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5th Grade Math : Operations

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

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Example Questions

Example Question #1 : Operations

Solve:

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

Possible Answers:

$\frac{45}{123}$ $\displaystyle \frac{45}{123}$

$\frac{10}{39}$ $\displaystyle \frac{10}{39}$

$\frac{9}{11}$ $\displaystyle \frac{9}{11}$

$\frac{8}{7}$ $\displaystyle \frac{8}{7}$

Correct answer:

$\frac{10}{39}$ $\displaystyle \frac{10}{39}$

Explanation:

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

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

$\frac{30}{117}$ $\displaystyle \frac{30}{117}$ can be reduced to $\frac{10}{39}$ $\displaystyle \frac{10}{39}$ by dividing both sides by $\displaystyle 3$ .

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

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Example Question #1 : Operations

Solve:

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

Possible Answers:

$\displaystyle 15$

$\displaystyle 10$

$\displaystyle 25$

$\displaystyle 50$

Correct answer:

$\displaystyle 10$

Explanation:

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

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

$\displaystyle 50-25=25$

$25\times2=50$ $\displaystyle 25\times2=50$

$50\div5=10$ $\displaystyle 50\div5=10$

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Example Question #2 : Operations

Heather collected $\small \frac{1}{2}$ $\displaystyle \small \frac{1}{2}$ of a bag of leaves. Matt collected $\displaystyle 3$ times as many bags as Heather. How many bags did Matt collect?

Possible Answers:

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

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

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

$\small 1$ $\displaystyle \small 1$

Correct answer:

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

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 $\small 1.$ $\displaystyle \small 1.$ Then we multiply like normal.

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

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

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

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Example Question #3 : Operations

Solve:

$3\times2+(10-8)$ $\displaystyle 3\times2+(10-8)$

Possible Answers:

$\displaystyle 14$

$\displaystyle 8$

$\displaystyle 10$

$\displaystyle 5$

Correct answer:

$\displaystyle 8$

Explanation:

$3\times2+(10-8)$ $\displaystyle 3\times2+(10-8)$

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

10-8=2 $\displaystyle 10-8=2$

$3\times2=6$ $\displaystyle 3\times2=6$

6+2=8 $\displaystyle 6+2=8$

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5th Grade Math : Operations

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

All 5th Grade Math Resources

Example Questions

Example Question #1 : Operations

Example Question #1 : Operations

Example Question #2 : Operations

Example Question #3 : Operations

All 5th Grade Math Resources

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