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

Solve:

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

Possible Answers:

\(\displaystyle 1390\)

\(\displaystyle 1410\)

\(\displaystyle 14000\)

\(\displaystyle 1400\)

Correct answer:

\(\displaystyle 1400\)

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, 50 is the multiplier and 28 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

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

Then, we multiply 0 and 2

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

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.

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

Next, we multiply 5 and 8

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

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

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

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

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

 

Example Question #113 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 9720\)

\(\displaystyle 982\)

\(\displaystyle 972\)

\(\displaystyle 962\)

Correct answer:

\(\displaystyle 972\)

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, 54 is the multiplier and 18 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 8

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

Then, we multiply 4 and 1 and add the 3 that was carried

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

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.

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

Next, we multiply 5 and 8

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

Then, we multiply 5 and 1and add the 4 that was carried

\(\displaystyle \begin{array}{r}\overset{4 \space{\ }}{\ 1} \space{\,}8\\ \times \phantom{0} 5\space{\,}4 \\ \hline \phantom{\,} \,7\,2 \\ \, 9 \, 0 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{4 \space{\ }}{\ 1} \space{\,}8\\ \times \phantom{0} 5\space{\,}4 \\ \hline \phantom{\,} \,7\,2 \\+\, 9 \, 0 \, 0\\ \hline 9\, 7 \, 2\end{array}\)

 

Example Question #114 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 1046\)

\(\displaystyle 1066\)

\(\displaystyle 10560\)

\(\displaystyle 1056\)

Correct answer:

\(\displaystyle 1056\)

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 16 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 6

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

Then, we multiply 6 and 1 and add the 3 that was carried

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

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.

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

Next, we multiply 6 and 6

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

Then, we multiply 6 and 1and add the 3 that was carried

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

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

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

 

Example Question #115 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\(\displaystyle 946\)

\(\displaystyle 936\)

\(\displaystyle 926\)

\(\displaystyle 9360\)

Correct answer:

\(\displaystyle 936\)

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 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 6 and 6

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

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

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

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.

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

Next, we multiply 3 and 6

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

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

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

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

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 2} \space{\,}6\\ \times \phantom{0} 3\space{\,}6 \\ \hline \phantom{\,}1\,5\,6 \\+\, 7 \, 8 \, 0\\ \hline 9\, 3 \, 6\end{array}\)

 

Example Question #641 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\(\displaystyle 40950\)

\(\displaystyle 4105\)

\(\displaystyle 4095\)

\(\displaystyle 4085\)

Correct answer:

\(\displaystyle 4095\)

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 65 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 5

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

Then, we multiply 3 and 6 and add the 1 that was carried

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

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.

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

Next, we multiply 6 and 5

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

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

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

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

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

 

Example Question #642 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\(\displaystyle 410\)

\(\displaystyle 420\)

\(\displaystyle 4200\)

\(\displaystyle 430\)

Correct answer:

\(\displaystyle 420\)

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, 20 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 0 and 1

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

Then, we multiply 0 and 2

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

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.

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

Next, we multiply 2 and 1

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

Then, we multiply 2 and 2

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

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

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

 

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

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

 

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