Ratios and Proportional Relationships: Solving Problems with Ratios, Rates, Percents, and Conversions (CCSS.6.RP.3)
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Common Core 6th Grade Math › Ratios and Proportional Relationships: Solving Problems with Ratios, Rates, Percents, and Conversions (CCSS.6.RP.3)
A store sells 6 apples for 3 dollars. What is the unit price per apple?
\$0.50 per apple
\$2 per apple
\$18 per apple
\$6 per apple
Explanation
Price per 1 apple: $3 ÷ 6 = $0.50 per apple.
A store sells 12 apples for \$6. What is the cost per apple?
\$0.50 per apple
\$2.00 per apple
\$6.00 per apple
\$0.60 per apple
Explanation
Find the cost for 1 apple: 6 ÷ 12 = \$0.50 per apple.
A bag of 12 apples costs \$9. What is the unit price per apple?
\$0.75 per apple
\$1.33 per apple
\$9.00 per apple
\$0.80 per apple
Explanation
Price per apple is total cost ÷ number of apples: $9 \div 12 = 0.75$. So it costs \$0.75 per apple. The \$1.33 comes from dividing backward ($12 \div 9$), and \$9.00$ forgets to divide.
A pack of 8 markers costs \$12. What is the price per marker?
\$1.50 per marker
\$0.67 per marker
\$20.00 per marker
\$96.00 per marker
Explanation
Find the cost per 1 marker by dividing total cost by number of markers: 12 ÷ 8 = 1.50 dollars per marker.
A pack of 6 bottles costs \$9. What is the unit price per bottle? Then, at this price, what would 4 bottles cost?
\$9 per bottle; \$36
\$1.50 per bottle; \$9
\$0.67 per bottle; \$2.68
\$1.50 per bottle; \$6
Explanation
Compute per 1 bottle: total cost ÷ number of bottles. $9 \div 6 = 1.5$ dollars per bottle. Extension: multiply by 4 bottles: $1.5 \times 4 = 6$ dollars. \$0.67$ comes from dividing the wrong way ($6 \div 9$), and some choices ignore the extension.
A bakery sells 12 muffins for 9 dollars. What is the price per muffin?
1.33 dollars per muffin
9 dollars per muffin
1.50 dollars per muffin
0.75 dollars per muffin
Explanation
Divide dollars by muffins: 9 ÷ 12 = 0.75 dollars per muffin. Don't reverse the division.
It took 7 hours to mow 4 lawns. What is the unit rate in lawns per hour?
1.75 lawns/hour
4 lawns/hour
28 lawns/hour
0.57 lawns/hour
Explanation
Per hour means lawns ÷ hours: 4 ÷ 7 ≈ 0.57 lawns per hour.
Jordan runs 3 laps in 12 minutes. What is the unit rate in minutes per lap?
12 minutes/lap
3 minutes/lap
0.25 minutes/lap
4 minutes/lap
Explanation
Minutes per lap means total minutes ÷ laps: $12 \div 3 = 4$. So it is 4 minutes/lap. The \$0.25$ comes from dividing backward ($3 \div 12$).
It took 7 hours to mow 4 lawns. At this rate, how many lawns can be mowed in 35 hours?
140 lawns
0.57 lawns
20 lawns
8.75 lawns
Explanation
Lawns per hour: 4 ÷ 7. In 35 hours: 35 × (4 ÷ 7) = 35 × 4/7 = 20 lawns.
A train travels 150 miles in 2 hours. What is the speed in miles per hour, and at that rate, how far will it go in 3 hours?
150 miles
75 miles
300 miles
225 miles
Explanation
First find the unit rate: 150 ÷ 2 = 75 miles/hour. Then extend: 75 × 3 = 225 miles.