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5th Grade Math : 5th Grade Math

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

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All 5th Grade Math Resources

8 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Number Sense

What is $6\times10^7$ in standard form?

Possible Answers:

$60\textup,000\textup,000$

$600\textup,000$

$60\textup,000$

$6\textup,000\textup,000$

Correct answer:

$60\textup,000\textup,000$

Explanation:

The power of tells us how to move our decimal. Because we have a positive power, we move our decimal over places to the right.

$6.\rightarrow 60000000.$

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Example Question #1 : Number Sense

What digit is in the hundredths place?

564.391

Possible Answers:

Correct answer:

Explanation:

When we have numbers that include decimals, the tenths place is always the first number to the right of the decimal, the hundredths place is to the right of the tenths place, and the thousandths place is to the right of the hundredths place. See the diagram below:

For the number in the problem:

564.391

The is in the hundredths position.

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Example Question #3 : Number Sense

What is 2.37 in expanded form?

Possible Answers:

$2\times1+3\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{100}\right)$

$2\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

$2\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)$

$2\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)$

Correct answer:

$2\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

Explanation:

When we write a number in expanded form, we multiply each digit by its place value.

is in the ones place, so we multiply by .

$2\times1=2$

is in the tenths place, so we multiply by $\frac{1}{10}$ .

$3\times\frac{1}{10}=.3$

is in the hundredths place, so we multiply by $\frac{1}{100}$ .

$7\times\frac{1}{100}=.07$

Then we add the products together to check our answer:

$\frac{\begin{array}[b]{r}2.00\\ +\ .30\\ .07 \end{array}}{ \ \ \space2.37}$

Thus, the correct answer is:

$2\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)$

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Example Question #1 : Operations

Solve:

$\frac{5}{9}\times \frac{6}{13}$

Possible Answers:

$\frac{45}{123}$

$\frac{10}{39}$

$\frac{9}{11}$

$\frac{8}{7}$

Correct answer:

$\frac{10}{39}$

Explanation:

When we multiply fractions, we multiply the numerator by the numerator and the denominator by the denominator.

$\frac{5}{9}\times \frac{6}{13}=\frac{30}{117}$

$\frac{30}{117}$ can be reduced to $\frac{10}{39}$ by dividing both sides by .

$\frac{30}{117}\frac{\div}{\div}\frac{3}{3}=\frac{10}{39}$

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Example Question #2 : Operations

Solve:

$2\times (50-25)\div5$

Possible Answers:

Correct answer:

Explanation:

$2\times (50-25)\div5$

When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then the division.

50-25=25

$25\times2=50$

$50\div5=10$

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Example Question #3 : Operations

Heather collected $\small \frac{1}{2}$ of a bag of leaves. Matt collected times as many bags as Heather. How many bags did Matt collect?

Possible Answers:

$\small 1\frac{1}{3}$

$\small 1$

$\small 1\frac{1}{2}$

$\small \frac{1}{6}$

Correct answer:

$\small 1\frac{1}{2}$

Explanation:

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{3}{1}\times\frac{1}{2}=\frac{3}{2}$

$\small \frac{3}{2}=1\frac{1}{2}$ Because can go into $\small 3$ only $\small 1$ time and $\small \frac{1}2{}$ is left over.

Matt collected $\small 1\frac{1}2{}$ bags of leaves.

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Example Question #4 : Operations

Solve:

$3\times2+(10-8)$

Possible Answers:

Correct answer:

Explanation:

$3\times2+(10-8)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication, and then the addition.

10-8=2

$3\times2=6$

6+2=8

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Example Question #1 : Data

What coordinate point is the red circle on?

Screen shot 2015 07 29 at 4.25.25 pm

Possible Answers:

(30,6)

(6,30)

(17,8)

(8,17)

Correct answer:

(30,6)

Explanation:

To find the location on a coordinate plane we first look at the -axis, which runs horizontal and then the -axis, which runs vertical. We write the point on the -axis first, followed by the point on the -axis. (x,y)

The red circle is over on the -axis and up on the -axis.

The correct answer is (30,6)

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Example Question #1 : Measurement

How many $\textup { centimeters}$ are in $5\textup { meters?}$

Possible Answers:

$50\textup { centimeters}$

$5\textup { centimeters}$

$500\textup { centimeters}$

$5\textup,000\textup { centimeters}$

Correct answer:

$500\textup { centimeters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{5\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 5\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 5\ meters}{.01\ meter}= x\ centimeters$

The meters will cancel and we are left with $500\ centimeters$

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Example Question #1 : Geometry

What is the volume of the shape below?

Screen shot 2015 07 28 at 3.39.34 pm

Possible Answers:

$\small 8cm^3$

$\small 7cm^3$

$\small 5cm^3$

$\small 6cm^3$

Correct answer:

$\small 6cm^3$

Explanation:

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

We can use this formula and plug in the value from the question:

$\small v=3\times1\times2$

$\small v=6cm^3$

Remember, volume is always labeled as units to the third power.

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5th Grade Math : 5th Grade Math

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

All 5th Grade Math Resources

Example Questions

Example Question #1 : Number Sense

Example Question #1 : Number Sense

Example Question #3 : Number Sense

Example Question #1 : Operations

Example Question #2 : Operations

Example Question #3 : Operations

Example Question #4 : Operations

Example Question #1 : Data

Example Question #1 : Measurement

Example Question #1 : Geometry

All 5th Grade Math Resources

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