Ratios / Proportions & Scale
Proportions & Scale
Solve proportions, find unit rates, and apply scale factors to real-world problems. Grades 4–5.
What is a Proportion?
A proportion says that two ratios are equal: a/b = c/d
If 3 pencils cost £1.20, how much do 7 pencils cost?
3 / 1.20 = 7 / x
Cross multiply: 3x = 7 × 1.20
3x = 8.40
x = £2.80
Method 1: Cross-Multiplication
Given: a/b = c/d
Cross multiply: a × d = b × c
Solve for the unknown.
2/5 = x/15
2 × 15 = 5 × x
30 = 5x → x = 6
Method 2: Ratio Table
Find the scale factor between known values, then apply to the unknown.
Bags
Apples
2
10
÷2 →
1
5
(unit rate)
6
30
×6
Unit Rates
A unit rate is a ratio with a denominator of 1. It tells you the amount "per one".
£3.60 for 4 items
£0.90 per item
120 km in 2 hours
60 km per hour
15 pages in 5 minutes
3 pages per minute
Scale Factors & Maps
A scale compares a drawing/model to the real object. Written as 1 : n where n = how many times bigger real life is.
Map scale 1 : 50,000
If two towns are 3.5 cm apart on the map:
Real distance = 3.5 × 50,000 cm = 175,000 cm = 1.75 km
Practice Drills
20
Example: 2 × 7