Adding and Subtracting Fractions for Woodworking

Woodworking runs on fractions. Tape measures, lumber dimensions, cut lists, dado widths, rabbet depths — they all use fractional inches. Whether you're adding up parts for a total length or subtracting a kerf from a board, fraction math is something every woodworker needs to handle confidently.

How fraction math works

The key to adding or subtracting fractions is giving them a common denominator — the same bottom number. You can only combine fractions when their denominators match.

Tape-measure fractions make this easier because the denominators are always powers of 2: halves, quarters, eighths, and sixteenths. The least common denominator is always the larger of the two.

Addition example

You need two boards end to end: one is 3 1/4" and the other is 1 7/8". What's the total?

1. Convert to the same denominator: 3 2/8 + 1 7/8
2. Add whole numbers: 3 + 1 = 4
3. Add fractions: 2/8 + 7/8 = 9/8 = 1 1/8
4. Combine: 4 + 1 1/8 = 5 1/8"

Subtraction example

You have a board that's 12 3/4" and need to remove 5 7/16". What remains?

1. Convert to sixteenths: 12 12/16 − 5 7/16
2. Subtract whole numbers: 12 − 5 = 7
3. Subtract fractions: 12/16 − 7/16 = 5/16
4. Result: 7 5/16"

Multiplication and division

Multiplication and division are actually simpler than addition — no common denominator needed.

To multiply fractions: multiply the numerators straight across, then multiply the denominators straight across. Convert mixed numbers to improper fractions first.

To divide fractions: flip the second fraction (reciprocal) and multiply.

Real scenario: shelf spacing

You're building a bookcase with 3 shelves, each made from 3/4" plywood. Each shelf sits in a 1/4"-deep dado. How much total height do the shelves consume?

Each shelf sticks out: 3/4 − 1/4 = 1/2" above the dado. But you need the full material: 3 shelves × 3/4" = 9/4 = 2 1/4" of total shelf thickness.

Another example

You need to divide a 27 3/4" opening into 4 equal sections:

27 3/4 ÷ 4 = 111/4 ÷ 4 = 111/16 = 6 15/16"

Reading your tape measure

Every mark on a tape measure is a power-of-2 fraction. Understanding the marks helps you read measurements and do math in the shop.

• Longest marks (after the inch) — 1/2"
• Next longest — 1/4" and 3/4"
• Shorter — eighths (1/8, 3/8, 5/8, 7/8)
• Shortest — sixteenths (1/16, 3/16, 5/16, etc.)

Notice that 1/3 never appears on a standard tape measure. That's because tape measures use binary fractions (powers of 2), and thirds don't divide evenly into that system. If a plan calls for dividing something into thirds, you'll need to convert to decimals (0.333") or use a fraction calculator to get the nearest sixteenth.

Some precision tapes show 32nds or even 64ths, but 16ths is the practical limit for most woodworking.

Common woodworking fraction scenarios

Cut lists

When building a cut list, you're constantly adding fractional dimensions. A face frame might need stiles at 1 1/2" + rails at 2 1/4" + a panel at 11 3/8". Getting the total right means getting the fractions right.

Dados and rabbets

A dado for 3/4" plywood is actually cut at 23/32" because plywood is undersized. You need to know that 23/32 is between 11/16 and 3/4 — and that a standard 3/4" dado bit will leave a sloppy joint.

Dividing boards equally

Ripping a 5 1/2" board into 3 equal strips means dividing 5 1/2 by 3. That's 11/2 ÷ 3 = 11/6 = 1 5/6". Since 5/6 doesn't land on a tape-measure mark, you'd round to the nearest 16th: approximately 1 13/16".

Kerf allowance

A typical table-saw blade has a 1/8" kerf. If you're cutting 4 pieces from one board, you lose 3 kerfs: 3 × 1/8 = 3/8" total. Add that to your cut list so you don't end up short on the last piece.