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

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

varsity tutors app store varsity tutors android store

Example Questions

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

\(\displaystyle 45\times 5=\)

\(\displaystyle 36\times 3=\)

Possible Answers:

\(\displaystyle 45\times5=225,\ 36\times3=108\)

\(\displaystyle 45\times5=215,\ 36\times3=108\)

\(\displaystyle 45\times5=225,\ 36\times3=208\)

\(\displaystyle 45\times5=220,\ 36\times3=118\)

\(\displaystyle 45\times5=215,\ 36\times3=109\)

Correct answer:

\(\displaystyle 45\times5=225,\ 36\times3=108\)

Explanation:

 

 

 

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

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}1 3\\ \times\ 11\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 164\)

\(\displaystyle 130\)

\(\displaystyle 113\)

\(\displaystyle 133\)

\(\displaystyle 143\)

Correct answer:

\(\displaystyle 143\)

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.

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

For this problem, \(\displaystyle 11\) is the multiplier and \(\displaystyle 13\) 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 \(\displaystyle 1\) and \(\displaystyle 3\)

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

Then, we multiply \(\displaystyle 1\) and \(\displaystyle 1\)

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 1\) and \(\displaystyle 3\)

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

Then, we multiply \(\displaystyle 1\) and \(\displaystyle 1\)

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

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

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

 

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

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}21\\ \times\ 17\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 257\)

\(\displaystyle 147\)

\(\displaystyle 210\)

\(\displaystyle 432\)

\(\displaystyle 357\)

Correct answer:

\(\displaystyle 357\)

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.

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

For this problem, \(\displaystyle 17\) is the multiplier and \(\displaystyle 21\) 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 \(\displaystyle 7\) and \(\displaystyle 1\)

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

Then, we multiply \(\displaystyle 7\) and \(\displaystyle 2\)

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 1\) and \(\displaystyle 1\)

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

Then, we multiply \(\displaystyle 1\) and \(\displaystyle 2\)

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

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

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

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

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}3 6\\ \times\ 12\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 256\)

\(\displaystyle 660\)

\(\displaystyle 486\)

\(\displaystyle 512\)

\(\displaystyle 432\)

Correct answer:

\(\displaystyle 432\)

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.

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

For this problem, \(\displaystyle 12\) is the multiplier and \(\displaystyle 36\) 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 \(\displaystyle 2\) and \(\displaystyle 6\)

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

Then, we multiply \(\displaystyle 2\) and \(\displaystyle 3\) and add the \(\displaystyle 1\) that was carried

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 1\) and \(\displaystyle 6\)

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

Then, we multiply \(\displaystyle 1\) and \(\displaystyle 3\)

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

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

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

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

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}3 3\\ \times\ 23\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 834\)

\(\displaystyle 627\)

\(\displaystyle 554\)

\(\displaystyle 759\)

\(\displaystyle 960\)

Correct answer:

\(\displaystyle 759\)

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.

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

For this problem, \(\displaystyle 23\) is the multiplier and \(\displaystyle 33\) 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 \(\displaystyle 3\) and \(\displaystyle 3\)

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

Then, we multiply \(\displaystyle 3\) and \(\displaystyle 3\)

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 2\) and \(\displaystyle 3\)

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

Then, we multiply \(\displaystyle 2\) and \(\displaystyle 3\)

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

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

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

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

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}14\\ \times\ 22\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 308\)

\(\displaystyle 396\)

\(\displaystyle 432\)

\(\displaystyle 226\)

\(\displaystyle 476\)

Correct answer:

\(\displaystyle 308\)

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.

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

For this problem, \(\displaystyle 14\) is the multiplier and \(\displaystyle 22\) 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 \(\displaystyle 2\) and \(\displaystyle 4\)

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

Then, we multiply \(\displaystyle 2\) and \(\displaystyle 1\)

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 2\) and \(\displaystyle 4\)

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

Then, we multiply \(\displaystyle 2\) and \(\displaystyle 1\)

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

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

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

Example Question #712 : Common Core Math: Grade 5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}43\\ \times\ 35\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 985\)

\(\displaystyle 932\)

\(\displaystyle 1\textup,505\)

\(\displaystyle 804\)

\(\displaystyle 876\)

Correct answer:

\(\displaystyle 1\textup,505\)

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.

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

For this problem, \(\displaystyle 35\) is the multiplier and \(\displaystyle 43\) 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 \(\displaystyle 5\) and \(\displaystyle 3\)

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

Then, we multiply \(\displaystyle 5\) and \(\displaystyle 4\) and add the \(\displaystyle 1\) that was carried

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 3\) and \(\displaystyle 3\)

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

Then, we multiply \(\displaystyle 3\) and \(\displaystyle 4\)

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

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

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

Example Question #713 : Common Core Math: Grade 5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}40\\ \times\ 10\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 400\)

\(\displaystyle 444\)

\(\displaystyle 420\)

\(\displaystyle 410\)

\(\displaystyle 440\)

Correct answer:

\(\displaystyle 400\)

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.

