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Common Core: 7th Grade Math : Ratios & Proportional Relationships

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #591 : Arithmetic

6 decreased by what percent is $4\frac{2}{3}$ ?

Select the closest answer.

Possible Answers:

$20 \%$

$30 \%$

$25 \%$

$15 \%$

Correct answer:

$20 \%$

Explanation:

The difference of 6 and $4\frac{2}{3}$ is

$6 - 4\frac{2}{3}$

$= \frac{6 \times 3}{3} - \frac{4 \times 3+ 2}{3}$

$= \frac{18}{3} - \frac{14}{3}$

$= \frac{18-14}{3}$

$= \frac{ 4}{3}$ .

Therefore, 6 is being decreased by $\frac{ 4}{3}$ ; to find out what percent this is of 6, we calculate:

$\frac{\frac{ 4}{3}}{6} \times 100 \%$

$=\left ( \frac{ 4}{3} \div 6 \right ) \times 100 \%$

$=\left ( \frac{ 4}{3} \times \frac{1}{6} \right ) \times 100 \%$

$=\left ( \frac{ 2}{3} \times \frac{1}{3} \right ) \times \frac{100 }{1}\%$

$=\left ( \frac{ 2 \times 1 \times 100}{3 \times 3 \times 1} \right ) \%$

$= \frac{ 2 00}{9} \%$

$2 00 \div 9 = 22 \textup{ R 2}$ , so

$\frac{ 2 00}{9} \% = 22\frac{ 2 }{9} \%$ .

The answer that comes closest among the four choices is 20%.

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Example Question #71 : Percentages

What is the percentage of male students in a class if are male out of students?

Possible Answers:

$100\%$

60%

$75\%$

$50\%$

Correct answer:

$75\%$

Explanation:

First you want to make a proportion so $\frac{15}{20}$ of the class are male.

You can reduce this fraction by since both the numerator and denominator are divisible by it.

This gives you $\frac{3}{4}$ which as a decimal is 0.75 .

To make that into a percentage, you multiple by 100 and add a "%" symbol.

So that gives you $75\%$ .

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Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

is 30% of ; is 42% of .

is what percent of ?

Possible Answers:

$140 \%$

$71 \frac{3}{7} \%$

$28 \frac{4}{7} \%$

$40 \%$

Correct answer:

$140 \%$

Explanation:

We can choose a specific value for ; the reasoning is independent of this value.

Assume C = 100 . Then

$A = 100 \cdot 30 \% = 100 \cdot \frac{30}{100} = 30$

and

$B = 100 \cdot 42 \% = 100 \cdot \frac{42}{100} = 42$

To find out what percent is of , calculate:

$\frac{B}{A} \times 100 \% = \frac{42}{30} \times 100 \% = 140 \%$

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Example Question #171 : Ratios & Proportional Relationships

If you get a 25% discount, what percentage of the original price will you have to pay?

Possible Answers:

$25\%$

$80\%$

$75\%$

$100\%$

Correct answer:

$75\%$

Explanation:

The original price will represent 100% of the item price since that represents the whole for the problem.

If you get 25% off, you must take that away from the 100%.

100-25=75

so you will have to pay 75% of the original price.

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Example Question #172 : Ratios & Proportional Relationships

What is the sale price of a product that costs $\$500$ if the sale is $40\%$ off the original price?

Possible Answers:

$\$540$

$\$700$

$\$200$

$\$800$

$\$300$

Correct answer:

$\$300$

Explanation:

First, find $40\%$ of $\$500$ :

$0.4\cdot \$500=\$200$

Then, subtract this value from the whole:

$\$500-\$200=\$300$

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Example Question #611 : Arithmetic

What is the sale price of a television if it is on sale for % off the original price of $\$175.00?$

Possible Answers:

$\$125.00$

$\$50.00$

$\$122.50$

$\$75.00$

$\$52.50$

Correct answer:

$\$52.50$

Explanation:

First, multiply:

$175.00\ast .70=122.50$

Then subtract that amount from the original price:

175.00-122.50=52.50

Answer: The sale price is $\$52.50$ .

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Example Question #173 : Ratios & Proportional Relationships

A sweater was originally $\$38.00$ , but the department store is running a $15\%$ off sale. What is the sale price of the sweater?

Possible Answers:

$\$22.70$

$\$32.30$

$\$12.50$

$\$30.00$

$\$5.70$

Correct answer:

$\$32.30$

Explanation:

In order to solve this problem, we need to calculate $15\%$ of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

$15\%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}38\\ \times\ .15\end{array}}{ \ \ \ \space 5.70}$

Remember, we are taking $15\%$ off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}38.00\\ -\ 5.70\end{array}}{ \ \ \ \space 32.30}$

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Example Question #174 : Ratios & Proportional Relationships

A sweater was originally $\$22.00$ , but the department store is running a $15\%$ off sale. What is the sale price of the sweater?

Possible Answers:

$\$15.00$

$\$11.23$

$\$18.70$

$\$3.30$

$\$7.80$

Correct answer:

$\$18.70$

Explanation:

In order to solve this problem, we need to calculate $15\%$ of $\$22.00$ . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

$15\%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}22\\ \times\ .15\end{array}}{ \ \ \ \space 3.30}$

Remember, we are taking $15\%$ off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}22.00\\ -\ 3.30\end{array}}{ \ \ \ \space 18.70}$

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Example Question #175 : Ratios & Proportional Relationships

A sweater was originally $\$41.00$ , but the department store is running a $15\%$ off sale. What is the sale price of the sweater?

Possible Answers:

$\$37.35$

$\$10.14$

$\$19.34$

$\$34.85$

$\$6.15$

Correct answer:

$\$34.85$

Explanation:

In order to solve this problem, we need to calculate $15\%$ of $\$41.00$ . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

$15\%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}41\\ \times\ .15\end{array}}{ \ \ \ \space 6.15}$

Remember, we are taking $15\%$ off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}41.00\\ -\ 6.15\end{array}}{ \ \ \ \space 34.85}$

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Example Question #176 : Ratios & Proportional Relationships

A sweater was originally $\$15.00$ , but the department store is running a $15\%$ off sale. What is the sale price of the sweater?

Possible Answers:

$\$2.25$

$\$20.75$

$\$12.75$

$\$2.75$

$\$15.50$

Correct answer:

$\$12.75$

Explanation:

In order to solve this problem, we need to calculate $15\%$ of $\$15.00$ . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

$15\%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}15\\ \times\ .15\end{array}}{ \ \ \ \space 2.25}$

Remember, we are taking $15\%$ off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}15.00\\ -\ 2.25\end{array}}{ \ \ \space 12.75}$

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Common Core: 7th Grade Math : Ratios & Proportional Relationships

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #591 : Arithmetic

Example Question #71 : Percentages

Example Question #11 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #171 : Ratios & Proportional Relationships

Example Question #172 : Ratios & Proportional Relationships

Example Question #611 : Arithmetic

Example Question #173 : Ratios & Proportional Relationships

Example Question #174 : Ratios & Proportional Relationships

Example Question #175 : Ratios & Proportional Relationships

Example Question #176 : Ratios & Proportional Relationships

All Common Core: 7th Grade Math Resources

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