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 #760 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\(\displaystyle 675\)

\(\displaystyle 6750\)

\(\displaystyle 665\)

\(\displaystyle 685\)

Correct answer:

\(\displaystyle 675\)

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 15 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

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

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

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

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.

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

Next, we multiply 4 and 5

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

Then, we multiply 4 and 1and add the 2 that was carried

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

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

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

 

Example Question #761 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\(\displaystyle 35840\)

\(\displaystyle 3594\)

\(\displaystyle 3584\)

\(\displaystyle 3574\)

Correct answer:

\(\displaystyle 3584\)

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, 64 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 4 and 6

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

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

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

Now, we multiply the digit in the tens place of the multiplier by each digit of the multiplicand. In order to do this, we need to start a new line in our math problem and put a 0 as a place holder in the ones position.

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

Next, we multiply 6 and 6

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

Then, we multiply 6 and 5and add the 3 that was carried

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

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

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

 

Example Question #762 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\(\displaystyle 12900\)

\(\displaystyle 1300\)

\(\displaystyle 1290\)

\(\displaystyle 1280\)

Correct answer:

\(\displaystyle 1290\)

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, 30 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 0 and 3

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

Then, we multiply 0 and 4

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

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.

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

Next, we multiply 3 and 3

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

Then, we multiply 3 and 4

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

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

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

 

Example Question #383 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 1168\)

\(\displaystyle 11680\)

\(\displaystyle 1158\)

\(\displaystyle 1178\)

Correct answer:

\(\displaystyle 1168\)

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, 16 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 6 and 3

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

Then, we multiply 6 and 7 and add the 1 that was carried

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

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.

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

Next, we multiply 1 and 3

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

Then, we multiply 1 and 7

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

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

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

 

Example Question #81 : How To Multiply

Solve:

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

Possible Answers:

\(\displaystyle 2850\)

\(\displaystyle 28400\)

\(\displaystyle 2830\)

\(\displaystyle 2840\)

Correct answer:

\(\displaystyle 2840\)

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 71 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

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

Then, we multiply 0 and 7

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

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.

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

Next, we multiply 4 and 1

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

Then, we multiply 4 and 7

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

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

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

 

Example Question #763 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\(\displaystyle 3118\)

\(\displaystyle 3108\)

\(\displaystyle 3098\)

\(\displaystyle 31080\)

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, 42 is the multiplier and 74 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 4

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

Then, we multiply 2 and 7

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

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.

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

Next, we multiply 4 and 4

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

Then, we multiply 4 and 7and add the 1 that was carried

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 7} \space{\,}4\\ \times \phantom{0} 4\space{\,}2 \\ \hline \phantom{\,}1\,4\,8 \\ \, 2 \, 9 \, 6 \, 0\end{array}\)

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

\(\displaystyle \begin{array}{r}\overset{1 \space{\ }}{\ 7} \space{\,}4\\ \times \phantom{0} 4\space{\,}2 \\ \hline \phantom{\,}1\,4\,8 \\+\, 2 \, 9 \, 6 \, 0\\ \hline 3\, 1 \, 0\, 8\end{array}\)

 

Example Question #383 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 656\)

\(\displaystyle 6460\)

\(\displaystyle 646\)

\(\displaystyle 636\)

Correct answer:

\(\displaystyle 646\)

Explanation:

 

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

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

For this problem, 38 is the multiplier and 17 is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply 8 and 7

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

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

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

Now, we multiply the digit in the tens place of the multiplier by each digit of the multiplicand. In order to do this, we need to start a new line in our math problem and put a 0 as a place holder in the ones position.

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

Next, we multiply 3 and 7

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

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

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

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

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

 

Example Question #384 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 1311\)

\(\displaystyle 1301\)

\(\displaystyle 1321\)

\(\displaystyle 13110\)

Correct answer:

\(\displaystyle 1311\)

Explanation:

 

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

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

For this problem, 23 is the multiplier and 57 is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply 3 and 7

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

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

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

Now, we multiply the digit in the tens place of the multiplier by each digit of the multiplicand. In order to do this, we need to start a new line in our math problem and put a 0 as a place holder in the ones position.

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

Next, we multiply 2 and 7

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

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

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

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

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

 

Example Question #385 : Numbers And Operations

Solve:

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

Possible Answers:

\(\displaystyle 6720\)

\(\displaystyle 6710\)

\(\displaystyle 6730\)

\(\displaystyle 67200\)

Correct answer:

\(\displaystyle 6720\)

Explanation:

 

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

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

For this problem, 84 is the multiplier and 80 is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply 4 and 0

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

Then, we multiply 4 and 8

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

Now, we multiply the digit in the tens place of the multiplier by each digit of the multiplicand. In order to do this, we need to start a new line in our math problem and put a 0 as a place holder in the ones position.

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

Next, we multiply 8 and 0

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

Then, we multiply 8 and 8

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

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

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

 

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

Solve:

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

Possible Answers:

\(\displaystyle 22440\)

\(\displaystyle 2244\)

\(\displaystyle 2234\)

\(\displaystyle 2254\)

Correct answer:

\(\displaystyle 2244\)

Explanation:

 

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

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

For this problem, 44 is the multiplier and 51 is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply 4 and 1

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

Then, we multiply 4 and 5

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

Now, we multiply the digit in the tens place of the multiplier by each digit of the multiplicand. In order to do this, we need to start a new line in our math problem and put a 0 as a place holder in the ones position.

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

Next, we multiply 4 and 1

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

Then, we multiply 4 and 5

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

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

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

 

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