ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

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

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Example Questions

Example Question #124 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 730\)

\(\displaystyle 740\)

\(\displaystyle 750\)

\(\displaystyle 7400\)

Correct answer:

\(\displaystyle 740\)

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, 37 is the multiplier and 20 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 0

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

Then, we multiply 7 and 2

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

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.

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

Next, we multiply 3 and 0

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

Then, we multiply 3 and 2

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

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

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

 

Example Question #125 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 23360\)

\(\displaystyle 2346\)

\(\displaystyle 2336\)

\(\displaystyle 2326\)

Correct answer:

\(\displaystyle 2336\)

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, 32 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 2 and 3

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

Then, we multiply 2 and 7

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

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.

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

Next, we multiply 3 and 3

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}2 \\ \hline \phantom{\,}1\,4\,6 \\ \, 9 \, 0\end{array}\)

Then, we multiply 3 and 7

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}2 \\ \hline \phantom{\,}1\,4\,6 \\ \, 2\, 1\, 9 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{~ \space{\ }}{\ 7} \space{\,}3\\ \times \phantom{0} 3\space{\,}2 \\ \hline \phantom{\,}1\,4\,6 \\+\, 2\, 1\, 9 \, 0\\ \hline 2\, 3 \, 3\, 6\end{array}\)

 

Example Question #124 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 1232\)

\(\displaystyle 12320\)

\(\displaystyle 1222\)

\(\displaystyle 1242\)

Correct answer:

\(\displaystyle 1232\)

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 56 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 6

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

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

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

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.

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

Next, we multiply 2 and 6

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

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

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

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

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

 

Example Question #125 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 3816\)

\(\displaystyle 38160\)

\(\displaystyle 3826\)

\(\displaystyle 3806\)

Correct answer:

\(\displaystyle 3816\)

Explanation:

 

In order to solve this problem using multiplication, we must multiply each digit of the multiplier by each digit of the multiplicand to get the answer, which is called the product.

\(\displaystyle \frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}\)

For this problem, 72 is the multiplier and 53 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 3

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

Then, we multiply 2 and 5

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

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.

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

Next, we multiply 7 and 3

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

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

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

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

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

 

Example Question #431 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 750\)

\(\displaystyle 7500\)

\(\displaystyle 760\)

\(\displaystyle 740\)

Correct answer:

\(\displaystyle 750\)

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, 15 is the multiplier and 50 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

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

Then, we multiply 5 and 5

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

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.

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

Next, we multiply 1 and 0

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

Then, we multiply 1 and 5

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

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

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

 

Example Question #1091 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 1882\)

\(\displaystyle 18920\)

\(\displaystyle 1892\)

\(\displaystyle 1902\)

Correct answer:

\(\displaystyle 1892\)

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 43 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 3

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

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

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

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.

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

Next, we multiply 4 and 3

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

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

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

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

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 4} \space{\,}3\\ \times \phantom{0} 4\space{\,}4 \\ \hline \phantom{\,}1\,7\,2 \\+\, 1 \, 7 \, 2 \, 0\\ \hline 1\, 8 \, 9\, 2\end{array}\)

 

Example Question #632 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\(\displaystyle 3118\)

\(\displaystyle 31080\)

\(\displaystyle 3098\)

\(\displaystyle 3108\)

Correct answer:

\(\displaystyle 3108\)

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, 37 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 7 and 4

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

Then, we multiply 7 and 8 and add the 2 that was carried

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

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.

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

Next, we multiply 3 and 4

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

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

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

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

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

 

Example Question #1093 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 2069\)

\(\displaystyle 2089\)

\(\displaystyle 2079\)

\(\displaystyle 20790\)

Correct answer:

\(\displaystyle 2079\)

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 33 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

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

Then, we multiply 3 and 3

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

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.

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

Next, we multiply 6 and 3

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

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

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

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

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

 

Example Question #1094 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 4260\)

\(\displaystyle 4250\)

\(\displaystyle 42600\)

\(\displaystyle 4270\)

Correct answer:

\(\displaystyle 4260\)

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, 71 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 1 and 0

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

Then, we multiply 1 and 6

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

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.

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

Next, we multiply 7 and 0

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

Then, we multiply 7 and 6

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

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

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

 

Example Question #1095 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\(\displaystyle 15180\)

\(\displaystyle 1508\)

\(\displaystyle 1528\)

\(\displaystyle 1518\)

Correct answer:

\(\displaystyle 1518\)

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 23 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 3

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

Then, we multiply 6 and 2 and add the 1 that was carried

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

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.

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

Next, we multiply 6 and 3

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

Then, we multiply 6 and 2and add the 1 that was carried

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

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

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

 

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