Practice · Grade 7 Percentages
Relative Change Practice
Relative change problems in rising difficulty plus a boss question. Answer as a factor, with a hint and full working. Grade 7, free.
Q1 of 7
0 correct
What is the relative change from 40 to 60?
(60 − 40) ÷ 40
Quick answer
What is the best way to practice relative change?
Work several problems with the formula (new − old) ÷ old and give the result first as a factor (e.g. 0.25), then as a percent (25%). Start with increases, then practice decreases with a negative sign, and finish with comparisons of differently sized values. Always check: old value · (1 + factor) must give the new value.
HowTo
A 4-step solving strategy
This order works for any pair of old and new value (as long as the old value is not zero).
- 1Step 1 of 4
Mark the old and new value
Read off which value is the starting (old) value and which is the end (new) value. With wording like "rises from … to …", the old value comes before "to".
- 2Step 2 of 4
Take the difference: new − old
Subtract the old value from the new value. Mind the sign — if the value falls, the difference is negative.
- 3Step 3 of 4
Divide by the old value
Divide the difference by the old value. The result is the relative change as a factor, e.g. 0.25.
- 4Step 4 of 4
Convert to percent and check
Multiply the factor by 100 to get the percent. Check: old value · (1 + factor) must give the new value.
Examples
Worked practice problems with full working
Four typical Grade 7 percentage problems. Try each yourself first, then compare with the working.
Easy
What is the relative change from 80 to 100?
new − old = 100 − 80 = 20
20 ÷ 80 = 0.25
0.25 · 100 = 25%
Check: 80 · 1.25 = 100 ✓
Standard increase. Take the difference first, then divide by the old value.
Easy
A value falls from 100 to 80. Relative change?
new − old = 80 − 100 = −20
−20 ÷ 100 = −0.2
−0.2 · 100 = −20%
Check: 100 · 0.8 = 80 ✓
Mind the sign: for a decrease the difference is negative, so the factor is too.
Medium
A stock rises from $50 to $75. Relative change?
new − old = 75 − 50 = 25
25 ÷ 50 = 0.5
0.5 · 100 = 50%
Check: 50 · 1.5 = 75 ✓
Half added — a factor of 0.5 equals +50%.
Hard
Boss: Revenue falls from $1000 to $950. Relative change?
new − old = 950 − 1000 = −50
−50 ÷ 1000 = −0.05
−0.05 · 100 = −5%
Check: 1000 · 0.95 = 950 ✓
Large numbers, small relative change — exactly why we divide by the old value.
Pitfalls
Common mistakes — and how to avoid them
These traps come up again and again with relative change.
Dividing by the new value
The reference point is the old value; it goes in the denominator. (new − old) ÷ old — not ÷ new.
Confusing factor and percent
The factor 0.25 is 25%, not 0.25%. Multiply by 100 to get the percent.
Forgetting the sign for a decrease
If the value falls, the difference is negative and so is the factor. −0.2 means −20%.
Comparing only differences
+150 on a starting value of 500 is relatively smaller than +150 on 100. Always compare the factor, not the raw difference.
Skipping the check
Plug the factor back in: old value · (1 + factor) must give the new value. Any slip shows up at once.
Study
Practice with a plan — three short tips
Factor first, then percent
Solve every problem as a factor first, then convert. That way you stop mixing up the two representations.
Mix increases and decreases
Deliberately practice falling values too, so the negative sign becomes routine and doesn't surprise you in a test.
On every wrong answer: why?
Was it the sign, the wrong denominator, or factor vs percent? Note the cause — next time you'll spot the mistake instantly.
FAQ
Frequently asked questions about practicing
Glossary
Terms in one sentence
- Relative change
- The difference new − old relative to the old value: (new − old) ÷ old.
- Absolute change
- The plain difference new − old, measured in the unit of the quantity.
- Factor
- The relative change as a dimensionless number, e.g. 0.25 for +25%.
- Percentage change
- The relative change times 100, expressed in percent.
- Starting value
- The old value that sits in the denominator and forms the reference point.
- Dimensionless
- Without a unit — the units cancel when you divide.
- Boss question
- The last and hardest problem in a practice set.