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

How much would a $\$30$ product sold for $20\%$ off cost?

Possible Answers:

$\$20$

$\$25$

$\$24$

$\$36$

Correct answer:

$\$24$

Explanation:

First, find $20\%$ of $\$30$ :

$0.2\cdot \$30=\$6$

Then, subtract this value from the whole:

$\$30-\$6=\$24$

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Example Question #2 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

How much would a $\$110$ product sold for $10\%$ off cost?

Possible Answers:

$\$10$

$\$99$

$\$11$

$\$100$

Correct answer:

$\$99$

Explanation:

First, find $10\%$ of $\$110$ :

$0.1\cdot \$110=\$11$

Then, subtract this value from the whole:

$\$110-\$11=\$99$

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

200 percent of what number is equal to the difference between 75 and 25?

Possible Answers:

$\small 20$

$\small 25$

$\small 50$

$\small 200$

$\small 30$

Correct answer:

$\small 25$

Explanation:

We must first start by finding the difference between $\small 75$ and $\small 25$ :

$\small 75-25 = 50$

Next find the decimal equivalent of $\small 200$ %, which is done by dividing by $\small 100$ :

$\small 200/100 = 2$

Now we divide $\small 50$ by $\small 2$ .

$\small 50/2 = 25$

Our final answer is $\small 25$ , because when it is multiplied by $\small 200$ %, it equals the difference between $\small 75$ and $\small 25$ .

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Example Question #541 : Arithmetic

What is the sale price of a game if it is % off the original price of $\$35.00$ ?

Possible Answers:

$\$22.00$

$\$27.00$

$\$35.00$

$\$34.65$

$\$22.75$

Correct answer:

$\$22.75$

Explanation:

First, multiply:

$35\ast .35=12.25$

Then subtract that amount from the original price:

35.00-12.25=22.75

Answer: The sale price is $\$22.75$ .

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Example Question #4 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the sale price of a carton of milk if it is % off the original price of $\$3.20$ ?

Possible Answers:

$\$1.00$

$\$2.88$

$\$3.00$

$\$2.30$

$\$1.20$

Correct answer:

$\$2.88$

Explanation:

First, multiply:

$3.20\ast .10=.32$

Then subtract that amount from the original price:

3.20-.32=2.88

Answer: The sale price is $\$2.88$ .

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Example Question #543 : Arithmetic

What is the sale price of a pair of shoes if it is % off the original price of $\$90.00$ ?

Possible Answers:

$\$62.50$

$\$49.50$

$\$60.00$

$\$32.00$

$\$50.00$

Correct answer:

$\$49.50$

Explanation:

First, multiply:

$90.00\ast .45=40.50$

Then subtract that amount from the original price:

90.00-40.50=49.50

Answer: The sale price is $\$49.50$ .

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Example Question #5 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

240 is 30% of what number?

Possible Answers:

800

960

720

Correct answer:

800

Explanation:

Set up the proportion statement and solve for :

$\frac{240}{N}= \frac{30}{100}$

Cross-multiply:

$N\cdot 30 = 240\cdot 100 = 24,000$

$N\cdot 30 \div 30= 24,000 \div 30$

N=800

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Example Question #6 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

420 is 150% of what number?

Possible Answers:

210

840

300

280

630

Correct answer:

280

Explanation:

Set up the proportion statement and solve for by cross-multiplying:

$\frac{420}{N}= \frac{150}{100}$

$N \cdot 150 = 420 \cdot 100 = 42,000$

$N \cdot 150 \div 150 = 42,000 \div 150$

N = 280

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Example Question #6 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What number increased by 25% is equal to 7?

Possible Answers:

$5\frac{5}{6}$

$5\frac{1}{4}$

$4\frac{2}{3}$

$5 \frac{3}{5}$

Correct answer:

$5 \frac{3}{5}$

Explanation:

To increase a number by 25% is to take

$(100 + 25) \% = 125 \%$ of the number, or, equivalently, multiply it by

$\frac{125}{100} = \frac{125 \div 25 }{100 \div 25 } = \frac{5}{4}$ .

Therefore, we divide 7 by $\frac{5}{4}$ :

$7 \div \frac{5}{4} = \frac{7 }{1}\div \frac{5}{4} = \frac{7 }{1}\times \frac{4} {5}= \frac{7\times 4 }{1\times 5} = \frac{28}{5}$

$28 \div 5 = 5 \textup{ R }3$ , so

$\frac{28}{5} = 5 \frac{3}{5}$ .

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

What number decreased by 25% is equal to 7?

Possible Answers:

$9 \frac{1}{3}$

$8\frac{2}{5}$

$8\frac{3}{4}$

$9 \frac{1}{7}$

Correct answer:

$9 \frac{1}{3}$

Explanation:

To decrease a number by 25% is to take

$(100 - 25) \% = 75 \%$ of the number, or, equivalently, multiply it by

$\frac{75}{100} = \frac{75 \div 25 }{100 \div 25 } = \frac{3}{4}$ .

Therefore, we divide 7 by $\frac{3}{4}$ :

$7 \div \frac{3}{4} = \frac{7 }{1}\div \frac{3}{4} = \frac{7 }{1}\times \frac{4} {3}= \frac{7\times 4 }{1\times 3} = \frac{28}{3}$

$28 \div 3 = 9 \textup{ R }1$ , so

$\frac{28}{3} = 9 \frac{1}{3}$ .

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

Example Question #2 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

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

Example Question #541 : Arithmetic

Example Question #4 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #543 : Arithmetic

Example Question #5 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #6 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #6 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

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

All Common Core: 7th Grade Math Resources

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