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

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Example Questions

Example Question #643 : Number & Operations In Base Ten

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}4\\ \times\phantom{0}5\space{\,}8 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 37120\)

\(\displaystyle 3722\)

\(\displaystyle 3702\)

\(\displaystyle 3712\)

Correct answer:

\(\displaystyle 3712\)

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, 58 is the multiplier and 64 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 8 and 4

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 6} \space{\,}4\\ \times \phantom{0} 5\space{\,}8\\ \hline \phantom{\,} \,2\end{array}\)

Then, we multiply 8 and 6 and add the 3 that was carried

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 6} \space{\,}4\\ \times \phantom{0} 5\space{\,}8 \\ \hline \phantom{\,}5\,1\,2\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}4\\ \times \phantom{0} 5\space{\,}8 \\ \hline \phantom{\,}5\,1\,2 \\ \, 0 \end{array}\)

Next, we multiply 5 and 4

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}4\\ \times \phantom{0} 5\space{\,}8 \\ \hline \phantom{\,}5\,1\,2 \\ \, 0 \, 0\end{array}\)

Then, we multiply 5 and 6and add the 2 that was carried

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}4\\ \times \phantom{0} 5\space{\,}8 \\ \hline \phantom{\,}5\,1\,2 \\ \, 3 \, 2 \, 0 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}4\\ \times \phantom{0} 5\space{\,}8 \\ \hline \phantom{\,}5\,1\,2 \\+\, 3 \, 2 \, 0 \, 0\\ \hline 3\, 7 \, 1\, 2\end{array}\)

 

Example Question #644 : Number & Operations In Base Ten

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 3} \space{\,}5\\ \times\phantom{0}5\space{\,}1 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 1775\)

\(\displaystyle 1795\)

\(\displaystyle 17850\)

\(\displaystyle 1785\)

Correct answer:

\(\displaystyle 1785\)

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, 51 is the multiplier and 35 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 1 and 5

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 5\space{\,}1 \\ \hline \phantom{\,} \,5\end{array}\)

Then, we multiply 1 and 3

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 5\space{\,}1 \\ \hline \phantom{\,} \,3\,5\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 5\space{\,}1 \\ \hline \phantom{\,} \,3\,5 \\ \, 0 \end{array}\)

Next, we multiply 5 and 5

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 5\space{\,}1 \\ \hline \phantom{\,} \,3\,5 \\ \, 5 \, 0\end{array}\)

Then, we multiply 5 and 3and add the 2 that was carried

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 5\space{\,}1 \\ \hline \phantom{\,} \,3\,5 \\ \, 1 \, 7 \, 5 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 5\space{\,}1 \\ \hline \phantom{\,} \,3\,5 \\+\, 1 \, 7 \, 5 \, 0\\ \hline 1\, 7 \, 8\, 5\end{array}\)

 

Example Question #645 : Number & Operations In Base Ten

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times\phantom{0}3\space{\,}3 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 1716\)

\(\displaystyle 1706\)

\(\displaystyle 17160\)

\(\displaystyle 1726\)

Correct answer:

\(\displaystyle 1716\)

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, 33 is the multiplier and 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 3 and 2

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,} \,6\end{array}\)

Then, we multiply 3 and 5

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}1\,5\,6\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}1\,5\,6 \\ \, 0 \end{array}\)

Next, we multiply 3 and 2

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}1\,5\,6 \\ \, 6 \, 0\end{array}\)

Then, we multiply 3 and 5

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}1\,5\,6 \\ \, 1\, 5\, 6 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}1\,5\,6 \\+\, 1\, 5\, 6 \, 0\\ \hline 1\, 7 \, 1\, 6\end{array}\)

 

Example Question #646 : Number & Operations In Base Ten

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}4\\ \times\phantom{0}2\space{\,}5 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 2100\)

\(\displaystyle 21000\)

\(\displaystyle 2110\)

\(\displaystyle 2090\)

Correct answer:

\(\displaystyle 2100\)

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, 25 is the multiplier and 84 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 5 and 4

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}5\\ \hline \phantom{\,} \,0\end{array}\)

Then, we multiply 5 and 8 and add the 2 that was carried

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}5 \\ \hline \phantom{\,}4\,2\,0\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}5 \\ \hline \phantom{\,}4\,2\,0 \\ \, 0 \end{array}\)

