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 #1001 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\displaystyle 1785

\displaystyle 17850

\displaystyle 1775

\displaystyle 1795

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.

For this problem, 35 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 5 and 1

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

Then, we multiply 5 and 5

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

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

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

Next, we multiply 3 and 1

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

Then, we multiply 3 and 5

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

 

Example Question #11 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\displaystyle 3672

\displaystyle 36720

\displaystyle 3662

\displaystyle 3682

Correct answer:

\displaystyle 3672

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.

For this problem, 68 is the multiplier and 54 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{\ }}{\ 5} \space{\,}4\\ \times \phantom{0} 6\space{\,}8\\ \hline \phantom{\,} \,2\end{array}

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

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

Next, we multiply 6 and 4

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

Then, we multiply 6 and 5and add the 2 that was carried

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

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

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

 

Example Question #342 : Numbers And Operations

Solve:

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

Possible Answers:

\displaystyle 4482

\displaystyle 4472

\displaystyle 44820

\displaystyle 4492

Correct answer:

\displaystyle 4482

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.

For this problem, 83 is the multiplier and 54 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 4

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

Then, we multiply 3 and 5 and add the 1 that was carried

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

Next, we multiply 8 and 4

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

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

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

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

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

 

Example Question #534 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 4464

\displaystyle 44640

\displaystyle 4474

\displaystyle 4454

Correct answer:

\displaystyle 4464

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.

For this problem, 62 is the multiplier and 72 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 2

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

Then, we multiply 2 and 7

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

Next, we multiply 6 and 2

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

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

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

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

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

 

Example Question #535 : Number & Operations In Base Ten

Solve:

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

Possible Answers:

\displaystyle 30820

\displaystyle 3092

\displaystyle 3072

\displaystyle 3082

Correct answer:

\displaystyle 3082

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.

For this problem, 67 is the multiplier and 46 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 6

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

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

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

Next, we multiply 6 and 6

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

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

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

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

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

 

Example Question #41 : How To Multiply

Solve:

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

Possible Answers:

\displaystyle 3203

\displaystyle 32130

\displaystyle 3213

\displaystyle 3223

Correct answer:

\displaystyle 3213

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.

For this problem, 51 is the multiplier and 63 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 3

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

Then, we multiply 1 and 6

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

Next, we multiply 5 and 3

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

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

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

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

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

 

Example Question #42 : How To Multiply

Solve:

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

Possible Answers:

\displaystyle 3266

\displaystyle 3286

\displaystyle 32760

\displaystyle 3276

Correct answer:

\displaystyle 3276

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.

For this problem, 78 is the multiplier and 42 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 2

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

Then, we multiply 8 and 4 and add the 1 that was carried

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

Next, we multiply 7 and 2

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

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

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

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

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

 

Example Question #21 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\displaystyle 10640

\displaystyle 1074

\displaystyle 1054

\displaystyle 1064

Correct answer:

\displaystyle 1064

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.

For this problem, 14 is the multiplier and 76 is the multiplicand. We start with the multiplier, and multiply the digit in the ones place by each digit of the multiplicand.

First, we multiply 4 and 6

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

Then, we multiply 4 and 7 and add the 2 that was carried

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

Next, we multiply 1 and 6

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

Then, we multiply 1 and 7

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

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

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

 

Example Question #41 : How To Multiply

Solve:

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

Possible Answers:

\displaystyle 1924

\displaystyle 1914

\displaystyle 1904

\displaystyle 19140

Correct answer:

\displaystyle 1914

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.

For this problem, 33 is the multiplier and 58 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 8

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

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

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

Next, we multiply 3 and 8

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

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

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

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

\displaystyle \begin{array}{r}\overset{2 \space{\ }}{\ 5} \space{\,}8\\ \times \phantom{0} 3\space{\,}3 \\ \hline \phantom{\,}1\,7\,4 \\+\, 1 \, 7 \, 4 \, 0\\ \hline 1\, 9 \, 1\, 4\end{array}

 

Example Question #23 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

\displaystyle 5465

\displaystyle 54750

\displaystyle 5475

\displaystyle 5485

Correct answer:

\displaystyle 5475

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.

For this problem, 73 is the multiplier and 75 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{\ }}{\ 7} \space{\,}5\\ \times \phantom{0} 7\space{\,}3\\ \hline \phantom{\,} \,5\end{array}

Then, we multiply 3 and 7 and add the 1 that was carried

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

Next, we multiply 7 and 5

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

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

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

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

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

 

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