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

For this problem, \(\displaystyle 10\) is the multiplier and \(\displaystyle 40\) 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 \(\displaystyle 0\) and \(\displaystyle 0\)

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

Then, we multiply \(\displaystyle 0\) and \(\displaystyle 4\)

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

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 \(\displaystyle 0\) as a place holder in the ones position. 

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

Next, we multiply \(\displaystyle 1\) and \(\displaystyle 0\)

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

Then, we multiply \(\displaystyle 1\) and \(\displaystyle 4\)

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

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

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

Example Question #714 : Common Core Math: Grade 5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}52\\ \times\ 43\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 1\textup,824\)

\(\displaystyle 2\textup,136\)

\(\displaystyle 2\textup,236\)

\(\displaystyle 1\textup,328\)

\(\displaystyle 2\textup,080\)

Correct answer:

\(\displaystyle 2\textup,236\)

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.

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

For this problem, \(\displaystyle 43\) is the multiplier and \(\displaystyle 52\) 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 \(\displaystyle 3\) and \(\displaystyle 2\)

\(\displaystyle \frac{\begin{array}[b]{r}5{\color{Red} 2}\\ \times\ {4\color{Red} 3}\end{array}}{\ \ \ \ \ 6}\)

Then, we multiply \(\displaystyle 3\) and \(\displaystyle 5\)

 \(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 5}2\\ \times\ {4\color{Red} 3}\end{array}}{\ \ 156}\)

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 \(\displaystyle 0\) as a place holder in the ones position. 

\(\displaystyle \frac{\begin{array}[b]{r}52\\ \times\ 43\end{array}}{\ \ 156 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}\)

Next, we multiply \(\displaystyle 4\) and \(\displaystyle 2\)

\(\displaystyle \frac{\begin{array}[b]{r}5 {\color{Red} 2}\\ \times\ {\color{Red} 4}3\end{array}}{\ \ 156 }\\ {\ \ \ \ \ \ \ \ \ \ 80}\)

Then, we multiply \(\displaystyle 4\) and \(\displaystyle 5\)

\(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 5} {\color{Black} 2}\\ \times\ {\color{Red} 4}3\end{array}}{\ \ 156 }\\ {\ \ \ \ \ \ \ 2080}\)

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

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

Example Question #715 : Common Core Math: Grade 5

Solve:

\(\displaystyle \frac{\begin{array}[b]{r}56\\ \times\ 17\end{array}}{\ \ \ \ }\)

Possible Answers:

\(\displaystyle 808\)

\(\displaystyle 781\)

\(\displaystyle 752\)

\(\displaystyle 952\)

\(\displaystyle 874\)

Correct answer:

\(\displaystyle 952\)

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.

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

For this problem, \(\displaystyle 17\) is the multiplier and \(\displaystyle 56\) 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 \(\displaystyle 7\) and \(\displaystyle 6\)

\(\displaystyle \frac{\begin{array}[b]{r}^45{\color{Red} 6}\\ \times\ {1\color{Red} 7}\end{array}}{\ \ \ \ \ 2}\)

Then, we multiply \(\displaystyle 7\) and \(\displaystyle 5\) and add the \(\displaystyle 4\) that was carried

 \(\displaystyle \frac{\begin{array}[b]{r}^{\color{Red} 4}{\color{Red} 5}6\\ \times\ {1\color{Red} 7}\end{array}}{\ \ 392}\)

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 \(\displaystyle 0\) as a place holder in the ones position. 

\(\displaystyle \frac{\begin{array}[b]{r}5 6\\ \times\ 17\end{array}}{\ \ 392 }\\ {\ \ \ \ \ \ \ \ \ \ \ 0}\)

Next, we multiply \(\displaystyle 1\) and \(\displaystyle 6\)

\(\displaystyle \frac{\begin{array}[b]{r}5 {\color{Red} 6}\\ \times\ {\color{Red} 1}7\end{array}}{\ \ 392 }\\ {\ \ \ \ \ \ \ \ \ \ 60}\)

Then, we multiply \(\displaystyle 1\) and \(\displaystyle 5\)

\(\displaystyle \frac{\begin{array}[b]{r}{\color{Red} 5} {\color{Black} 6}\\ \times\ {\color{Red} 1}7\end{array}}{\ \ 392 }\\ {\ \ \ \ \ \ \ \ 560}\)

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

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

Learning Tools by Varsity Tutors