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Fractions on a tape

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

3 4 1/2 1/4 3/4 1/8 1/16
Between 3 and 4: the longest mark is the half, the next longest are the quarters, then the eighths, then the sixteenths. Sixteen small steps make the inch.

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.

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.

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This drill needs JavaScript to generate and mark questions. Turn it on to practice — the explanation below works either way.

Questions people ask

Why is a tape in sixteenths and not tenths?

Because a tape is made by halving. An inch halved is a half, halved again is a quarter, then an eighth, then a sixteenth. Every mark is a halving of the one before, which means any mark can be named by counting how many of the smallest marks it is from the inch line. Tenths would need a different ruler in your head; halves you can see.

What does "reduce" mean?

Write the fraction with the smallest numbers that still mean the same amount. 8/16 is the same distance as 1/2, and 6/16 is the same as 3/8. You reduce by dividing top and bottom by the same number until nothing divides both. On a tape, "reduced" is just the name of the longest mark that lands there.

How do I add two fractions with different bottoms?

Turn them into the same bottom first — on a tape, sixteenths. 3/8 is 6/16; 5/16 is already sixteenths. Then add the tops: 6 + 5 = 11, so 11/16. If the tops add past 16, carry an inch. That is all there is to it, and the drill below is nothing but that move.

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