Percentage Change worksheet

1. Decreased value: 168

1. Find the amount of change: the starting number times the percent, divided by 100

   $\frac{200\times 16}{100}$$=32$

2. Subtract the change from the starting value

   $200-32$$=168$

2. Original value: 45.16

1. Turn the 24% increase into a multiplier: the number the original was multiplied by

   $1+\frac{24}{100}$$=1.24$

2. Undo the change by dividing the new number by that multiplier. Subtracting the same percent would not work, because the percent was taken of the original

   $\frac{56}{1.24}$$=45.16129$

3. Check your answer: apply the change to the original, and you get back the new number

   $45.16129\times 1.24$$=56$

3. Increased value: 214.6

1. Find the amount of change: the starting number times the percent, divided by 100

   $\frac{185\times 16}{100}$$=29.6$

2. Add the change to the starting value

   $185+29.6$$=214.6$

4. Percent change: 25%

1. Find how much it changed: subtract the original number from the new one

   $75-60$$=15$

2. Divide by the size of the original, so the change is compared with where you started

   $\frac{15}{\left|60\right|}$$=0.25$

3. Multiply by 100 to turn it into a percent (positive means an increase)

   $0.25\times 100$$=\mathrm{25\%}$

5. Percent change: 19.57%

1. Find how much it changed: subtract the original number from the new one

   $55-46$$=9$

2. Divide by the size of the original, so the change is compared with where you started

   $\frac{9}{\left|46\right|}$$=0.195652$

3. Multiply by 100 to turn it into a percent (positive means an increase)

   $0.195652\times 100$$=\mathrm{19.565217\%}$

6. Percent change: 90%

1. Find how much it changed: subtract the original number from the new one

   $76-40$$=36$

2. Divide by the size of the original, so the change is compared with where you started

   $\frac{36}{\left|40\right|}$$=0.9$

3. Multiply by 100 to turn it into a percent (positive means an increase)

   $0.9\times 100$$=\mathrm{90\%}$

7. Increased value: 335.5

1. Find the amount of change: the starting number times the percent, divided by 100

   $\frac{275\times 22}{100}$$=60.5$

2. Add the change to the starting value

   $275+60.5$$=335.5$

8. Original value: 48.39

1. Turn the 24% increase into a multiplier: the number the original was multiplied by

   $1+\frac{24}{100}$$=1.24$

2. Undo the change by dividing the new number by that multiplier. Subtracting the same percent would not work, because the percent was taken of the original

   $\frac{60}{1.24}$$=48.387097$

3. Check your answer: apply the change to the original, and you get back the new number

   $48.387097\times 1.24$$=60$

9. Decreased value: 178

1. Find the amount of change: the starting number times the percent, divided by 100

   $\frac{200\times 11}{100}$$=22$

2. Subtract the change from the starting value

   $200-22$$=178$

10. Increased value: 207.1

1. Find the amount of change: the starting number times the percent, divided by 100

   $\frac{190\times 9}{100}$$=17.1$

2. Add the change to the starting value

   $190+17.1$$=207.1$