Now that you can work with parentheses, brackets and braces, you can turn words into expressions. Words like sum, difference, product and quotient each name one result: the answer to an addition, a subtraction, a multiplication or a division.
Key idea
Write the operations in the order the words ask for. If a step the words do first would not come first by the order of operations, put it in parentheses: “3 times the sum of 8 and 7” is $3 \times (8 + 7)$.
Why it works
“The sum of 8 and 7” is one amount, 15. Three times that amount is three groups of 15. Without parentheses, $3 \times 8 + 7$ would multiply first and add 7 only once, which is a different amount.
Worked examples
Worked example: Words to an expression
Write “add 6 and 9, then multiply by 4” and find its value.
- The words add first. Multiplying would normally come first, so the sum needs parentheses: $(6 + 9) \times 4$.
- Inside the parentheses: $6 + 9 = 15$.
- Multiply: $15 \times 4 = 60$.
Answer: $(6 + 9) \times 4 = 60$
Worked example: No parentheses needed
Write “5 less than the product of 7 and 3.”
- “The product of 7 and 3” is $7 \times 3$.
- “5 less than” it means take 5 away from it: $7 \times 3 - 5$.
- Multiplying comes first anyway, so no parentheses are needed. The value is $21 - 5 = 16$.
Answer: $7 \times 3 - 5$
Worked example: Compare without calculating
How does $4 \times (2{,}318 + 976)$ compare with $2{,}318 + 976$?
- The parentheses make $2{,}318 + 976$ one amount.
- $4 \times$ that amount is 4 groups of it.
Answer: It is 4 times as large, and you never had to add.
Common mistake
Writing $3 \times 8 + 7$ for “3 times the sum of 8 and 7.” Check by reading your expression back in words: $3 \times 8 + 7$ says “multiply 3 by 8, then add 7,” which is not what you were told.