Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: 5th Grade Math : Number & Operations in Base Ten

Study concepts, example questions & explanations for Common Core: 5th Grade Math

Create An Account

All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #121 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

2221

22110

2211

2201

Correct answer:

2211

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.

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

For this problem, 33 is the multiplier and 67 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

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

Then, we multiply 3 and 6 and add the 2 that was carried

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

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.

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

Next, we multiply 3 and 7

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

Then, we multiply 3 and 6and add the 2 that was carried

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

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

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

Report an Error

Example Question #122 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

4320

43200

4330

4310

Correct answer:

4320

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.

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

For this problem, 72 is the multiplier and 60 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

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

Then, we multiply 2 and 6

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

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

Next, we multiply 7 and 0

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

Then, we multiply 7 and 6

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

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

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

Report an Error

Example Question #131 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

4077

40870

4087

4097

Correct answer:

4087

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.

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

For this problem, 67 is the multiplier and 61 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 1

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

Then, we multiply 7 and 6

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

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

Next, we multiply 6 and 1

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

Then, we multiply 6 and 6

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

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

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

Report an Error

Example Question #132 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

27470

2737

2747

2757

Correct answer:

2747

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.

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

For this problem, 41 is the multiplier and 67 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 7

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

Then, we multiply 1 and 6

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

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

Next, we multiply 4 and 7

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

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

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

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

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

Report an Error

Example Question #133 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Solve:

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

Possible Answers:

19320

1942

1922

1932

Correct answer:

1932

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.

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

For this problem, 23 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 3 and 4

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

Then, we multiply 3 and 8 and add the 1 that was carried

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

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

Next, we multiply 2 and 4

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

Then, we multiply 2 and 8

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

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

$\begin{array}{r}\overset{~ \space{\ }}{\ 8} \space{\,}4\\ \times \phantom{0} 2\space{\,}3 \\ \hline \phantom{\,}2\,5\,2 \\+\, 1\, 6\, 8 \, 0\\ \hline 1\, 9 \, 3\, 2\end{array}$

Report an Error

Example Question #1 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

$3828\div 22=$

Possible Answers:

503

356

132

174

Correct answer:

174

Explanation:

Report an Error

Example Question #2 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

$13{\overline{\smash{)}143}}$

Possible Answers:

Correct answer:

Explanation:

Before we begin, let's review the pieces of a division problem:

${\begin{array}[b]{r} \ \textup{ quotient}\\ \textup{ divisor}{\overline{\smash{)}\ \textup{dividend}}}\\\end{array}}{ \ \ \ \space}$

The quotient is the answer to the division problem. The dividend is the number that gets divided by the divisor.

One way to solve a division problem is to create an area model. The divisor equals the number of squares that make up the base of the area model. The dividend equals the number of total squares used. Fill the squares up from the base until you've used the correct number of squares. The height of the area model will be the quotient:

Another way to solve a division problem is to think of it as a multiplication problem. What number times the divisor equals the dividend?

$13\times$ __________ =143

$\frac{\begin{array}[b]{r}13\\ \times \ \ \ 11\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 13}\\ \ +\ {\color{black} 130} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 143}$

This means that $13\times {\color{Red} 11}=143$ ; thus, ${\begin{array}[b]{r} \ \textup{ {\color{Red} 11}}\\ \textup{ 13}{\overline{\smash{)}\ \textup{143}}}\\\end{array}}{ \ \ \ \space}$

Report an Error

Example Question #3 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

$21{\overline{\smash{)}357}}$

Possible Answers:

Correct answer:

Explanation:

Before we begin, let's review the pieces of a division problem:

${\begin{array}[b]{r} \ \textup{ quotient}\\ \textup{ divisor}{\overline{\smash{)}\ \textup{dividend}}}\\\end{array}}{ \ \ \ \space}$

The quotient is the answer to the division problem. The dividend is the number that gets divided by the divisor.

Another way to solve a division problem is to think of it as a multiplication problem. What number times the divisor equals the dividend?

