Les fractions sur un ruban

Nobody hands you a calculator at the saw. You read one mark, you read another, and you add them in your head while the pipe is still in your hand. This page is that skill: what the marks on a tape actually are, how to say a fraction the short way, and how to add two of them without writing anything down.

A tape is made by halving

Look at the lengths of the marks. The inch lines are the longest. Halfway between them is the next longest: the half. Halfway between an inch line and the half is the quarter. Halve again and you get the eighths; halve once more and you have the sixteenths, the shortest marks. That is the whole tape: four halvings. A fraction on a tape is just a count of the smallest marks — 11/16 means eleven of the small steps past the inch line.

Saying it the short way: reducing

If the mark you land on is a long one, it has a shorter name. Eight sixteenths is the half mark, so you say 1/2. Twelve sixteenths is the three-quarter mark: 3/4. Six sixteenths lands on an eighth mark: 3/8. The rule is: while the top and the bottom are both even, halve them both. 12/16 → 6/8 → 3/4, and you stop because 3 is odd. On the tape you can see it — the name of a mark is the longest tick that lands there.

• 8/16 = 1/2halve, halve, halve
• 12/16 = 3/4halve twice, then 3 is odd — stop
• 10/16 = 5/8halve once, then 5 is odd — stop
• 7/16 = 7/167 is odd already; it stays a sixteenth

Three worked examples

1. Add 3/8" and 5/16"

1. Same bottom first. 3/8 is 6/16 (double top and bottom). 5/16 stays.
2. Add the tops: 6 + 5 = 11. So 11/16.
3. Reduce? 11 is odd. 11/16".

See it on the tape

Put your finger on the 3/8 mark — that is the sixth small step. Now count five more small steps. You land on the eleventh: 11/16. Adding fractions is just walking the tape.

2. Add 3/4" and 7/16" — past the inch

1. 3/4 is 12/16. 7/16 stays.
2. 12 + 7 = 19 sixteenths. That is more than 16, so carry an inch: 19 − 16 = 3.
3. One inch and 3/16. 1 3/16".

3. Add 2 5/8" and 1 1/2" — mixed numbers

1. Whole inches first: 2 + 1 = 3.
2. Fractions in sixteenths: 5/8 = 10/16, 1/2 = 8/16. Add: 18/16. Carry: 1 and 2/16.
3. 3 + 1 = 4 inches, and 2/16 reduces to 1/8. 4 1/8".

The shortcut for halves

Adding a half is the commonest case: just move to the next long mark of the same kind. 2 5/8 plus a half is 3 1/8 — the 5/8 mark and the 1/8 mark are a half apart, and you carried an inch. Practise that one until it is a reflex.

Try one: 7/8" + 3/16"

7/8 = 14/16. 14 + 3 = 17. Carry: 1 and 1/16. Answer: 1 1/16".

Drill it

Two marks, add them, tap the answer. Print twenty for a worksheet with the key at the foot.

Questions fréquentes

Voir aussi

• Reading a tape the fast way — the next lesson.
• Fraction / decimal drill — the same fractions as decimals, for when the spec sheet speaks decimal.
• All trade math lessons