ISEE Middle Level Quantitative : Numbers and Operations

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

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Example Questions

Example Question #98 : Whole Numbers

Solve:

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

Possible Answers:

\(\displaystyle 6600\)

\(\displaystyle 66000\)

\(\displaystyle 6590\)

\(\displaystyle 6610\)

Correct answer:

\(\displaystyle 6600\)

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, 75 is the multiplier and 88 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 8

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

Then, we multiply 5 and 8 and add the 4 that was carried

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

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.

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

Next, we multiply 7 and 8

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

Then, we multiply 7 and 8and add the 5 that was carried

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

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

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

 

Example Question #99 : Whole Numbers

Solve:

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

Possible Answers:

\(\displaystyle 31200\)

\(\displaystyle 3110\)

\(\displaystyle 3130\)

\(\displaystyle 3120\)

Correct answer:

\(\displaystyle 3120\)

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, 40 is the multiplier and 78 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

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

Then, we multiply 0 and 7

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

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.

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

Next, we multiply 4 and 8

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

Then, we multiply 4 and 7and add the 3 that was carried

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

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

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

 

Example Question #100 : Whole Numbers

Solve:

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

Possible Answers:

\(\displaystyle 110\)

\(\displaystyle 130\)

\(\displaystyle 1200\)

\(\displaystyle 120\)

Correct answer:

\(\displaystyle 120\)

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, 12 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 2 and 0

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

Then, we multiply 2 and 1

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

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.

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

Next, we multiply 1 and 0

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

Then, we multiply 1 and 1

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

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

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

 

Example Question #101 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 2500\)

\(\displaystyle 2490\)

\(\displaystyle 24900\)

\(\displaystyle 2480\)

Correct answer:

\(\displaystyle 2490\)

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, 83 is the multiplier and 30 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

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

Then, we multiply 3 and 3

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

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.

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

Next, we multiply 8 and 0

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

Then, we multiply 8 and 3

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

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

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

 

Example Question #102 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 3462\)

\(\displaystyle 3472\)

\(\displaystyle 34720\)

\(\displaystyle 3482\)

Correct answer:

\(\displaystyle 3472\)

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, 56 is the multiplier and 62 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 2

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

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

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

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.

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

Next, we multiply 5 and 2

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

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

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

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

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

 

Example Question #103 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 2110\)

\(\displaystyle 2100\)

\(\displaystyle 21000\)

\(\displaystyle 2090\)

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, 35 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 5 and 0

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

Then, we multiply 5 and 6

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

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.

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

Next, we multiply 3 and 0

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

Then, we multiply 3 and 6

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

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

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

 

Example Question #81 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 835\)

\(\displaystyle 825\)

\(\displaystyle 8250\)

\(\displaystyle 815\)

Correct answer:

\(\displaystyle 825\)

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, 75 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 5 and 1

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

Then, we multiply 5 and 1

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

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.

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

Next, we multiply 7 and 1

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

Then, we multiply 7 and 1

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

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

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

 

Example Question #781 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\(\displaystyle 6070\)

\(\displaystyle 60800\)

\(\displaystyle 6090\)

\(\displaystyle 6080\)

Correct answer:

\(\displaystyle 6080\)

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, 80 is the multiplier and 76 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 6

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

Then, we multiply 0 and 7

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

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.

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

Next, we multiply 8 and 6

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

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

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

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

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

 

Example Question #83 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 4601\)

\(\displaystyle 46110\)

\(\displaystyle 4611\)

\(\displaystyle 4621\)

Correct answer:

\(\displaystyle 4611\)

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, 53 is the multiplier and 87 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

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

Then, we multiply 3 and 8 and add the 2 that was carried

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

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.

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

Next, we multiply 5 and 7

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

Then, we multiply 5 and 8and add the 3 that was carried

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

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

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

 

Example Question #84 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 3366\)

\(\displaystyle 3356\)

\(\displaystyle 33660\)

\(\displaystyle 3376\)

Correct answer:

\(\displaystyle 3366\)

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 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 6 and 1

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

Then, we multiply 6 and 5

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

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.

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

Next, we multiply 6 and 1

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

Then, we multiply 6 and 5

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

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

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

 

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