ISEE Middle Level Quantitative : How to multiply

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

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Example Questions

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

Solve:

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

Possible Answers:

\displaystyle 3886

\displaystyle 3876

\displaystyle 3866

\displaystyle 38760

Correct answer:

\displaystyle 3876

Explanation:

 

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

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

For this problem, 57 is the multiplier and 68 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 8

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

Then, we multiply 7 and 6 and add the 5 that was carried

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

Next, we multiply 5 and 8

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

Then, we multiply 5 and 6and add the 4 that was carried

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

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

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

 

Example Question #1052 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\displaystyle 693

\displaystyle 683

\displaystyle 703

\displaystyle 6930

Correct answer:

\displaystyle 693

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 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 3 and 1

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

Then, we multiply 3 and 2

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

Next, we multiply 3 and 1

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

Then, we multiply 3 and 2

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

 

Example Question #591 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 320

\displaystyle 3300

\displaystyle 330

\displaystyle 340

Correct answer:

\displaystyle 330

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 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 3 and 0

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

Then, we multiply 3 and 1

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

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

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

Next, we multiply 3 and 0

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

Then, we multiply 3 and 1

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

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

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

 

Example Question #1054 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\displaystyle 2356

\displaystyle 2366

\displaystyle 23560

\displaystyle 2346

Correct answer:

\displaystyle 2356

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, 62 is the multiplier and 38 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 8

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

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

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

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

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

Next, we multiply 6 and 8

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

Then, we multiply 6 and 3and add the 4 that was carried

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

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

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

 

Example Question #592 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 38880

\displaystyle 3888

\displaystyle 3878

\displaystyle 3898

Correct answer:

\displaystyle 3888

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, 81 is the multiplier and 48 is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply 1 and 8

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

Then, we multiply 1 and 4

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

Next, we multiply 8 and 8

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

Then, we multiply 8 and 4and add the 6 that was carried

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

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

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

 

Example Question #593 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 342

\displaystyle 352

\displaystyle 3520

\displaystyle 362

Correct answer:

\displaystyle 352

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 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 2 and 1

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

Then, we multiply 2 and 1

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

Next, we multiply 3 and 1

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

Then, we multiply 3 and 1

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

 

Example Question #594 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 450

\displaystyle 430

\displaystyle 4400

\displaystyle 440

Correct answer:

\displaystyle 440

Explanation:

 

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

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

For this problem, 11 is the multiplier and 40 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{\ }}{\ 4} \space{\,}0\\ \times \phantom{0} 1\space{\,}1 \\ \hline \phantom{\,} \,0\end{array}

Then, we multiply 1 and 4

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

Next, we multiply 1 and 0

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

Then, we multiply 1 and 4

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

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

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

 

Example Question #93 : How To Multiply

Solve:

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

Possible Answers:

\displaystyle 66000

\displaystyle 6590

\displaystyle 6600

\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 #595 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 3120

\displaystyle 3110

\displaystyle 3130

\displaystyle 31200

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 #402 : Numbers And Operations

Solve:

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

Possible Answers:

\displaystyle 130

\displaystyle 110

\displaystyle 120

\displaystyle 1200

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}

 

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