Practice
Proportions Practice
Fifty original questions covering verification, missing terms, expressions, correspondence, decimals, scales, group proportions, error analysis, and area scaling.
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Question 1
Explanation
Compare the cross products: \(3(24)=72\) and \(8(9)=72\). They are equal, so the ratios form a proportion.
Question 2
Explanation
Compare the cross products: \(5(40)=200\) and \(12(15)=180\). They are unequal, so the ratios do not form a proportion.
Question 3
Explanation
Compare the cross products: \(1.4(7)=9.8\) and \(3.5(2.8)=9.8\). They are equal, so the ratios form a proportion.
Question 4
Explanation
Compare the cross products: \(7(45)=315\) and \(18(21)=378\). They are unequal, so the ratios do not form a proportion.
Question 5
Explanation
Compare the cross products: \(2.25(10)=22.5\) and \(6(3.75)=22.5\). They are equal, so the ratios form a proportion.
Question 6
Explanation
Cross products give \(7x=4(35)=140\). Dividing by \(7\) yields \(x=20\), which reproduces the same simplified ratio.
Question 7
Explanation
Cross products give \(12x=5(60)=300\). Dividing by \(12\) yields \(x=25\), which reproduces the same simplified ratio.
Question 8
Explanation
Cross products give \(9x=7(45)=315\). Dividing by \(9\) yields \(x=35\), which reproduces the same simplified ratio.
Question 9
Explanation
Cross products give \(11x=3(77)=231\). Dividing by \(11\) yields \(x=21\), which reproduces the same simplified ratio.
Question 10
Explanation
Cross products give \(15x=8(75)=600\). Dividing by \(15\) yields \(x=40\), which reproduces the same simplified ratio.
Question 11
Explanation
Cross products give \(6x=14(9)=126\). Therefore \(x=126/6=21\), and the denominator is nonzero.
Question 12
Explanation
Cross products give \(8x=20(14)=280\). Therefore \(x=280/8=35\), and the denominator is nonzero.
Question 13
Explanation
Cross products give \(15x=24(25)=600\). Therefore \(x=600/15=40\), and the denominator is nonzero.
Question 14
Explanation
Cross products give \(9x=27(5)=135\). Therefore \(x=135/9=15\), and the denominator is nonzero.
Question 15
Explanation
Cross products give \(16x=28(20)=560\). Therefore \(x=560/16=35\), and the denominator is nonzero.
Question 16
Explanation
Require \(x\ne-1\). Cross products give \(70=10(x+1)\), so \(70=10x+10\) and \(x=6\), which is allowed.
Question 17
Explanation
Cross products give \(6(x-2)=36\), so \(x-2=6\) and \(x=8\).
Question 18
Explanation
The denominator restriction is \(x\ne3/2\). Cross products give \(35=2x-3\), hence \(2x=38\) and \(x=19\).
Question 19
Explanation
Cross products give \(4(3x+1)=40\), so \(12x+4=40\), \(12x=36\), and \(x=3\).
Question 20
Explanation
Restrictions are \(x\ne4,-2\). Cross products give \(6(x+2)=9(x-4)\), so \(6x+12=9x-36\), \(48=3x\), and \(x=16\).
Question 21
Explanation
Align model over actual: \(2/7=9/x\). Cross products give \(2x=7(9)\), so \(x=31.5\) kilometers.
Question 22
Explanation
Align model over actual: \(3/14=10.5/x\). Cross products give \(3x=14(10.5)\), so \(x=49\) feet.
Question 23
Explanation
Align model over actual: \(4/6=15/x\). Cross products give \(4x=6(15)\), so \(x=22.5\) meters.
Question 24
Explanation
Align model over actual: \(5/12=22.5/x\). Cross products give \(5x=12(22.5)\), so \(x=54\) meters.
Question 25
Explanation
Align model over actual: \(1.5/8=6/x\). Cross products give \(1.5x=8(6)\), so \(x=32\) feet.
Question 26
Explanation
Match passes over dollars: \(4/9=x/27\). Thus \(9x=4(27)\), giving \(x=12\).
Question 27
Explanation
Match kilograms over crates: \(6/15=x/20\). Thus \(15x=6(20)\), giving \(x=8\).
Question 28
Explanation
Match liters over minutes: \(8/12=x/30\). Thus \(12x=8(30)\), giving \(x=20\).
Question 29
Explanation
Match workers over tasks: \(5/18=x/36\). Thus \(18x=5(36)\), giving \(x=10\).
Question 30
Explanation
Match tickets over points: \(7/20=x/60\). Thus \(20x=7(60)\), giving \(x=21\).
Question 31
Explanation
Cross products give \(3x=1.2(4.8)=5.76\). Divide by \(3\) to obtain \(x=1.92\), retaining precision until the final result.
Question 32
Explanation
Cross products give \(4x=2.5(14.4)=36\). Divide by \(4\) to obtain \(x=9\), retaining precision until the final result.
