Practice · Grade 7 Percentages
Absolute Change — Practice
Practice problems in rising difficulty plus a boss question on absolute change, new − old. A hint and full working for each. Grade 7, free.
Q1 of 7
0 correct
Find the absolute change.
200 → 250
Quick answer
How do I best practice absolute change?
Work several problems in rising difficulty and always compute new − old, never old − new. Start with whole numbers like 200 → 250 (+50), then a decrease such as 250 → 200 (−50), a decimal problem like 12.5 → 18 (+5.5), and finish with a special case, e.g. from −15 to 40. Watch the sign and state the unit in your answer.
HowTo
A 4-step solving strategy
This order works for any pair of old and new values.
- 1Step 1 of 4
Label old and new
Mark clearly which value is the starting (old) value and which is the end (new) value. In "200 → 250", 200 is old and 250 is new. This labelling decides the sign.
- 2Step 2 of 4
Take the difference new − old
Plug straight into the formula: new − old. For 200 → 250 that is 250 − 200. Never compute old − new, or the sign flips.
- 3Step 3 of 4
Check the sign and special cases
Positive = increase, negative = decrease, 0 = no change. If the old value is negative, "− (−15)" becomes "+ 15". Put negative values in brackets.
- 4Step 4 of 4
Add the unit and verify
Attach the unit ($, items, kg …) and check: old + change must give new again. 200 + 50 = 250 ✓.
Examples
Worked examples with full working
Four typical problems. Try each one first, then compare with the solution.
Easy
Find the absolute change from 200 to 250.
old = 200, new = 250
Δ = new − old = 250 − 200
Δ = +50
Check: 200 + 50 = 250 ✓
Standard case: an increase. A positive sign means the value went up.
Easy
Find the absolute change from 1000 to 950.
old = 1000, new = 950
Δ = 950 − 1000
Δ = −50
Check: 1000 + (−50) = 950 ✓
A decrease. The new value is smaller than the old, so the result is negative.
Medium
Find the absolute change from 12.5 to 18.
old = 12.5, new = 18
Δ = 18 − 12.5
Δ = +5.5
Check: 12.5 + 5.5 = 18 ✓
The same formula holds with decimals. Line up the decimal places when subtracting.
Hard
Boss: find the absolute change from −15 to 40.
old = −15, new = 40
Δ = 40 − (−15)
Δ = 40 + 15 = +55
Check: −15 + 55 = 40 ✓
Negative starting value: subtracting a negative becomes adding. Use brackets, then compute safely.
Pitfalls
Common mistakes — and how to avoid them
These traps come up again and again when practicing absolute change.
Order reversed
It is new − old, not old − new. Reversing it gives the right number with the wrong sign. Write "new − old" in the margin.
Sign with a negative starting value
In 40 − (−15) the double minus becomes plus: 40 + 15 = 55. Always put negative values in brackets.
Confused with percentage change
Absolute change is a number with a unit (+$50). Percentage change relates it to the old value (+25%). The task asks only for the plain difference.
Unit omitted
An absolute change without a unit is ambiguous. State $, items or kg in your answer sentence.
Missing the zero case
If the value stays the same (7 → 7), the change is 0 — not "no answer". Zero is a valid result.
Study
Practice with a plan — three quick tips
Type first, then check the solution
Work out the difference in your head or on paper before revealing the hint. Active recall sticks far better than passively reading along.
Say the sign out loud
For each problem say "increase" or "decrease" before you write the number. This builds a feel for the sign and prevents careless slips.
For every wrong answer, ask why
Was it a sign error, a reversed order or a lost decimal point? Note the cause — next time you will spot it instantly.
FAQ
Frequently asked questions about practicing
Glossary
Terms in one line
- Absolute change
- The plain difference new − old, given in the unit of the quantity.
- Old value
- The starting value before the change.
- New value
- The end value after the change.
- Difference
- The result of a subtraction (here new − old).
- Sign
- Plus for an increase, minus for a decrease — it shows the direction.
- Percentage change
- The difference relative to the old value, in percent.
- Check
- Verification via old + change = new.