Common Core: 5th Grade Math : Fluently Divide Multi-Digit Whole Numbers: CCSS.Math.Content.5.NBT.B.6

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

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Example Questions

Example Question #1 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

\(\displaystyle 3828\div 22=\)

Possible Answers:

\(\displaystyle 503\)

\(\displaystyle 356\)

\(\displaystyle 174\)

\(\displaystyle 132\)

\(\displaystyle 96\)

Correct answer:

\(\displaystyle 174\)

Explanation:

 

 

 

Example Question #2 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

\(\displaystyle 13{\overline{\smash{)}143}}\)

Possible Answers:

\(\displaystyle 12\)

\(\displaystyle 10\)

\(\displaystyle 11\)

\(\displaystyle 9\)

\(\displaystyle 13\)

Correct answer:

\(\displaystyle 11\)

Explanation:

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

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

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: 

1

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

\(\displaystyle 13\times\) __________ \(\displaystyle =143\)

\(\displaystyle \frac{\begin{array}[b]{r}13\\ \times \ \ \ 11\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 13}\\ \ +\ {\color{black} 130} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 143}\)

 

This means that \(\displaystyle 13\times {\color{Red} 11}=143\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 11}}\\ \textup{ 13}{\overline{\smash{)}\ \textup{143}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #3 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

\(\displaystyle 21{\overline{\smash{)}357}}\)

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 16\)

\(\displaystyle 17\)

\(\displaystyle 20\)

\(\displaystyle 18\)

Correct answer:

\(\displaystyle 17\)

Explanation:

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

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

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: 

2

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

\(\displaystyle 21\times\) __________ \(\displaystyle =357\)

\(\displaystyle \frac{\begin{array}[b]{r}21\\ \times \ \ \ 17\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 147}\\ \ +\ {\color{black} 210} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 357}\)

This means that \(\displaystyle 21\times {\color{Red} 17}=357\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 17}}\\ \textup{ 21}{\overline{\smash{)}\ \textup{357}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #841 : Common Core Math: Grade 5

Solve:

\(\displaystyle 12{\overline{\smash{)}432}}\)

Possible Answers:

\(\displaystyle 36\)

\(\displaystyle 34\)

\(\displaystyle 33\)

\(\displaystyle 32\)

\(\displaystyle 35\)

Correct answer:

\(\displaystyle 36\)

Explanation:

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

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

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: 

3

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

\(\displaystyle 12\times\) __________ \(\displaystyle =432\)

\(\displaystyle \frac{\begin{array}[b]{r}36\\ \times \ \ \ 12\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 72}\\ \ +\ {\color{black} 360} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 432}\)

This means that \(\displaystyle 12\times {\color{Red} 36}=432\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 36}}\\ \textup{ 12}{\overline{\smash{)}\ \textup{432}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #4 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

\(\displaystyle 33{\overline{\smash{)}759}}\)

Possible Answers:

\(\displaystyle 21\)

\(\displaystyle 25\)

\(\displaystyle 22\)

\(\displaystyle 24\)

\(\displaystyle 23\)

Correct answer:

\(\displaystyle 23\)

Explanation:

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

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

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: 

4

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

\(\displaystyle 33\times\) __________ \(\displaystyle =759\)

\(\displaystyle \frac{\begin{array}[b]{r}33\\ \times \ \ \ 23\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 99}\\ \ +\ {\color{black} 660} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 759}\)

This means that \(\displaystyle 33\times {\color{Red} 23}=759\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 23}}\\ \textup{ 33}{\overline{\smash{)}\ \textup{759}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #2 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

\(\displaystyle 14{\overline{\smash{)}308}}\)

Possible Answers:

\(\displaystyle 26\)

\(\displaystyle 24\)

\(\displaystyle 25\)

\(\displaystyle 23\)

\(\displaystyle 22\)

Correct answer:

\(\displaystyle 22\)

