ISEE Middle Level Quantitative : How to multiply

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #1071 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 386\)

\(\displaystyle 406\)

\(\displaystyle 396\)

\(\displaystyle 3960\)

Correct answer:

\(\displaystyle 396\)

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, 11 is the multiplier and 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 1 and 6

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

Then, we multiply 1 and 3

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

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.

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

Next, we multiply 1 and 6

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

Then, we multiply 1 and 3

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

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

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

 

Example Question #1072 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 3516\)

\(\displaystyle 3536\)

\(\displaystyle 35260\)

\(\displaystyle 3526\)

Correct answer:

\(\displaystyle 3526\)

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, 43 is the multiplier and 82 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

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

Then, we multiply 3 and 8

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

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.

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

Next, we multiply 4 and 2

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

Then, we multiply 4 and 8

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

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

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

 

Example Question #1077 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 2399\)

\(\displaystyle 24090\)

\(\displaystyle 2409\)

\(\displaystyle 2419\)

Correct answer:

\(\displaystyle 2409\)

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 73 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 3

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,} \,9\end{array}\)

Then, we multiply 3 and 7

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,1\,9\end{array}\)

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.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,1\,9 \\ \, 0 \end{array}\)

Next, we multiply 3 and 3

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,1\,9 \\ \, 9 \, 0\end{array}\)

Then, we multiply 3 and 7

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,1\,9 \\ \, 2\, 1\, 9 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}2\,1\,9 \\+\, 2\, 1\, 9 \, 0\\ \hline 2\, 4 \, 0\, 9\end{array}\)

 

Example Question #1078 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 661\)

\(\displaystyle 681\)

\(\displaystyle 6710\)

\(\displaystyle 671\)

Correct answer:

\(\displaystyle 671\)

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 11 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 1

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

Then, we multiply 1 and 1

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

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.

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

Next, we multiply 6 and 1

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

Then, we multiply 6 and 1

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

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

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

 

Example Question #1079 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 3600\)

\(\displaystyle 370\)

\(\displaystyle 350\)

\(\displaystyle 360\)

Correct answer:

\(\displaystyle 360\)

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, 36 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 6 and 0

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

Then, we multiply 6 and 1

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

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.

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

Next, we multiply 3 and 0

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

Then, we multiply 3 and 1

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

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

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

 

Example Question #91 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 6365\)

\(\displaystyle 63750\)

\(\displaystyle 6375\)

\(\displaystyle 6385\)

Correct answer:

\(\displaystyle 6375\)

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, 85 is the multiplier and 75 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 5

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

Then, we multiply 5 and 7 and add the 2 that was carried

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

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.

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

Next, we multiply 8 and 5

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

Then, we multiply 8 and 7and add the 4 that was carried

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

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

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

 

Example Question #91 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 4800\)

\(\displaystyle 470\)

\(\displaystyle 490\)

\(\displaystyle 480\)

Correct answer:

\(\displaystyle 480\)

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, 10 is the multiplier and 48 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 0 and 8

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

Then, we multiply 0 and 4

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

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.

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

Next, we multiply 1 and 8

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

Then, we multiply 1 and 4

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

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

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

 

Example Question #92 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 2555\)

\(\displaystyle 2565\)

\(\displaystyle 25650\)

\(\displaystyle 2575\)

Correct answer:

\(\displaystyle 2565\)

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, 45 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 5 and 7

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

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

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

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.

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

Next, we multiply 4 and 7

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

Then, we multiply 4 and 5and add the 2 that was carried

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

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

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

 

Example Question #801 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\(\displaystyle 5498\)

\(\displaystyle 55080\)

\(\displaystyle 5508\)

\(\displaystyle 5518\)

Correct answer:

\(\displaystyle 5508\)

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, 68 is the multiplier and 81 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 1

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

Then, we multiply 8 and 8

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

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.

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

Next, we multiply 6 and 1

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

Then, we multiply 6 and 8

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

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

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

 

Example Question #91 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 3239\)

\(\displaystyle 3249\)

\(\displaystyle 3259\)

\(\displaystyle 32490\)

Correct answer:

\(\displaystyle 3249\)

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 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 7 and 7

\(\displaystyle \begin{array}{r}\overset{4 \space{\ }}{\ 5} \space{\,}7\\ \times \phantom{0} 5\space{\,}7\\ \hline \phantom{\,} \,9\end{array}\)

Then, we multiply 7 and 5 and add the 4 that was carried

\(\displaystyle \begin{array}{r}\overset{4 \space{\ }}{\ 5} \space{\,}7\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,}3\,9\,9\end{array}\)

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.

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 5} \space{\,}7\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,}3\,9\,9 \\ \, 0 \end{array}\)

Next, we multiply 5 and 7

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 5} \space{\,}7\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,}3\,9\,9 \\ \, 5 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 5} \space{\,}7\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,}3\,9\,9 \\ \, 2 \, 8 \, 5 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{3 \space{\ }}{\ 5} \space{\,}7\\ \times \phantom{0} 5\space{\,}7 \\ \hline \phantom{\,}3\,9\,9 \\+\, 2 \, 8 \, 5 \, 0\\ \hline 3\, 2 \, 4\, 9\end{array}\)

 

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