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Common Core: 4th Grade Math : Use place value understanding and properties of operations to perform multi-digit arithmetic

Study concepts, example questions & explanations for Common Core: 4th Grade Math

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All Common Core: 4th Grade Math Resources

7 Diagnostic Tests 189 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #531 : How To Divide

Solve $6{\overline{\smash{)}45}}$ by making a rectangular array.

Possible Answers:

$6\ R2$

$6\ R3$

$7\ R2$

$7\ R3$

$7\ R4$

Correct answer:

$7\ R3$

Explanation:

Using our problem to make a rectangular array, we know that we are going to use a total of squares, and one dimension of the rectangular array is going to have squares, we'll make that the width. Our answer will be how many squares high the rectangle array is, or the height.

We can start with squares and keep adding on top of the previous until we've used all squares. Our rectangular array is squares high with squares left over, which is our remainder.

$45\div6=7\ R3$

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Example Question #3808 : Numbers And Operations

Solve $6{\overline{\smash{)}91}}$ by making a rectangular array.

Possible Answers:

$14\ R1$

$14\ R2$

$13\ R1$

$15\ R2$

$15\ R1$

Correct answer:

$15\ R1$

Explanation:

We can start with squares and keep adding on top of the previous until we've used all squares. Our rectangular array is squares high with square left over, which is our remainder.

$91\div6=15\ R1$

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Example Question #532 : How To Divide

Solve $9{\overline{\smash{)}70}}$ by making a rectangular array.

Possible Answers:

$7\ R5$

$7\ R3$

$7\ R7$

$7\ R4$

$7\ R6$

Correct answer:

$7\ R7$

Explanation:

We can start with squares and keep adding on top of the previous until we've used all squares. Our rectangular array is squares high with squares left over, which is our remainder.

$70\div9=7\ R7$

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Example Question #31 : Use Place Value Understanding And Properties Of Operations To Perform Multi Digit Arithmetic

Solve $9{\overline{\smash{)}100}}$ by making a rectangular array.

Possible Answers:

$10\ R1$

$11\ R2$

$10\ R2$

$11\ R1$

$9\ R1$

Correct answer:

$11\ R1$

Explanation:

Using our problem to make a rectangular array, we know that we are going to use a total of 100 squares, and one dimension of the rectangular array is going to have squares, we'll make that the width. Our answer will be how many squares high the rectangle array is, or the height.

We can start with squares and keep adding on top of the previous until we've used all 100 squares. Our rectangular array is squares high with square left over, which is our remainder.

$100\div9=11\ R1$

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Example Question #233 : Number & Operations In Base Ten

Solve $9{\overline{\smash{)}119}}$ by making a rectangular array.

Possible Answers:

$12\ R3$

$13\ R4$

$12\ R2$

$13\ R2$

$13\ R5$

Correct answer:

$13\ R2$

Explanation:

Using our problem to make a rectangular array, we know that we are going to use a total of 119 squares, and one dimension of the rectangular array is going to have squares, we'll make that the width. Our answer will be how many squares high the rectangle array is, or the height.

We can start with squares and keep adding on top of the previous until we've used all 119 squares. Our rectangular array is squares high with squares left over, which is our remainder.

$119\div9=13\ R2$

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Example Question #31 : Use Place Value Understanding And Properties Of Operations To Perform Multi Digit Arithmetic

Solve $5{\overline{\smash{)}49}}$ by making a rectangular array.

Possible Answers:

$8\ R2$

$8\ R3$

$9\ R4$

$9\ R3$

$8\ R4$

Correct answer:

$9\ R4$

Explanation:

We can start with squares and keep adding on top of the previous until we've used all squares. Our rectangular array is squares high with squares left over, which is our remainder.

$49\div5=9\ R4$

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Example Question #1 : Adding Multi Digit Numbers

Solve:

$\frac{\begin{array}[b]{r}687\\ +\ 410\end{array}}{\space }$

Possible Answers:

$1\textup,097$

$1\textup,095$

$1\textup,098$

$1\textup,096$

Correct answer:

$1\textup,097$

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left to the tens place, followed by the hundreds place.

