Proportions
Two equal ratios; solve using cross-multiplication.
Key idea
Two equal ratios; solve using cross-multiplication.
In depth
A proportion says two ratios are equal: a/b = c/d. Cross-multiplying gives ad = bc, which lets you solve for an unknown. It models any situation where quantities scale together.
Worked example
If 3 pens cost 4.50, then 7 pens cost x: 3/4.5 = 7/x, so x = 4.5 × 7 / 3 = 10.50.
Formula
Real-world uses
- Scaling a recipe for more guests
- Estimating the height of a tree from its shadow
- Dosing medicine by weight
Common mistake
Setting up with mismatched order, such as pens over price on one side and price over pens on the other.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Proportions?
Two equal ratios; solve using cross-multiplication. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Proportions?
The key formula is a/b = c/d ⇒ ad = bc.
Where is Proportions used in real life?
Real-world examples: Scaling a recipe for more guests; Estimating the height of a tree from its shadow; Dosing medicine by weight.
What should I learn before Proportions?
Make sure you are comfortable with Ratios, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Proportions?
Setting up with mismatched order, such as pens over price on one side and price over pens on the other.
How can I practise Proportions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Proportions?
Move on to Rates and Unit Rates next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.