Let's solve each problem step by step.
We are asked to calculate the
percentage increase or decrease from an original amount to a new amount.
Formula:
$$
\text{Percentage Change} = \left( \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \right) \times 100\%
$$
- If the result is
positive, it's a
percentage increase.
- If the result is
negative, it's a
percentage decrease.
---
Let’s go through each row:
---
1. Original: 990 → New: 396
Change: $ 396 - 990 = -594 $ (decrease)
$$
\frac{-594}{990} \times 100\% = -0.6 \times 100\% = -60\%
$$
✔ 60% decrease
---
2. Original: 830 → New: 249
Change: $ 249 - 830 = -581 $
$$
\frac{-581}{830} \times 100\% \approx -0.70 \times 100\% = -70\%
$$
✔ 70% decrease
---
3. Original: 980 → New: 147
Change: $ 147 - 980 = -833 $
$$
\frac{-833}{980} \times 100\% \approx -0.8499 \times 100\% \approx -85\%
$$
✔ 85% decrease
---
4. Original: 165 → New: 33
Change: $ 33 - 165 = -132 $
$$
\frac{-132}{165} \times 100\% = -0.8 \times 100\% = -80\%
$$
✔ 80% decrease
---
5. Original: 640 → New: 512
Change: $ 512 - 640 = -128 $
$$
\frac{-128}{640} \times 100\% = -0.2 \times 100\% = -20\%
$$
✔ 20% decrease
---
6. Original: 520 → New: 598
Change: $ 598 - 520 = 78 $ (increase)
$$
\frac{78}{520} \times 100\% = 0.15 \times 100\% = 15\%
$$
✔ 15% increase
---
7. Original: 520 → New: 546
Change: $ 546 - 520 = 26 $
$$
\frac{26}{520} \times 100\% = 0.05 \times 100\% = 5\%
$$
✔ 5% increase
---
8. Original: 930 → New: 1023
Change: $ 1023 - 930 = 93 $
$$
\frac{93}{930} \times 100\% = 0.1 \times 100\% = 10\%
$$
✔ 10% increase
---
9. Original: 940 → New: 1551
Change: $ 1551 - 940 = 611 $
$$
\frac{611}{940} \times 100\% \approx 0.65 \times 100\% = 65\%
$$
✔ 65% increase
---
10. Original: 286 → New: 429
Change: $ 429 - 286 = 143 $
$$
\frac{143}{286} \times 100\% = 0.5 \times 100\% = 50\%
$$
✔ 50% increase
---
Final Answers Table:
| Original | New | Increase/Decrease | Percentage Change |
|--------|-----|-------------------|--------------------|
| 990 → 396 | ↓ |
60% decrease |
| 830 → 249 | ↓ |
70% decrease |
| 980 → 147 | ↓ |
85% decrease |
| 165 → 33 | ↓ |
80% decrease |
| 640 → 512 | ↓ |
20% decrease |
| 520 → 598 | ↑ |
15% increase |
| 520 → 546 | ↑ |
5% increase |
| 930 → 1023 | ↑ |
10% increase |
| 940 → 1551 | ↑ |
65% increase |
| 286 → 429 | ↑ |
50% increase |
---
✔ All calculations are complete and accurate.
Let me know if you'd like this formatted as a printable table!
Parent Tip: Review the logic above to help your child master the concept of percent of change worksheet answers.