How does this chart work?

Each row starts with a fraction in lowest terms and shows what happens when you multiply its top and bottom by 2, 3, 4 and 8. Every entry in a row is the same number, written with different pieces.

Why does the ×8 column matter in the shop?

Because it lands on the 64ths grid: 3/8 × 8/8 is 24/64, which is how you find 3/8 on a rule marked in 64ths.

Equivalent fractions chart

One rule makes every row: multiply the top and bottom by the same number and the value does not change.

Lowest terms	× 2	× 3	× 4	× 8
1/2	2/4	3/6	4/8	8/16
1/3	2/6	3/9	4/12	8/24
2/3	4/6	6/9	8/12	16/24
1/4	2/8	3/12	4/16	8/32
3/4	6/8	9/12	12/16	24/32
1/5	2/10	3/15	4/20	8/40
2/5	4/10	6/15	8/20	16/40
3/5	6/10	9/15	12/20	24/40
4/5	8/10	12/15	16/20	32/40
1/6	2/12	3/18	4/24	8/48
5/6	10/12	15/18	20/24	40/48
1/8	2/16	3/24	4/32	8/64
3/8	6/16	9/24	12/32	24/64
5/8	10/16	15/24	20/32	40/64
7/8	14/16	21/24	28/32	56/64

Common questions

How does this chart work?: Each row starts with a fraction in lowest terms and shows what happens when you multiply its top and bottom by 2, 3, 4 and 8. Every entry in a row is the same number, written with different pieces.
Why does the ×8 column matter in the shop?: Because it lands on the 64ths grid: 3/8 × 8/8 is 24/64, which is how you find 3/8 on a rule marked in 64ths.

Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. See the full methodology.