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 #383 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 656\)

\(\displaystyle 6460\)

\(\displaystyle 646\)

\(\displaystyle 636\)

Correct answer:

\(\displaystyle 646\)

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, 38 is the multiplier and 17 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 7

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

Then, we multiply 8 and 1 and add the 5 that was carried

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

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.

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

Next, we multiply 3 and 7

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

Then, we multiply 3 and 1and add the 2 that was carried

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

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

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

 

Example Question #384 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 1311\)

\(\displaystyle 1301\)

\(\displaystyle 1321\)

\(\displaystyle 13110\)

Correct answer:

\(\displaystyle 1311\)

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, 23 is the multiplier and 57 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

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

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

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

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.

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

Next, we multiply 2 and 7

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

Then, we multiply 2 and 5and add the 1 that was carried

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

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

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

 

Example Question #385 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 6720\)

\(\displaystyle 6710\)

\(\displaystyle 6730\)

\(\displaystyle 67200\)

Correct answer:

\(\displaystyle 6720\)

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, 84 is the multiplier and 80 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 0

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

Then, we multiply 4 and 8

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

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.

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

Next, we multiply 8 and 0

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

Then, we multiply 8 and 8

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

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

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

 

Example Question #1051 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 22440\)

\(\displaystyle 2244\)

\(\displaystyle 2234\)

\(\displaystyle 2254\)

Correct answer:

\(\displaystyle 2244\)

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, 44 is the multiplier and 51 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 1

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

Then, we multiply 4 and 5

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

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.

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

Next, we multiply 4 and 1

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

Then, we multiply 4 and 5

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

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

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

 

Example Question #81 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 836\)

\(\displaystyle 8360\)

\(\displaystyle 826\)

\(\displaystyle 846\)

Correct answer:

\(\displaystyle 836\)

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, 22 is the multiplier and 38 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 8

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

Then, we multiply 2 and 3 and add the 1 that was carried

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

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.

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

Next, we multiply 2 and 8

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

Then, we multiply 2 and 3and add the 1 that was carried

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

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

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

 

Example Question #61 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 1026\)

\(\displaystyle 1036\)

\(\displaystyle 1016\)

\(\displaystyle 10260\)

Correct answer:

\(\displaystyle 1026\)

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, 27 is the multiplier and 38 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 8

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

Then, we multiply 7 and 3 and add the 5 that was carried

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

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.

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

Next, we multiply 2 and 8

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

Then, we multiply 2 and 3and add the 1 that was carried

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

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

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

 

Example Question #1053 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 1628\)

\(\displaystyle 1638\)

\(\displaystyle 1648\)

\(\displaystyle 16380\)

Correct answer:

\(\displaystyle 1638\)

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, 63 is the multiplier and 26 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 6

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

Then, we multiply 3 and 2 and add the 1 that was carried

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

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.

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

Next, we multiply 6 and 6

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

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

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

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

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

 

Example Question #1051 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 3886\)

\(\displaystyle 3876\)

\(\displaystyle 3866\)

\(\displaystyle 38760\)

Correct answer:

\(\displaystyle 3876\)

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 68 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 8

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

Then, we multiply 7 and 6 and add the 5 that was carried

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

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.

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

Next, we multiply 5 and 8

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

Then, we multiply 5 and 6and add the 4 that was carried

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

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

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

 

Example Question #1052 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 693\)

\(\displaystyle 683\)

\(\displaystyle 703\)

\(\displaystyle 6930\)

Correct answer:

\(\displaystyle 693\)

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 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 3 and 1

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

Then, we multiply 3 and 2

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

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.

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

Next, we multiply 3 and 1

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

Then, we multiply 3 and 2

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

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

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

 

Example Question #591 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\(\displaystyle 320\)

\(\displaystyle 3300\)

\(\displaystyle 330\)

\(\displaystyle 340\)

Correct answer:

\(\displaystyle 330\)

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 10 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 0

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

Then, we multiply 3 and 1

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

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.

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

Next, we multiply 3 and 0

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

Then, we multiply 3 and 1

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

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

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

 

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