Ratio, Proportion & Percentages

The MYP 2 rules for spotting direct vs inverse proportion and mastering every type of percentage question

Split illustration comparing a straight-line direct proportion graph and a curved inverse proportion graph

Subject

Mathematics

Curriculum

IB MYP

Grade

MYP 2

Topic

Ratio, Proportion & Percentages

Reading

6 min

Difficulty

Standard

Quick facts

Difficulty

★★☆☆☆

Exam weight

Core Number & Algebra — Criteria A & C

Prerequisites

Fractions, decimals, basic algebra

You'll learn

Direct/inverse proportion tests, percentage methods, reverse percentages

Revision time

30-40 minutes

Every ratio, proportion and percentage question in IB MYP 2 asks the same underlying thing: does one quantity change in a fixed, predictable multiple of the other? Get that right and direct proportion, inverse proportion, percentage increase, percentage decrease and reverse percentages all become the same handful of moves applied in different directions. Get it wrong — usually by forgetting that a flat fee or fixed charge breaks the clean relationship — and marks slip away even when the arithmetic is correct. This teaser walks through the five ideas that show up in almost every unit test and eAssessment: spotting direct and inverse proportion from a table or graph, working with simple percentages, applying the multiplier method for increase and decrease, and undoing percentage change to find an original value. The full revision notes go deeper with worked traps and mark-scheme language for Criterion C explanations.

What you’ll be able to do

✓Test whether a table shows direct proportion using the constant ratio

✓Test whether a table shows inverse proportion using the constant product

✓Write and use the equations y=kx and xy=k

✓Find x% of an amount and find what % one amount is of another

✓Apply the multiplier method for percentage increase and decrease

✓Explain why successive percentage changes don't simply add

✓Reverse a percentage change to recover an original value

✓Identify real-life situations (fees, discounts) that break proportionality

Direct Proportion: Constant Ratio, Line Through the Origin

Two quantities are directly proportional when doubling one doubles the other — the ratio $y \div x$ stays the same for every pair, and that fixed value is the constant $k$ in $y = k x$ . On a graph this always looks like a straight line passing through the origin. If the numbers increase together but the line has a $y$ -intercept, it's just a linear relationship, not direct proportion.

Table and graph showing notebooks vs cost as direct proportion

Exam tip

Always calculate $k$ from a labelled data point rather than eyeballing the gradient off the axis gridlines — misreading the scale is a classic error.

Common mistake

Swapping the variables, e.g. writing $n = 3 C$ instead of $C = k n$ — match the letter that changes BECAUSE of the other quantity.

Inverse Proportion: Constant Product, Decreasing Curve

Inverse proportion is the opposite pattern: as one quantity doubles, the other halves, so the PRODUCT $x \times y$ stays constant at $k$ , giving $y = \frac{k}{x}$ . The graph is a curve that gets closer and closer to both axes but never touches them. Classic real examples are speed and time for a fixed distance, or number of workers and time to finish a fixed job.

Curve graph showing inverse proportion between workers and days to finish a job

Exam tip

To confirm inverse proportion, multiply each matching pair — if $x \times y$ gives the same value every time, that's your constant $k$ .

Simple Percentages: Two Core Moves

A percentage is a fraction out of 100, so 23% simply means $\frac{23}{100}$ . Nearly every basic question is one of two moves: finding $x %$ of an amount using $\frac{x}{100} \times Total$ , or finding what percentage one amount is of another using $\frac{Part}{Whole} \times 100$ . Remember that percentages above 100% are completely normal — 150% just means 1.5 times the whole.

Diagram showing the two percentage formulas side by side with a quiz score example

Common mistake

Dividing the wrong way round when finding 'what % is X of Y' — the WHOLE always goes on the bottom. A quiz score coming out above 200% is an instant red flag.

Percentage Increase and Decrease: The Multiplier Method

To increase by $r %$ , multiply the original by $(1 + \frac{r}{100})$ ; to decrease by $r %$ , multiply by $(1 - \frac{r}{100})$ — one clean calculation instead of two separate steps. Successive changes don't add together: a 20% increase followed by a 20% decrease does NOT return you to the original value, because the second change acts on a different, already-changed amount.

Number line showing $80 jacket price increasing by 15% using a multiplier

Common mistake

Assuming two 10% increases equal a 20% increase — actually $1.10 \times 1.10 = 1.21$ , a 21% overall rise. Always multiply the multipliers, never add the percentages.

