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

Solve:

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

Possible Answers:

\displaystyle 7470

\displaystyle 74800

\displaystyle 7480

\displaystyle 7490

Correct answer:

\displaystyle 7480

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, 88 is the multiplier and 85 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 5

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

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

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

Next, we multiply 8 and 5

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

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

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

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

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

 

Example Question #43 : How To Multiply

Solve:

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

Possible Answers:

\displaystyle 28710

\displaystyle 2881

\displaystyle 2871

\displaystyle 2861

Correct answer:

\displaystyle 2871

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 87 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{\ }}{\ 8} \space{\,}7\\ \times \phantom{0} 3\space{\,}3\\ \hline \phantom{\,} \,1\end{array}

Then, we multiply 3 and 8 and add the 2 that was carried

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

Next, we multiply 3 and 7

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

Then, we multiply 3 and 8and add the 2 that was carried

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

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

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

 

Example Question #731 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\displaystyle 2762

\displaystyle 2782

\displaystyle 2772

\displaystyle 27720

Correct answer:

\displaystyle 2772

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, 63 is the multiplier and 44 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{\ }}{\ 4} \space{\,}4\\ \times \phantom{0} 6\space{\,}3\\ \hline \phantom{\,} \,2\end{array}

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

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

Next, we multiply 6 and 4

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

Then, we multiply 6 and 4and add the 2 that was carried

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

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

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

 

Example Question #732 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\displaystyle 4274

\displaystyle 4294

\displaystyle 4284

\displaystyle 42840

Correct answer:

\displaystyle 4284

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 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 1 and 4

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

Then, we multiply 1 and 8

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

Next, we multiply 5 and 4

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

Then, we multiply 5 and 8and add the 2 that was carried

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

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

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

 

Example Question #733 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\displaystyle 1166

\displaystyle 1186

\displaystyle 1176

\displaystyle 11760

Correct answer:

\displaystyle 1176

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, 28 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} 2\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} 2\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} 2\space{\,}8 \\ \hline \phantom{\,}3\,3\,6 \\ \, 0 \end{array}

Next, we multiply 2 and 2

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

Then, we multiply 2 and 4

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

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

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

 

Example Question #734 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\displaystyle 890

\displaystyle 9000

\displaystyle 900

\displaystyle 910

Correct answer:

\displaystyle 900

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, 20 is the multiplier and 45 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 5

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

Then, we multiply 0 and 4

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

Next, we multiply 2 and 5

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

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

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

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

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

 

Example Question #735 : Common Core Math: Grade 5

Solve:

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

Possible Answers:

\displaystyle 1320

\displaystyle 13200

\displaystyle 1310

\displaystyle 1330

Correct answer:

\displaystyle 1320

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, 40 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 0 and 3

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

Then, we multiply 0 and 3

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

Next, we multiply 4 and 3

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

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

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

 

Example Question #1011 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\displaystyle 3393

\displaystyle 34030

\displaystyle 3413

\displaystyle 3403

Correct answer:

\displaystyle 3403

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 41 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{\ }}{\ 4} \space{\,}1\\ \times \phantom{0} 8\space{\,}3 \\ \hline \phantom{\,} \,3\end{array}

Then, we multiply 3 and 4

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

Next, we multiply 8 and 1

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

Then, we multiply 8 and 4

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

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

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

 

Example Question #1012 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\displaystyle 14850

\displaystyle 1475

\displaystyle 1495

\displaystyle 1485

Correct answer:

\displaystyle 1485

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, 55 is the multiplier and 27 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 7

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

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

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

Next, we multiply 5 and 7

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

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

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

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

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

 

Example Question #1013 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

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

Possible Answers:

\displaystyle 4274

\displaystyle 4264

\displaystyle 42640

\displaystyle 4254

Correct answer:

\displaystyle 4264

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, 82 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 2 and 2

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

Then, we multiply 2 and 5

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

Next, we multiply 8 and 2

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

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

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

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

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

 

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