$21\times$ __________ =357

$\frac{\begin{array}[b]{r}21\\ \times \ \ \ 17\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 147}\\ \ +\ {\color{black} 210} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 357}$

This means that $21\times {\color{Red} 17}=357$ ; thus, ${\begin{array}[b]{r} \ \textup{ {\color{Red} 17}}\\ \textup{ 21}{\overline{\smash{)}\ \textup{357}}}\\\end{array}}{ \ \ \ \space}$

Report an Error

Example Question #841 : Common Core Math: Grade 5

Solve:

$12{\overline{\smash{)}432}}$

Possible Answers:

Correct answer:

Explanation:

Before we begin, let's review the pieces of a division problem:

${\begin{array}[b]{r} \ \textup{ quotient}\\ \textup{ divisor}{\overline{\smash{)}\ \textup{dividend}}}\\\end{array}}{ \ \ \ \space}$

The quotient is the answer to the division problem. The dividend is the number that gets divided by the divisor.

Another way to solve a division problem is to think of it as a multiplication problem. What number times the divisor equals the dividend?

$12\times$ __________ =432

$\frac{\begin{array}[b]{r}36\\ \times \ \ \ 12\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 72}\\ \ +\ {\color{black} 360} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 432}$

This means that $12\times {\color{Red} 36}=432$ ; thus, ${\begin{array}[b]{r} \ \textup{ {\color{Red} 36}}\\ \textup{ 12}{\overline{\smash{)}\ \textup{432}}}\\\end{array}}{ \ \ \ \space}$

Report an Error

Example Question #4 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Solve:

$33{\overline{\smash{)}759}}$

Possible Answers:

Correct answer:

Explanation:

Before we begin, let's review the pieces of a division problem:

${\begin{array}[b]{r} \ \textup{ quotient}\\ \textup{ divisor}{\overline{\smash{)}\ \textup{dividend}}}\\\end{array}}{ \ \ \ \space}$

The quotient is the answer to the division problem. The dividend is the number that gets divided by the divisor.

Another way to solve a division problem is to think of it as a multiplication problem. What number times the divisor equals the dividend?

$33\times$ __________ =759

$\frac{\begin{array}[b]{r}33\\ \times \ \ \ 23\end{array}}{\frac{\begin{array}[b]{r}{\color{black} 99}\\ \ +\ {\color{black} 660} \end{array}}{\ }} \\ {\ \ \ \ \ \ \ \ \ \ \ 759}$

This means that $33\times {\color{Red} 23}=759$ ; thus, ${\begin{array}[b]{r} \ \textup{ {\color{Red} 23}}\\ \textup{ 33}{\overline{\smash{)}\ \textup{759}}}\\\end{array}}{ \ \ \ \space}$

Report an Error

View Tutors

Patrick
Certified Tutor

LeTourneau University, Bachelors, Electrical Engineering. LeTourneau University, Masters, Electrical Engineering.

View Tutors

Jamie
Certified Tutor

East Central University, Bachelors, Special Education.

View Tutors

Kenneth
Certified Tutor

North Georgia University, Bachelors, Accounting. Brenau University, Masters, Business.

All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Phoenix, ISEE Tutors in Miami, Math Tutors in New York City, ACT Tutors in Atlanta, Calculus Tutors in Phoenix, Calculus Tutors in Philadelphia, ISEE Tutors in Houston, Physics Tutors in Washington DC, ISEE Tutors in Denver, Computer Science Tutors in Phoenix

Popular Courses & Classes

LSAT Courses & Classes in San Diego, GRE Courses & Classes in San Diego, GRE Courses & Classes in Houston, GMAT Courses & Classes in Atlanta, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Seattle, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Boston, LSAT Courses & Classes in New York City

Popular Test Prep

ISEE Test Prep in Denver, ACT Test Prep in Los Angeles, LSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Seattle, LSAT Test Prep in Chicago, GRE Test Prep in Philadelphia, MCAT Test Prep in Houston, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, SAT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Common Core: 5th Grade Math : Number & Operations in Base Ten

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #121 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #122 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #131 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #132 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #133 : Fluently Multiply Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.5

Example Question #1 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Example Question #2 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Example Question #3 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

Example Question #841 : Common Core Math: Grade 5

Example Question #4 : Fluently Divide Multi Digit Whole Numbers: Ccss.Math.Content.5.Nbt.B.6

All Common Core: 5th Grade Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: