Practice
Ratios and Rates Practice
Fifty original questions covering ratio order, equivalent ratios, unit price, rates, density, mileage, totals, geometry, and multi-step ratio reasoning.
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Question 1
Explanation
The requested order places blue tiles first. Divide both parts of \(18:12\) by their greatest common factor, \(6\), to obtain \(3:2\).
Question 2
Explanation
The requested order places violinists first. Divide both parts of \(21:14\) by their greatest common factor, \(7\), to obtain \(3:2\).
Question 3
Explanation
The requested order places oak trees first. Divide both parts of \(32:24\) by their greatest common factor, \(8\), to obtain \(4:3\).
Question 4
Explanation
The requested order places digital tickets first. Divide both parts of \(45:30\) by their greatest common factor, \(15\), to obtain \(3:2\).
Question 5
Explanation
The requested order places copper beads first. Divide both parts of \(28:42\) by their greatest common factor, \(14\), to obtain \(2:3\).
Question 6
Explanation
The first ratio part was multiplied by \(8\), because \(24/3=8\). Multiply the second part by the same factor: \(5(8)=40\).
Question 7
Explanation
The first ratio part was multiplied by \(6\), because \(24/4=6\). Multiply the second part by the same factor: \(7(6)=42\).
Question 8
Explanation
The first ratio part was multiplied by \(9\), because \(45/5=9\). Multiply the second part by the same factor: \(2(9)=18\).
Question 9
Explanation
The first ratio part was multiplied by \(4\), because \(28/7=4\). Multiply the second part by the same factor: \(3(4)=12\).
Question 10
Explanation
The first ratio part was multiplied by \(7\), because \(14/2=7\). Multiply the second part by the same factor: \(9(7)=63\).
Question 11
Explanation
Unit price is package price divided by number of units: \(\$11.20/8=\$1.40\) per notebook. The denominator is \(1\) item, so this is a unit rate.
Question 12
Explanation
Unit price is package price divided by number of units: \(\$18.75/15=\$1.25\) per tea packet. The denominator is \(1\) item, so this is a unit rate.
Question 13
Explanation
Unit price is package price divided by number of units: \(\$9.60/24=\$0.40\) per storage label. The denominator is \(1\) item, so this is a unit rate.
Question 14
Explanation
Unit price is package price divided by number of units: \(\$16.50/6=\$2.75\) per art brush. The denominator is \(1\) item, so this is a unit rate.
Question 15
Explanation
Unit price is package price divided by number of units: \(\$13.00/20=\$0.65\) per seed envelope. The denominator is \(1\) item, so this is a unit rate.
Question 16
Explanation
Divide output by elapsed time: \(144/12=12\). The resulting compound unit is pages per minute.
Question 17
Explanation
Divide output by elapsed time: \(84/4=21\). The resulting compound unit is kilometers per hour.
Question 18
Explanation
Divide output by elapsed time: \(360/9=40\). The resulting compound unit is liters per minute.
Question 19
Explanation
Divide output by elapsed time: \(525/15=35\). The resulting compound unit is images per minute.
Question 20
Explanation
Divide output by elapsed time: \(132/3=44\). The resulting compound unit is miles per hour.
Question 21
Explanation
Use the named rate's unit order: \(336\) miles divided by \(12\) gallons equals \(28\) miles per gallon.
Question 22
Explanation
Use the named rate's unit order: \(468\) grams divided by \(36\) cubic centimeters equals \(13\) grams per cubic centimeter.
Question 23
Explanation
Use the named rate's unit order: \(960\) megabytes divided by \(8\) seconds equals \(120\) megabytes per second.
Question 24
Explanation
Use the named rate's unit order: \(255\) liters divided by \(15\) days equals \(17\) liters per day.
Question 25
Explanation
Use the named rate's unit order: \(728\) kilograms divided by \(14\) plots equals \(52\) kilograms per plot.
Question 26
Explanation
There are \(7\) ratio parts, so one part is \(63/(7)=9\). The requested category has 2 parts, giving \(18\).
Question 27
Explanation
There are \(10\) ratio parts, so one part is \(90/(10)=9\). The requested category has 7 parts, giving \(63\).
Question 28
Explanation
There are \(13\) ratio parts, so one part is \(104/(13)=8\). The requested category has 4 parts, giving \(32\).
Question 29
Explanation
There are \(13\) ratio parts, so one part is \(156/(13)=12\). The requested category has 8 parts, giving \(96\).
Question 30
Explanation
There are \(18\) ratio parts, so one part is \(216/(18)=12\). The requested category has 7 parts, giving \(84\).
Question 31
Explanation
The ratio contains \(2+3+5=10\) total parts. One part is \(120/10=12\), so the \(2\)-part category contains \(2(12)=24\).
Question 32
Explanation
The ratio contains \(1+4+7=12\) total parts. One part is \(144/12=12\), so the \(7\)-part category contains \(7(12)=84\).
Question 33
Explanation
The ratio contains \(3+5+8=16\) total parts. One part is \(192/16=12\), so the \(5\)-part category contains \(5(12)=60\).
