Writing a Ratio
A ratio compares parts: 2 spoons blue to 3 spoons green is 2 : 3, read ‘two to three’. The order follows the words: blue : green = 2 : 3, so green : blue = 3 : 2 — a different ratio. Count each part, write them in order with a colon.
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Maths · Free sample lesson
Writing & Simplifying Ratios
Write a ratio from a description or picture and simplify it using common factors.
- About 25 minutes
- Ages 11+
Tonight's destination
Fumblebrew's Tower
Writing & Simplifying Ratios
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01Story opener
Story
Fumblebrew's Tower
The top of the alchemy tower: a bench crowded with glowing vials, twin measuring spoons, a silver dropper, a great measuring flask on a brass balance, a golden ladle hung above the cauldron, maps and an hourglass on the shelf.
Order matters, and both parts scale together. Earn the twin measuring spoons.
Two parts blue to three parts green — two to three! Four to six? Same brew, my assistant!
02
Core Concept
Key Concepts
Simplifying
Ratios simplify like fractions: divide every part by the same common factor. 4 : 6 → ÷ 2 → 2 : 3. 12 : 18 → ÷ 6 → 2 : 3. 10 : 15 : 25 → ÷ 5 → 2 : 3 : 5. Simplest form has no common factor but 1. Equivalent ratios describe the same mixture.
Order and the Part-Whole Trap
2 : 3 means 2 parts to 3 parts — 5 parts in all. So blue is 2/5 of the mixture, not 2/3. The trap is turning 2 : 3 into the fraction ⅔ — that compares blue to green, not blue to the whole. And never swap the order: 3 : 2 is a different, greener brew.
03
Guided Practice
Fill in the Missing Values
Work through each question carefully. Take your time.
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2 spoons blue to 3 spoons green is written Drop here.
4 : 6 simplifies to Drop here.
12 : 18 simplifies to Drop here.
2 spoons blue to 3 spoons green, in the ratio 2 : 3, blue is Drop here of the mixture.
Answer Bank
Tap or drag a word into a gap. Tap a placed word to send it back.
2 : 32 : 32 : 32/5
04
Guided Practice
Match the Pairs
Work through each question carefully. Take your time.
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Matching Game5 pairs
Match the Pairs
Drag items from the left to match them with items on the right
Left Items
Right Items
05
Guided Practice
Knowledge Check
Work through each question carefully. Take your time.
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06
Independent Practice
Brewing Challenge
Now it's your turn. Apply what you've learned on your own.
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07
Recap
Well Done!
Written true, my assistant! Ratios in order, simplified by common factors, equivalent when scaled together — and 2 : 3 is 2 parts of 5, never two-thirds. The twin measuring spoons are yours. Next, scaling.
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