Next, we multiply 2 and 4

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}5 \\ \hline \phantom{\,}4\,2\,0 \\ \, 8 \, 0\end{array}\)

Then, we multiply 2 and 8

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}5 \\ \hline \phantom{\,}4\,2\,0 \\ \, 1\, 6\, 8 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}5 \\ \hline \phantom{\,}4\,2\,0 \\+\, 1\, 6\, 8 \, 0\\ \hline 2\, 1 \, 0\, 0\end{array}\)

 

Example Question #451 : Numbers And Operations

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times\phantom{0}6\space{\,}1 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 31720\)

\(\displaystyle 3172\)

\(\displaystyle 3182\)

\(\displaystyle 3162\)

Correct answer:

\(\displaystyle 3172\)

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, 61 is the multiplier and 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 1 and 2

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 6\space{\,}1 \\ \hline \phantom{\,} \,2\end{array}\)

Then, we multiply 1 and 5

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 6\space{\,}1 \\ \hline \phantom{\,} \,5\,2\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 6\space{\,}1 \\ \hline \phantom{\,} \,5\,2 \\ \, 0 \end{array}\)

Next, we multiply 6 and 2

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 6\space{\,}1 \\ \hline \phantom{\,} \,5\,2 \\ \, 2 \, 0\end{array}\)

Then, we multiply 6 and 5and add the 1 that was carried

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 6\space{\,}1 \\ \hline \phantom{\,} \,5\,2 \\ \, 3 \, 1 \, 2 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 5} \space{\,}2\\ \times \phantom{0} 6\space{\,}1 \\ \hline \phantom{\,} \,5\,2 \\+\, 3 \, 1 \, 2 \, 0\\ \hline 3\, 1 \, 7\, 2\end{array}\)

 

Example Question #452 : Numbers And Operations

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 3} \space{\,}5\\ \times\phantom{0}6\space{\,}6 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 2310\)

\(\displaystyle 2320\)

\(\displaystyle 23100\)

\(\displaystyle 2300\)

Correct answer:

\(\displaystyle 2310\)

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, 66 is the multiplier and 35 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 6 and 5

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 6\space{\,}6\\ \hline \phantom{\,} \,0\end{array}\)

Then, we multiply 6 and 3 and add the 3 that was carried

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 6\space{\,}6 \\ \hline \phantom{\,}2\,1\,0\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 6\space{\,}6 \\ \hline \phantom{\,}2\,1\,0 \\ \, 0 \end{array}\)

Next, we multiply 6 and 5

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 6\space{\,}6 \\ \hline \phantom{\,}2\,1\,0 \\ \, 0 \, 0\end{array}\)

Then, we multiply 6 and 3and add the 3 that was carried

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 6\space{\,}6 \\ \hline \phantom{\,}2\,1\,0 \\ \, 2 \, 1 \, 0 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 3} \space{\,}5\\ \times \phantom{0} 6\space{\,}6 \\ \hline \phantom{\,}2\,1\,0 \\+\, 2 \, 1 \, 0 \, 0\\ \hline 2\, 3 \, 1\, 0\end{array}\)

 

Example Question #453 : Numbers And Operations

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 1} \space{\,}2\\ \times\phantom{0}5\space{\,}7 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 674\)

\(\displaystyle 6840\)

\(\displaystyle 694\)

\(\displaystyle 684\)

Correct answer:

\(\displaystyle 684\)

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, 57 is the multiplier and 12 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 7 and 2

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 1} \space{\,}2\\ \times \phantom{0} 5\space{\,}7\\ \hline \phantom{\,} \,4\end{array}\)

Then, we multiply 7 and 1 and add the 1 that was carried

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 1} \space{\,}2\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,} \,8\,4\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 1} \space{\,}2\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,} \,8\,4 \\ \, 0 \end{array}\)

Next, we multiply 5 and 2

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 1} \space{\,}2\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,} \,8\,4 \\ \, 0 \, 0\end{array}\)

Then, we multiply 5 and 1and add the 1 that was carried

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 1} \space{\,}2\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,} \,8\,4 \\ \, 6 \, 0 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 1} \space{\,}2\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,} \,8\,4 \\+\, 6 \, 0 \, 0\\ \hline 6\, 8 \, 4\end{array}\)