Reverse Percentages: Working Backwards to the Original

Reverse percentage questions give you the AFTER value and ask for the BEFORE value — the opposite direction from a normal increase or decrease question. The rule is to divide the final value by the multiplier $(1 \pm \frac{r}{100})$ , never to take $r %$ of the final value and add or subtract it, since the final value is already the changed amount.

Diagram showing a $68 sale price being divided by 0.80 to find the original price

Exam tip

Spot the keyword pattern: 'after a discount of r%, the price is $X... find the original price' always signals a reverse percentage question — divide, don't add.

Common mistake

Taking 20% of the discounted $68 (=$ 13.60) and adding it back to get $81.60 — this is wrong because 20% of the ORIGINAL price is a different amount than 20% of the sale price.

Quick formula sheet

y = k x

Direct proportion equation, where k is the constant of proportionality. — Straight line through the origin, no y-intercept.

k = \frac{y}{x}

Finding the constant of proportionality from any matching pair in a direct proportion table.

y = \frac{k}{x} or x y = k

Inverse proportion equation — the product of the two quantities stays fixed. — One goes up, the other goes down — product stays put.

Amount = \frac{x}{100} \times Total

Finding x% of a total amount.

x = \frac{Part}{Whole} \times 100

Finding what percentage the part is of the whole — the word 'of' tells you the denominator.

New value = Original \times (1 + \frac{r}{100})

Multiplier method for a percentage increase of r%.

New value = Original \times (1 - \frac{r}{100})

Multiplier method for a percentage decrease of r%.

% change = \frac{New - Original}{Original} \times 100

Percentage change always uses the ORIGINAL value as the denominator.

Original = \frac{Final value}{1 \pm \frac{r}{100}}

Reverse percentage formula — undoing a known percentage change to find the original value.

Practice questions

Easy

A table shows x: 1,2,3,4 and y: 2,4,6,8. Is this direct proportion? State the value of k.
Find 20% of $150.
Use the multiplier method to increase $60 by 10%.

Medium

4 workers can build a wall in 9 days. If the job is inversely proportional to the number of workers, how long would 6 workers take?
A class scored 27 out of 30 on a test. Express this as a percentage.
A shirt priced at $45 is reduced by 15%. Find the sale price using the multiplier method.

Challenge

A price increases by 25% and then decreases by 25%. Is the final price equal to the original price? Explain using multipliers.
A laptop is on sale for $680 after a 15% discount. Find the original price.
A delivery service charges $12 f or 1 i t e m,$ 22 for 2 items, and $32 for 3 items. Explain, with evidence, why this is NOT direct proportion.

Frequently asked questions

What's the difference between direct and inverse proportion?+

In direct proportion, the ratio y ÷ x stays constant and both quantities increase together (y = kx). In inverse proportion, the product x × y stays constant, so as one quantity increases the other decreases (xy = k).

How do I know if a graph shows direct proportion?+

It must be a straight line that passes through the origin. If it's a straight line but has a y-intercept, it's a linear relationship, not direct proportion.

Why doesn't a 20% increase followed by a 20% decrease return to the original price?+

Because the second percentage change acts on a different (already changed) amount. You must multiply the multipliers step by step, not add the percentages.

How do I solve a reverse percentage question?+

Divide the final value by the multiplier (1 ± r/100) — never take r% of the final value and add or subtract it, since the final value is already the changed amount.

What's the difference between a percentage point and a percentage change?+

A percentage point difference is a simple subtraction between two percentages (e.g. 45% to 50% is a 5 percentage point rise), while a percentage change is calculated relative to the original value using (change ÷ original) × 100.

Why isn't 'both quantities increase together' enough evidence for direct proportion?+

A fixed fee or flat charge can make two quantities increase together without the ratio staying constant. You must check that y ÷ x is the same for every pair AND that the graph passes through the origin.

Get the full Ratio, Proportion & Percentages revision notes

Step-by-step breakdowns of every proportion and percentage trap with full explanations Worked examples matching MYP Criterion A and Criterion C mark schemes Original mock papers and exam-style questions to test your understanding Quick-reference formula sheet for last-minute revision

Get the Ratio, Proportion & Percentages notes on RevisionPrep →

Maths: Naming the Pattern, Solving the Term Maths:Statistics — Grouped Data and Averages