Reading a tape measure and shop fractions

Count the spaces between two inch marks on your tape. If there are 16, each space is 1/16 in; if there are 32, each is 1/32 in. The longest mark in the middle is 1/2, the next longest are the quarters (1/4, 3/4), then the eighths, then the sixteenths.

Arithmetic: exact by definition

To read a length, take the last whole inch the end passed, then count the small spaces after it. Thirteen sixteenth-spaces past 1 in reads 1 13/16 in. Fractions are always written in their lowest terms: 8/16 is 1/2, 12/16 is 3/4, 6/16 is 3/8.

Arithmetic: exact by definition

Put both fractions over the same bottom number before adding. 5 3/8 + 2 3/4 is 5 3/8 + 2 6/8 = 7 9/8, and 9/8 is 1 1/8, so the total is 8 1/8 in. To subtract, borrow an inch as 8/8 or 16/16 when the top fraction is the smaller one.

Arithmetic: exact by definition

A shortcut that never fails: turn everything into sixteenths. 3/8 is 6/16, 3/4 is 12/16, and 6/16 + 12/16 = 18/16 = 1 2/16 = 1 1/8.

Arithmetic: exact by definition

A fraction is a division: 11/16 is 11 ÷ 16 = 0.6875. Going the other way, multiply the decimal by 16 and round to the nearest whole number: 0.59 × 16 = 9.44, so the nearest sixteenth is 9/16. Machine settings, calipers and plans often use decimals, so this conversion comes up all the time.

Arithmetic: exact by definition

An inch is exactly 25.4 mm, by definition. So 3/4 in is 0.75 × 25.4 = 19.05 mm, and 18 mm is 18 ÷ 25.4 = 0.709 in, a little under 3/4.

Arithmetic: exact by definition

The fraction chart lists every sixteenth, thirty-second and sixty-fourth with its decimal and millimetres; the calculator converts any of them, and the board foot calculator takes shop fractions straight from your tape.

Arithmetic: exact by definition