How to Calculate Percentage Change - Free Printable

To solve the problems, we will use the formula for percentage change:

\[
\text{Percentage Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100
\]

Problem 1:

A Labrador retriever weighs 48 kg. After a diet and exercise program, the dog weighs 41 kg. What is the percentage loss in weight?

- Original weight: 48 kg
- New weight: 41 kg

\[
\text{Percentage Loss} = \left( \frac{41 - 48}{48} \right) \times 100 = \left( \frac{-7}{48} \right) \times 100 \approx -14.58\%
\]

Rounding to the nearest percent: -15%

Problem 2:

A DVD normally costs $15. It is reduced to $9.75 in a sale. How much is the percentage reduction?

- Original price: $15
- New price: $9.75

\[
\text{Percentage Reduction} = \left( \frac{9.75 - 15}{15} \right) \times 100 = \left( \frac{-5.25}{15} \right) \times 100 \approx -35\%
\]

Rounding to the nearest percent: -35%

Problem 3:

Sally is in a long-jump competition. Her first jump is 5.7 m. Her second jump is 6.2 m. What is her percentage increase in jump length?

- Original jump: 5.7 m
- New jump: 6.2 m

\[
\text{Percentage Increase} = \left( \frac{6.2 - 5.7}{5.7} \right) \times 100 = \left( \frac{0.5}{5.7} \right) \times 100 \approx 8.77\%
\]

Rounding to the nearest percent: 9%

Problem 4:

Tyger is trying to eat less sugar in his diet. He reduces his sugar intake from 15 spoons a day to 9 ½ spoons a day. What is the percentage reduction in his sugar intake?

- Original intake: 15 spoons
- New intake: 9.5 spoons

\[
\text{Percentage Reduction} = \left( \frac{9.5 - 15}{15} \right) \times 100 = \left( \frac{-5.5}{15} \right) \times 100 \approx -36.67\%
\]

Rounding to the nearest percent: -37%

Problem 5:

Frazer is training for a cycle race. In the first week, he cycles 195 miles. In the second week, he manages 243 miles. What is the percentage increase in distance?

- Original distance: 195 miles
- New distance: 243 miles

\[
\text{Percentage Increase} = \left( \frac{243 - 195}{195} \right) \times 100 = \left( \frac{48}{195} \right) \times 100 \approx 24.62\%
\]

Rounding to the nearest percent: 25%

Problem 6:

Frazer cycles the first 20 miles at an average speed of 21 mph. The second part is more uphill, and he only manages 13 mph. By what percentage did his speed decrease?

- Original speed: 21 mph
- New speed: 13 mph

\[
\text{Percentage Decrease} = \left( \frac{13 - 21}{21} \right) \times 100 = \left( \frac{-8}{21} \right) \times 100 \approx -38.10\%
\]

Rounding to the nearest percent: -38%

Final Answers:

1. -15%
2. -35%
3. 9%
4. -37%
5. 25%
6. -38%

\boxed{-15\%, -35\%, 9\%, -37\%, 25\%, -38\%}