Add the numbers in the ones place:

7+0=7

Add the numbers in the tens place:

8+1=9

Add the numbers in the hundreds place:

6+4=10

Your final answer should be 1097:

$\frac{\begin{array}[b]{r}687\\ +\ 410\end{array}}{\ \ 1097}$

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Example Question #2 : Adding Multi Digit Numbers

Solve:

$\frac{\begin{array}[b]{r}412\\ +\ 896\end{array}}{\space }$

Possible Answers:

$1\textup,307$

$1\textup,308$

$1\textup,309$

$1\textup,310$

Correct answer:

$1\textup,308$

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left to the tens place, followed by the hundreds place.

Add the numbers in the ones place:

2+6=8

Add the numbers in the tens place:

1+9=10

Because this sum is greater than , we write the from the ones place and carry the from the tens place over to the left. Your work should look something like this:

$\frac{\begin{array}[b]{r}^{{\color{Red} 1}}412\\ +\ 896\end{array}}{\ \ \ \ \ 08 }$

Add the numbers in the hundreds place, including the that was carried over:

1+4+8=13

Your final answer should be 1308:

$\frac{\begin{array}[b]{r}^{1}412\\ +\ 896\end{array}}{\ \ 1308 }$

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Example Question #241 : Number & Operations In Base Ten

Solve:

$\frac{\begin{array}[b]{r}569\\ +\ 221\end{array}}{\space }$

Possible Answers:

790

792

793

791

Correct answer:

790

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left to the tens place, followed by the hundreds place.

Add the numbers in the ones place:

9+1=10

Because this sum is greater than , we write the from the ones place and carry the from the tens place over to the left. Your work should look something like this:

$\frac{\begin{array}[b]{r}5^{{\color{Red} 1}}6\ 9\\ +\ 2\ 2\ 1\end{array}}{\ \ \ \ \ \ \ \ 0 }$

Add the numbers in the tens place, including the that was carried over:

1+6+2=9

Add the numbers in the hundreds place:

5+2=7

Your final answer should be 790:

$\frac{\begin{array}[b]{r}569\\ +\ 221\end{array}}{\ \ \ 790 }$

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Example Question #3 : Adding Multi Digit Numbers

Solve:

$\frac{\begin{array}[b]{r}495\\ +\ 519\end{array}}{\space }$

Possible Answers:

$1\textup,012$

$1\textup,011$

$1\textup,013$

$1\textup,014$

Correct answer:

$1\textup,014$

Explanation:

When we add with multi-digit numbers, we start with the numbers in the ones place, and then move to the left to the tens place, followed by the hundreds place.

Add the numbers in the ones place:

5+9=14

Because this sum is greater than , we write the from the ones place and carry the from he tens place over to the left. Your work should look something like this:

$\frac{\begin{array}[b]{r}4^{{\color{Red} 1}}9\ 5\\ +\ 5\ 1\ 9\end{array}}{\ \ \ \ \ \ \ \ 4 }$

Add the numbers in the tens place, including the that was carried over:

1+9+1=11

Because this sum is greater than , we write the from the ones place and carry the from the tens place over to the left. Your work should look something like this:

$\frac{\begin{array}[b]{r}^{{\color{Red} 1}}4^{{\color{Red} 1}}9\ 5\\ +\ 5\ 1\ 9\end{array}}{\ \ \ \ \ \ 1\ 4 }$

Add the numbers in the hundreds place, including the that was carried over:

1+4+5=10

Your final answer should be 1014:

$\frac{\begin{array}[b]{r}295\\ +\ 519\end{array}}{\ \ 1014}$

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All Common Core: 4th Grade Math Resources

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Common Core: 4th Grade Math : Use place value understanding and properties of operations to perform multi-digit arithmetic

Study concepts, example questions & explanations for Common Core: 4th Grade Math

All Common Core: 4th Grade Math Resources

Example Questions

Example Question #531 : How To Divide

Example Question #3808 : Numbers And Operations

Example Question #532 : How To Divide

Example Question #31 : Use Place Value Understanding And Properties Of Operations To Perform Multi Digit Arithmetic

Example Question #233 : Number & Operations In Base Ten

Example Question #31 : Use Place Value Understanding And Properties Of Operations To Perform Multi Digit Arithmetic

Example Question #1 : Adding Multi Digit Numbers

Example Question #2 : Adding Multi Digit Numbers

Example Question #241 : Number & Operations In Base Ten

Example Question #3 : Adding Multi Digit Numbers

All Common Core: 4th Grade Math Resources

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