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).
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.
3 · The parts must be EQUAL
The pieces must be the same size. 4 equal parts = fourths. Unequal parts are not fourths.
4 · Fractions of a group
A fraction can also mean part of a group. 2 of these 6 dots are shaded → 2/6.
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.
6 · Different fractions, same amount
Some fractions look different but are the same amount — equivalent. 1/2 and 2/4 shade the same, so 1/2 = 2/4.
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.
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.
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.
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! 🎉
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