Explanation:

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

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

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: 

5

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

\(\displaystyle 14\times\) __________ \(\displaystyle =308\)

\(\displaystyle \frac{\begin{array}[b]{r}14\\ \times \ \ \ 22\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 28}\\ \ +\ {\color{black} 280} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 308}\)

This means that \(\displaystyle 13\times {\color{Red} 22}=308\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 22}}\\ \textup{ 14}{\overline{\smash{)}\ \textup{308}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #662 : Number & Operations In Base Ten

Solve:

\(\displaystyle 43{\overline{\smash{)}1\textup,505}}\)

Possible Answers:

\(\displaystyle 36\)

\(\displaystyle 34\)

\(\displaystyle 32\)

\(\displaystyle 33\)

\(\displaystyle 35\)

Correct answer:

\(\displaystyle 35\)

Explanation:

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

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

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: 

6

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

\(\displaystyle 43\times\) __________ \(\displaystyle =1,505\)

\(\displaystyle \frac{\begin{array}[b]{r}43\\ \times \ \ \ 35\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 215}\\ \ +\ {\color{black} 1290} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 1505}\)

This means that \(\displaystyle 43\times {\color{Red} 35}=1\textup,505\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 35}}\\ \textup{ 43}{\overline{\smash{)}\ \textup{1\textup,505}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #663 : Number & Operations In Base Ten

Solve:

\(\displaystyle 40{\overline{\smash{)}400}}\)

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 10\)

\(\displaystyle 11\)

\(\displaystyle 12\)

\(\displaystyle 13\)

Correct answer:

\(\displaystyle 10\)

Explanation:

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

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

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: 

7

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

\(\displaystyle 40\times\) __________ \(\displaystyle =400\)

\(\displaystyle \frac{\begin{array}[b]{r}40\\ \times \ \ \ 10\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 00}\\ \ +\ {\color{black} 400} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 400}\) 

This means that \(\displaystyle 40\times {\color{Red} 10}=400\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 10}}\\ \textup{ 40}{\overline{\smash{)}\ \textup{400}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #664 : Number & Operations In Base Ten

Solve:

\(\displaystyle 52{\overline{\smash{)}2\textup,236}}\)

Possible Answers:

\(\displaystyle 46\)

\(\displaystyle 45\)

\(\displaystyle 43\)

\(\displaystyle 42\)

\(\displaystyle 44\)

Correct answer:

\(\displaystyle 43\)

Explanation:

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

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

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: 

8

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

\(\displaystyle 52\times\) __________ \(\displaystyle =2\textup,236\)

\(\displaystyle \frac{\begin{array}[b]{r}52\\ \times \ \ \ 43\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 156}\\ \ +\ {\color{black} 2080} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 2236}\)

This means that \(\displaystyle 52\times {\color{Red} 43}=2\textup,236\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 43}}\\ \textup{ 52}{\overline{\smash{)}\ \textup{2\textup,236}}}\\\end{array}}{ \ \ \ \space}\)

Example Question #665 : Number & Operations In Base Ten

Solve:

\(\displaystyle 56{\overline{\smash{)}952}}\)

Possible Answers:

\(\displaystyle 21\)

\(\displaystyle 17\)

\(\displaystyle 19\)

\(\displaystyle 18\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 17\)

Explanation:

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

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

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: 

9

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

\(\displaystyle 56\times\) __________ \(\displaystyle =952\)

\(\displaystyle \frac{\begin{array}[b]{r}56\\ \times \ \ \ 17\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 392}\\ \ +\ {\color{black} 560} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 952}\) 

This means that \(\displaystyle 56\times {\color{Red} 17}=952\); thus, \(\displaystyle {\begin{array}[b]{r} \ \textup{ {\color{Red} 17}}\\ \textup{ 56}{\overline{\smash{)}\ \textup{952}}}\\\end{array}}{ \ \ \ \space}\)

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