Ratios · Ratios · 1.2

Three ways to write it.

The same ratio can be written three ways: with a colon (3:4), as a fraction (3/4), or in words ("3 to 4"). All mean the same comparison.

01 / THE IDEA

See it work.

Watch the method

Three ways to write a ratio

3:4 = 3/4 = "3 to 4".

1 / 1
4:64 : 6
1

Write the ratio

Put the first quantity to the second, in order.

4:64:6
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type lowest terms, e.g. 3:4.

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Three notations

a:b, a/b, and "a to b" are interchangeable ways to write a ratio.

Why it works

3:4, 3/4, three to four.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Write the ratio 7 to 3 (simplest form).

1

Write the ratio

Put the first quantity to the second, in order. 7:3

EX 2medium

Write the ratio 9 to 4 (simplest form).

1

Write the ratio

Put the first quantity to the second, in order. 9:4

EX 3hard

Write the ratio 4 to 5 (simplest form).

1

Write the ratio

Put the first quantity to the second, in order. 4:5

04 / COMMON TRAPS

Where students slip.

Trap

Reading a/b as a division result.

Fix

As a ratio, 3/4 means the comparison 3:4.

Trap

Forgetting to simplify.

Fix

Ratios reduce like fractions.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Write the ratio 3 to 8 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
C2

Write the ratio 5 to 9 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
C3

Write the ratio 4 to 5 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
C4

Write the ratio 5 to 7 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
Apply

Apply (4)

A1

Write the ratio 7 to 3 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
A2

Write the ratio 9 to 3 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
A3

Write the ratio 6 to 5 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
A4

Write the ratio 7 to 3 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
Extension

Extension (4)

E1

Write the ratio 9 to 3 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
E2

Write the ratio 5 to 4 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
E3

Write the ratio 9 to 5 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.
E4

Write the ratio 6 to 9 (simplest form).

Need a hint?
  • Pick any of the three forms.
  • Simplify to lowest terms.