★ Free tutorial · Grade 3

Fractions — a gentle walkthrough for Grade 3

Learn fractions from the very beginning, one drawing at a time. A short 24-question test waits at the end.

1 · What is a fraction?

A fraction is equal parts of one whole — like slices of one pizza. Split a bar in 2 and shade 1: that is one half (1/2).

one whole
1/2 (one half)

2 · The top and bottom numbers

The bottom = how many equal parts in all. The top = how many you count. So 1/4 means 4 equal parts, count 1.

Surprise: 2/4, 4/12, 3/12 shade the same as 1/2, 1/3, 1/4 — one piece can have more than one name.

1/2
1/3
1/4
2/4
4/12
3/12

3 · The parts must be EQUAL

The pieces must be the same size. 4 equal parts = fourths. Unequal parts are not fourths.

fair fourths ✓
these are thirds (1/3)

4 · Fractions of a group

A fraction can also mean part of a group. 2 of these 6 dots are shaded → 2/6.

2/6 of the dots are shaded

5 · Fractions live on the number line

Split the line from 0 to 1 into equal steps. This dot sits on the 3rd of 4 steps → 3/4.

01
the dot is at 3/4

6 · Different fractions, same amount

Some fractions look different but are the same amountequivalent. 1/2 and 2/4 shade the same, so 1/2 = 2/4.

1/22/4
same shaded amount

7 · Comparing fractions

Same bottom: more pieces wins → 3/5 > 2/5.

Same top: fewer pieces wins (bigger pieces) → 1/4 > 1/6.

Different bottoms? Rename so they match, then compare tops: 1/4 = 6/24, 1/6 = 4/24 → 1/4 > 1/6.

3/52/5
same bottom → more pieces wins
1/41/6
same top → bigger pieces win
14×66=62416×44=424
rename both to 24ths
6/244/24
now 6 beats 4, so 1/4 > 1/6

8 · The whole — adding and subtracting

Shade all the parts = one whole: 4/4 = 1.

Same bottom: add or subtract the tops, keep the bottom. 1/4 + 2/4 = 3/4, and 3/4 − 1/4 = 2/4.

4/4 = 1 whole
1/4 + 2/4 = 3/4
3/4 − 1/4 = 2/4

9 · Whole numbers are fractions too

Any whole number is that number over 1: 1 = 1/1, 2 = 2/1, 3 = 3/1.

If the top divides evenly by the bottom, it is a whole number: 8/2 = 4, 50/10 = 5.

1/1 = 1
2/1 = 2
3/1 = 3
8/2 = 4 (eight halves)
50/10 = 5 (fifty tenths)

10 · A peek ahead: multiply & divide

Fractions can also multiply and divide. Half of a half is a quarter: 1/2 × 1/2 = 1/4.

You don't need these yet — naming, comparing, adding, and subtracting is a great start! 🎉

1/2 × 1/2 = 1/4
½ a pizza…
…shared by 2 = ¼ each

Ready to check what stuck?

Take the free 24-question test — it starts easy and builds to harder, ISEE-style reasoning. It's auto-scored, and you can review every answer afterward.