Writing expressions from words

Writing expressions from words

Writing expressions from words

Reading is the hard part of word problems. Translating English (or any language) into a calculation is a skill you train. Once you can write the expression, the arithmetic is easy.

Match keywords to operations

Watch for these signal words:

WordsOperation
sum, total, plus, add, more, increased by+
difference, minus, less, decreased by, fewer−
product, times, of (with a fraction), multiplied by×
quotient, divided by, per, each, average÷

These aren't strict rules, but they're a strong starting point.

Translate step by step

"Five more than the product of 3 and 7"

Identify pieces:

  • "product of 3 and 7" → `3 × 7`
  • "five more than _" → `_ + 5`

Combine: `3 × 7 + 5`.

By the order of operations, × first: `21 + 5 = 26`.

Brackets save the meaning

Sometimes the words demand brackets — without them, the order of operations would give a different answer.

"Twice the sum of 4 and 5"

Pieces:

  • "sum of 4 and 5" → `4 + 5`
  • "twice the _" → `2 × _`

Combine literally: `2 × (4 + 5)`. The brackets are essential. Without them, `2 × 4 + 5 = 13` — but the problem wants `2 × 9 = 18`.

"Half of the difference between 20 and 8"

  • "difference between 20 and 8" → `20 − 8`
  • "half of _" → `_ ÷ 2`

Combine: `(20 − 8) ÷ 2 = 12 ÷ 2 = 6`.

Worked examples

"Add 3 and 7, then multiply by 4."

Comma-separated steps. The bracket follows the first comma:

`(3 + 7) × 4 = 10 × 4 = 40`.

"Multiply 3 and 7, then add 4."

Same structure but × first, no brackets needed:

`3 × 7 + 4 = 21 + 4 = 25`.

"Subtract 3 from the sum of 8 and 9."

  • "sum of 8 and 9" → `8 + 9`
  • "subtract 3 from _" → `_ − 3`

`(8 + 9) − 3 = 17 − 3 = 14`.

"Subtract the sum of 3 and 4 from 20."

  • "sum of 3 and 4" → `3 + 4`
  • "subtract _ from 20" → `20 − _`

`20 − (3 + 4) = 20 − 7 = 13`.

Common traps in word phrasing

  • "Less than" reverses the order. "5 less than 12" is `12 − 5`, not `5 − 12`.
  • "Subtract A from B" is `B − A`, not `A − B`. Same with "from".
  • "Divided by" vs "divided into": "15 divided by 3" is `15 ÷ 3`, but "15 divided into 3" sometimes means how many 3s fit into 15 — read carefully.

When the words have several operations

"Three times 5 plus twice 4"

Two parts joined by "plus":

  • "three times 5" → `3 × 5`
  • "twice 4" → `2 × 4`

Combine: `3 × 5 + 2 × 4 = 15 + 8 = 23`.

Here we didn't need brackets — the × operations were inside the phrases, and "plus" connects the two products.

What's next

Try it out