Evaluate the terms first, then add
Work out every term, and only then add.
Tara’s bill
A pencil box costs ₹6. Tara buys 3 pencil boxes and one ₹10 sharpener. She writes her bill as 3 × 6 + 10.
What is her bill?
What this lesson covers
The idea
When an expression has multiplication or division and no brackets fixing the order, its value is found by first evaluating each term and then adding all the terms.
Tara’s bill
A pencil box costs ₹6. Tara buys 3 pencil boxes and one ₹10 sharpener. She writes her bill as 3 × 6 + 10.
What is her bill?
- ₹28
- ₹48
- ₹18
Terms first
Tap the signs in the right order: brackets first, then every × and ÷ (each term), and only then the + signs.
Terms, then the sum
A product like 5 × 4 is a single term, so it is worked out before it is added to anything. A bracket inside a term is worked out first of all.
When an expression has × or ÷ and no brackets fix the order, first evaluate each term, then add all the terms.
- Expression | Terms worked out, then added
- 30 + 5 × 4 | 30 + 20 = 50
- 4 + 100 ÷ 2 | 4 + 50 = 54
- 2 + (−10) + 4 × 6 | 2 + (−10) + 24 = 16
- 5 × (3 + 2) + 7 × 8 + 3 | 25 + 56 + 3 = 84
Notes
With × or ÷ and no brackets to fix the order, first evaluate each term, then add all the terms.
Check yourself
Work out 8 + 6 × 3.
Answer: 26
The terms are 8 and 6 × 3. 6 × 3 = 18, and 8 + 18 = 26.
Dev buys 4 notebooks at ₹12 each and one ₹5 pen. Which expression gives his bill?
Work out 7 × 4 + 18 ÷ 3.
Answer: 34
7 × 4 = 28 and 18 ÷ 3 = 6. Then 28 + 6 = 34.
Work out 5 × (2 + 1) + (−4) + 3 × 2.
Answer: 17
5 × (2 + 1) = 15, the middle term is −4, and 3 × 2 = 6. Then 15 + (−4) + 6 = 17.
- 4 × 12 + 5 = 53 — correct. Yes! The notebooks are one term, 4 × 12 = 48. The pen is the other term. 48 + 5 = 53.
- 4 × (12 + 5) = 68. That is 4 notebooks and 4 pens. Dev buys only one pen.
- 4 + 12 × 5 = 64. That is 12 pens at ₹5 plus 4 more. It does not match 4 notebooks at ₹12.