \ \ \ 35\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 215}\\ \ +\ {\color{Red} 1290} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 1505}$

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Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

$\frac{\begin{array}[b]{r}40\\ \times\ 10\end{array}}{\ \ \ \ }$

Possible Answers:

420

440

410

444

400

Correct answer:

400

Explanation:

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}4{\color{Red} 0}\\ \times\ {1\color{Red} 0}\end{array}}{\ \ \ \ \ 0}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red}4}0\\ \times\ {1\color{Red} 0}\end{array}}{\ \ \ 00}$

$\frac{\begin{array}[b]{r}40\\ \times\ 10\end{array}}{\ \ \ 00 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}4 {\color{Red} 0}\\ \times\ {\color{Red} 1}0\end{array}}{\ \ \ \ 00 }\\ {\ \ \ \ \ \ \ \ \ \ 00}$

Then, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 4} {\color{Black} 0}\\ \times\ {\color{Red} 1}0\end{array}}{\ \ \ \ 00 }\\ {\ \ \ \ \ \ \ \ 400}$

Finally, we add the two products together to find our final answer

$\frac{\begin{array}[b]{r}40\\ \times \ \ \ 10\end{array}}{\frac{\begin{array}[b]{r}{\color{Red} 00}\\ \ +\ {\color{Red} 400} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 400}$

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All Common Core: 5th Grade Math Resources

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Common Core: 5th Grade Math : Number & Operations in Base Ten

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

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #521 : Number & Operations In Base Ten

Example Question #82 : Round Decimals: Ccss.Math.Content.5.Nbt.A.4

Example Question #522 : Number & Operations In Base Ten

Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #3 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #4 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #23 : How To Multiply

Example Question #2 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

All Common Core: 5th Grade Math Resources

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