Question 34
Explanation
The ratio contains \(4+6+9=19\) total parts. One part is \(228/19=12\), so the \(4\)-part category contains \(4(12)=48\).
Question 35
Explanation
The ratio contains \(5+7+13=25\) total parts. One part is \(300/25=12\), so the \(13\)-part category contains \(13(12)=156\).
Question 36
Explanation
The \(12\) parts total \(180^\circ\), so one part is \(15^\circ\). The largest angle is \(5(15)=75^\circ\).
Question 37
Explanation
Let length \(=7x\) and width \(=4x\). Then \(2(7x)+2(4x)=132\), so \(22x=132\), \(x=6\), and width \(=24\).
Question 38
Explanation
The angles total \(180^\circ\). Nine ratio parts make \(180^\circ\), so one part is \(20^\circ\) and the smallest angle is \(2(20)=40^\circ\).
Question 39
Explanation
The scale factor is \(63/9=7\), so width is \(5(7)=35\) inches. Area is \(63(35)=2{,}205\) square inches.
Question 40
Explanation
The \(19\) ratio parts total \(114\), so one part is \(6\). The longest side is \(9(6)=54\) centimeters.
Question 41
Explanation
Miles per gallon requires miles in the numerator and gallons in the denominator, so \(420/14=30\) miles per gallon.
Question 42
Explanation
Density is mass divided by volume: \(275/25=11\) grams per cubic centimeter.
Question 43
Explanation
Requested units place cups above servings. Thus \(6/15=0.4\) cup per serving; the reciprocal answers servings per cup.
Question 44
Explanation
Dollars per hour is \(153/9=17\). The reciprocal numerical value is \(9/153=1/17\), so the difference is \(17-1/17=288/17\).
Question 45
Explanation
Pages per cartridge is \(4{,}800/3=1{,}600\). Reversing the order gives its reciprocal, \(3/4{,}800=1/1{,}600\) cartridge per page.
Question 46
Explanation
Divide by \(5\): \(p=(3/5)q\), so \(p/q=3/5\) and \(p:q=3:5\).
Question 47
Explanation
Let \(x=4k\) and \(y=7k\). Then \(2(4k)+3(7k)=29k=145\), so \(k=5\) and \(x=20\).
Question 48
Explanation
The difference is \(9k-2k=7k=56\), so \(k=8\). The total is \((2+5+9)8=128\).
Question 49
Explanation
Originally A \(=7k\) and B \(=3k\). Then \(7k/(3k+8)=7/5\), so \(35k=21k+56\), \(k=4\), and the original total is \(10k=40\) liters.
Question 50
Explanation
The largest-smallest difference is \(10k-4k=6k=18{,}000\), so \(k=3{,}000\). The total is \(20k=60{,}000\) dollars.
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- Question 1Simplifying and interpreting ratiosEasy
- Question 2Simplifying and interpreting ratiosEasy
- Question 3Simplifying and interpreting ratiosEasy
- Question 4Simplifying and interpreting ratiosEasy
- Question 5Simplifying and interpreting ratiosEasy
- Question 6Equivalent ratiosEasy
- Question 7Equivalent ratiosEasy
- Question 8Equivalent ratiosEasy
- Question 9Equivalent ratiosEasy
- Question 10Equivalent ratiosEasy
- Question 11Unit priceEasy
- Question 12Unit priceEasy
- Question 13Unit priceEasy
- Question 14Unit priceEasy
- Question 15Unit priceEasy
- Question 16Constant unit ratesMedium
- Question 17Constant unit ratesMedium
- Question 18Constant unit ratesMedium
- Question 19Constant unit ratesMedium
- Question 20Constant unit ratesMedium
- Question 21Measurement rates and unitsMedium
- Question 22Measurement rates and unitsMedium
- Question 23Measurement rates and unitsMedium
- Question 24Measurement rates and unitsMedium
- Question 25Measurement rates and unitsMedium
- Question 26Two-part ratio totalsMedium
- Question 27Two-part ratio totalsMedium
- Question 28Two-part ratio totalsMedium
- Question 29Two-part ratio totalsMedium
- Question 30Two-part ratio totalsMedium
- Question 31Multi-part ratio distributionMedium
- Question 32Multi-part ratio distributionMedium
- Question 33Multi-part ratio distributionMedium
- Question 34Multi-part ratio distributionMedium
- Question 35Multi-part ratio distributionMedium
- Question 36Geometry ratio applicationsMedium
- Question 37Geometry ratio applicationsMedium
- Question 38Geometry ratio applicationsMedium
- Question 39Geometry ratio applicationsMedium
- Question 40Geometry ratio applicationsMedium
- Question 41Reciprocal rates and unit orientationHard
- Question 42Reciprocal rates and unit orientationHard
- Question 43Reciprocal rates and unit orientationHard
- Question 44Reciprocal rates and unit orientationHard
- Question 45Reciprocal rates and unit orientationHard
- Question 46Algebraic and changing-ratio reasoningHard
- Question 47Algebraic and changing-ratio reasoningHard
- Question 48Algebraic and changing-ratio reasoningHard
- Question 49Algebraic and changing-ratio reasoningHard
- Question 50Algebraic and changing-ratio reasoningHard