Practice
Percent of Change Practice
Fifty original questions covering conversions, percent-change bases, multipliers, reverse change, successive changes, comparisons, and error analysis.
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Question 1
Explanation
Multiply the decimal by \(100\): \(0.42(100)=42\). Therefore the equivalent percent is \(42\%\).
Question 2
Explanation
Multiply the decimal by \(100\): \(0.075(100)=7.5\). Therefore the equivalent percent is \(7.5\%\).
Question 3
Explanation
Multiply the decimal by \(100\): \(1.36(100)=136\). Therefore the equivalent percent is \(136\%\).
Question 4
Explanation
Multiply the decimal by \(100\): \(0.006(100)=0.6\). Therefore the equivalent percent is \(0.6\%\).
Question 5
Explanation
Multiply the decimal by \(100\): \(2.125(100)=212.5\). Therefore the equivalent percent is \(212.5\%\).
Question 6
Explanation
Divide to obtain \(3/8=0.375\), then multiply by \(100\) to get \(37.5\%\).
Question 7
Explanation
Divide to obtain \(7/20=0.35\), then multiply by \(100\) to get \(35\%\).
Question 8
Explanation
Divide to obtain \(11/25=0.44\), then multiply by \(100\) to get \(44\%\).
Question 9
Explanation
Divide to obtain \(9/16=0.5625\), then multiply by \(100\) to get \(56.25\%\).
Question 10
Explanation
Divide to obtain \(13/40=0.325\), then multiply by \(100\) to get \(32.5\%\).
Question 11
Explanation
Divide \(175\) by \(100\): \(175\%=1.75\). Writing \(175/100\) and simplifying gives \(7/4\).
Question 12
Explanation
Divide \(0.4\) by \(100\): \(0.4\%=0.004\). Writing \(0.4/100\) and simplifying gives \(1/250\).
Question 13
Explanation
Divide \(62.5\) by \(100\): \(62.5\%=0.625\). Writing \(62.5/100\) and simplifying gives \(5/8\).
Question 14
Explanation
Divide \(240\) by \(100\): \(240\%=2.4\). Writing \(240/100\) and simplifying gives \(12/5\).
Question 15
Explanation
Divide \(2.5\) by \(100\): \(2.5\%=0.025\). Writing \(2.5/100\) and simplifying gives \(1/40\).
Question 16
Explanation
The amount of change is \(|294-240|=54\). Divide by the original value: \(54/240=0.225\), or \(22.5\%\) increase.
Question 17
Explanation
The amount of change is \(|448-560|=112\). Divide by the original value: \(112/560=0.2\), or \(20\%\) decrease.
Question 18
Explanation
The amount of change is \(|1525-1250|=275\). Divide by the original value: \(275/1250=0.22\), or \(22\%\) increase.
Question 19
Explanation
The amount of change is \(|62-80|=18\). Divide by the original value: \(18/80=0.225\), or \(22.5\%\) decrease.
Question 20
Explanation
The amount of change is \(|423-360|=63\). Divide by the original value: \(63/360=0.175\), or \(17.5\%\) increase.
Question 21
Explanation
A percent increase of \(18\%\) uses multiplier \(1.18\). Thus \(450(1.18)=531\).
Question 22
Explanation
A percent decrease of \(24\%\) uses multiplier \(0.76\). Thus \(625(0.76)=475\).
Question 23
Explanation
A percent increase of \(7.5\%\) uses multiplier \(1.075\). Thus \(960(1.075)=1032\).
Question 24
Explanation
A percent decrease of \(12.5\%\) uses multiplier \(0.875\). Thus \(384(0.875)=336\).
Question 25
Explanation
A percent increase of \(35\%\) uses multiplier \(1.35\). Thus \(280(1.35)=378\).
Question 26
Explanation
Let the original value be \(x\). The final relationship is \(1.16x=870\), so \(x=870/1.16=750\).
Question 27
Explanation
Let the original value be \(x\). The final relationship is \(0.72x=540\), so \(x=540/0.72=750\).
Question 28
Explanation
Let the original value be \(x\). The final relationship is \(1.25x=1125\), so \(x=1125/1.25=900\).
Question 29
Explanation
Let the original value be \(x\). The final relationship is \(0.875x=700\), so \(x=700/0.875=800\).
Question 30
Explanation
Let the original value be \(x\). The final relationship is \(1.6x=512\), so \(x=512/1.6=320\).
Question 31
Explanation
Multiply the change factors: \(1.2(0.85)=1.02\). This leaves \(102\%\) of the original, a \(2\%\) increase.
Question 32
Explanation
Multiply the change factors: \(1.3(0.7)=0.91\). This leaves \(91\%\) of the original, a \(9\%\) decrease.
Question 33
Explanation
Multiply the change factors: \(0.75(1.12)=0.84\). This leaves \(84\%\) of the original, a \(16\%\) decrease.
Question 34
Explanation
Multiply the change factors: \(1.4(0.9)=1.26\). This leaves \(126\%\) of the original, a \(26\%\) increase.
Question 35
Explanation
Multiply the change factors: \(0.8(0.85)=0.68\). This leaves \(68\%\) of the original, a \(32\%\) decrease.
Question 36
Explanation
The quantity after ‘than’ is the base \(60\). Divide the difference by that base: \(24/60=0.4\), or \(40\%\).
Question 37
Explanation
The quantity after ‘than’ is the base \(72\). Divide the difference by that base: \(18/72=0.25\), or \(25\%\).
Question 38
Explanation
The quantity after ‘than’ is the base \(90\). Divide the difference by that base: \(45/90=0.5\), or \(50\%\).
Question 39
Explanation
The quantity after ‘than’ is the base \(80\). Divide the difference by that base: \(12/80=0.15\), or \(15\%\).
Question 40
Explanation
The quantity after ‘than’ is the base \(40\). Divide the difference by that base: \(6/40=0.15\), or \(15\%\).
Question 41
Explanation
The original price is the percent-change base. Thus \((250-200)/200=0.25=25\%\).
Question 42
Explanation
Percent means per hundred, so \(0.5/100=0.005\).
Question 43
Explanation
The point difference is \(52-40=12\), while relative percent increase is \(12/40=30\%\).
Question 44
Explanation
The decrease acts on the enlarged value. Multiplying factors gives the actual net effect.
Question 45
Explanation
Comparison language uses the referenced value after ‘than’ as the denominator.
Question 46
Explanation
Each change uses its own multiplier on the current value, so the two factors multiply.
Question 47
Explanation
The factor is \((1+r/100)(1-r/100)=1-r^2/10{,}000\). The decrease as a percent is \(100(r^2/10{,}000)=r^2/100\%\).
Question 48
Explanation
Let \(B=1\), so \(A=1.6\). Relative to \(A\), the decrease is \((1.6-1)/1.6=0.375=37.5\%\).
Question 49
Explanation
The two-year factor is \(1.12^2=1.2544\), giving a \(25.44\%\) increase.
Question 50
Explanation
A decrease uses factor \(1-p/100\). Solve \(1-p/100=0.68\), giving \(p=32\).
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