 

Example Question #454 : Numbers And Operations

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}6\\ \times\phantom{0}3\space{\,}4 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 2934\)

\(\displaystyle 2914\)

\(\displaystyle 2924\)

\(\displaystyle 29240\)

Correct answer:

\(\displaystyle 2924\)

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, 34 is the multiplier and 86 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 4 and 6

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 8} \space{\,}6\\ \times \phantom{0} 3\space{\,}4\\ \hline \phantom{\,} \,4\end{array}\)

Then, we multiply 4 and 8 and add the 2 that was carried

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 8} \space{\,}6\\ \times \phantom{0} 3\space{\,}4 \\ \hline \phantom{\,}3\,4\,4\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}6\\ \times \phantom{0} 3\space{\,}4 \\ \hline \phantom{\,}3\,4\,4 \\ \, 0 \end{array}\)

Next, we multiply 3 and 6

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 8} \space{\,}6\\ \times \phantom{0} 3\space{\,}4 \\ \hline \phantom{\,}3\,4\,4 \\ \, 8 \, 0\end{array}\)

Then, we multiply 3 and 8and add the 1 that was carried

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 8} \space{\,}6\\ \times \phantom{0} 3\space{\,}4 \\ \hline \phantom{\,}3\,4\,4 \\ \, 2 \, 5 \, 8 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 8} \space{\,}6\\ \times \phantom{0} 3\space{\,}4 \\ \hline \phantom{\,}3\,4\,4 \\+\, 2 \, 5 \, 8 \, 0\\ \hline 2\, 9 \, 2\, 4\end{array}\)

 

Example Question #651 : Number & Operations In Base Ten

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}7\\ \times\phantom{0}3\space{\,}3 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 2221\)

\(\displaystyle 2211\)

\(\displaystyle 2201\)

\(\displaystyle 22110\)

Correct answer:

\(\displaystyle 2211\)

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, 33 is the multiplier and 67 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 3 and 7

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}7\\ \times \phantom{0} 3\space{\,}3\\ \hline \phantom{\,} \,1\end{array}\)

Then, we multiply 3 and 6 and add the 2 that was carried

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}7\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,0\,1\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}7\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,0\,1 \\ \, 0 \end{array}\)

Next, we multiply 3 and 7

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}7\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,0\,1 \\ \, 1 \, 0\end{array}\)

Then, we multiply 3 and 6and add the 2 that was carried

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}7\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,0\,1 \\ \, 2 \, 0 \, 1 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 6} \space{\,}7\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,0\,1 \\+\, 2 \, 0 \, 1 \, 0\\ \hline 2\, 2 \, 1\, 1\end{array}\)

 

Example Question #652 : Number & Operations In Base Ten

Solve:

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times\phantom{0}7\space{\,}2 \\ \hline \phantom{\,}\end{array}\)

Possible Answers:

\(\displaystyle 4330\)

\(\displaystyle 4310\)

\(\displaystyle 43200\)

\(\displaystyle 4320\)

Correct answer:

\(\displaystyle 4320\)

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, 72 is the multiplier and 60 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 2 and 0

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times \phantom{0} 7\space{\,}2 \\ \hline \phantom{\,} \,0\end{array}\)

Then, we multiply 2 and 6

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times \phantom{0} 7\space{\,}2 \\ \hline \phantom{\,}1\,2\,0\end{array}\)

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 0 as a place holder in the ones position.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times \phantom{0} 7\space{\,}2 \\ \hline \phantom{\,}1\,2\,0 \\ \, 0 \end{array}\)

Next, we multiply 7 and 0

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times \phantom{0} 7\space{\,}2 \\ \hline \phantom{\,}1\,2\,0 \\ \, 0 \, 0\end{array}\)

Then, we multiply 7 and 6

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times \phantom{0} 7\space{\,}2 \\ \hline \phantom{\,}1\,2\,0 \\ \, 4\, 2\, 0 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 6} \space{\,}0\\ \times \phantom{0} 7\space{\,}2 \\ \hline \phantom{\,}1\,2\,0 \\+\, 4\, 2\, 0 \, 0\\ \hline 4\, 3 \, 2\, 0\end{array}\)

 

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