Fractions as positions
Between 0 and 1, split into d equal steps; n/d is the n-th step. Bigger fractions sit further right.
Why it works
3/4 is most of the way from 0 to 1.
Fractions · What is a fraction? · 1.2
On the number line.
Fractions live on the number line between the whole numbers. Split each unit into the denominator’s many equal steps and count up the numerator.
See it work.
On the number line
Where does it sit?
Watch the method
On the number line
3/4 sits three of four steps from 0 to 1.
1
Name the fraction
Shaded parts on top, total parts on the bottom.
Practice until it feels automatic.
Your turn
Work it out.
Type a fraction like 3/4 or 1 1/2.
streak 0
best 0
… =
The idea underneath.
From easy to tricky.
1 parts are shaded out of 2 — write the fraction.
1
Name the fraction
Shaded parts on top, total parts on the bottom. 1/2
3 parts are shaded out of 6 — write the fraction.
1
Name the fraction
Shaded parts on top, total parts on the bottom. 3/6
3 parts are shaded out of 8 — write the fraction.
1
Name the fraction
Shaded parts on top, total parts on the bottom. 3/8
Where students slip.
Trap
Splitting into the wrong number of steps.
Fix
Use the denominator for the number of steps in each unit.
Trap
Counting from 1 instead of 0.
Fix
Start counting steps from 0.
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
1 parts are shaded out of 2 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
C2
2 parts are shaded out of 6 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
C3
2 parts are shaded out of 4 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
C4
5 parts are shaded out of 8 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
Apply
Apply (4)
A1
3 parts are shaded out of 6 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
A2
2 parts are shaded out of 7 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
A3
5 parts are shaded out of 7 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
A4
2 parts are shaded out of 3 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
Extension
Extension (4)
E1
3 parts are shaded out of 8 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
E2
4 parts are shaded out of 7 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
E3
3 parts are shaded out of 8 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.
E4
2 parts are shaded out of 3 — write the fraction.
Need a hint?
- Each unit splits into d equal steps.
- Count n steps from 0.