Question 33
Explanation
Cross products give \(2.5x=0.75(15)=11.25\). Divide by \(2.5\) to obtain \(x=4.5\), retaining precision until the final result.
Question 34
Explanation
Cross products give \(8x=3.6(30)=108\). Divide by \(8\) to obtain \(x=13.5\), retaining precision until the final result.
Question 35
Explanation
Cross products give \(3.5x=1.25(11.2)=14\). Divide by \(3.5\) to obtain \(x=4\), retaining precision until the final result.
Question 36
Explanation
Set \(3/8=x/40\), giving \(x=15\) coaches. The requested total is \(15+40=55\), not merely the missing category.
Question 37
Explanation
Set \(5/12=x/60\), giving \(x=25\) librarians. The requested total is \(25+60=85\), not merely the missing category.
Question 38
Explanation
Set \(7/9=x/63\), giving \(x=49\) designers. The requested total is \(49+63=112\), not merely the missing category.
Question 39
Explanation
Set \(4/11=x/88\), giving \(x=32\) guides. The requested total is \(32+88=120\), not merely the missing category.
Question 40
Explanation
Set \(6/13=x/78\), giving \(x=36\) supervisors. The requested total is \(36+78=114\), not merely the missing category.
Question 41
Explanation
The first ratio is pens over dollars, so the second must also be pens over dollars. The written second ratio is dollars over pens.
Question 42
Explanation
Cross products join diagonally opposite terms: \(4(21)=7x\), not \(4x=7(21)\).
Question 43
Explanation
Proportional pairs use one multiplicative scale factor. The model doubled, while the actual measure did not.
Question 44
Explanation
Original denominators must be nonzero. Substituting \(x=3\) makes the expression undefined, so it cannot be a solution.
Question 45
Explanation
A linear scale factor applies independently in two dimensions. The area factor is the square of the length factor.
Question 46
Explanation
The linear factor is \(4/2.5=1.6\) meters per centimeter. Actual dimensions are \(12\) and \(19.2\) meters, so area is \(12(19.2)=230.4\) square meters.
Question 47
Explanation
Require \(x\ne-3\). Cross products give \(4(2x-1)=5(x+3)\), so \(8x-4=5x+15\), \(3x=19\), and \(x=19/3\).
Question 48
Explanation
From \(ad=bc\), divide both sides by nonzero \(cd\) to get \(a/c=b/d\). The additive statements do not follow from proportionality.
Question 49
Explanation
The area factor is \(864/54=16\). The positive linear scale factor is \(\sqrt{16}=4\), so one drawing centimeter represents \(4\) meters.
Question 50
Explanation
A preserved ratio requires one common multiplicative factor. If original amounts are \(3k\) and \(8k\), equality \((3k+10)/(8k+10)=3/8\) simplifies to \(80=30\), which is impossible.
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Questions to review
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- Question 1Verifying proportionsEasy
- Question 2Verifying proportionsEasy
- Question 3Verifying proportionsEasy
- Question 4Verifying proportionsEasy
- Question 5Verifying proportionsEasy
- Question 6Solving for a missing numeratorEasy
- Question 7Solving for a missing numeratorEasy
- Question 8Solving for a missing numeratorEasy
- Question 9Solving for a missing numeratorEasy
- Question 10Solving for a missing numeratorEasy
- Question 11Solving for a missing denominatorEasy
- Question 12Solving for a missing denominatorEasy
- Question 13Solving for a missing denominatorEasy
- Question 14Solving for a missing denominatorEasy
- Question 15Solving for a missing denominatorEasy
- Question 16Expression-based proportionsMedium
- Question 17Expression-based proportionsMedium
- Question 18Expression-based proportionsMedium
- Question 19Expression-based proportionsMedium
- Question 20Expression-based proportionsMedium
- Question 21Scale proportionsMedium
- Question 22Scale proportionsMedium
- Question 23Scale proportionsMedium
- Question 24Scale proportionsMedium
- Question 25Scale proportionsMedium
- Question 26Corresponding quantitiesMedium
- Question 27Corresponding quantitiesMedium
- Question 28Corresponding quantitiesMedium
- Question 29Corresponding quantitiesMedium
- Question 30Corresponding quantitiesMedium
- Question 31Decimal proportionsMedium
- Question 32Decimal proportionsMedium
- Question 33Decimal proportionsMedium
- Question 34Decimal proportionsMedium
- Question 35Decimal proportionsMedium
- Question 36Group proportionsMedium
- Question 37Group proportionsMedium
- Question 38Group proportionsMedium
- Question 39Group proportionsMedium
- Question 40Group proportionsMedium
- Question 41Proportion error analysisHard
- Question 42Proportion error analysisHard
- Question 43Proportion error analysisHard
- Question 44Proportion error analysisHard
- Question 45Proportion error analysisHard
- Question 46Advanced proportional reasoningHard
- Question 47Advanced proportional reasoningHard
- Question 48Advanced proportional reasoningHard
- Question 49Advanced proportional reasoningHard
- Question 50Advanced proportional reasoningHard