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Is 30 + 5 × 4 equal to 140 or 50? Students who work left to right get 140; the correct answer is 50. NCERT's new Class 7 book does not lean on a memorised mnemonic to settle this. It teaches a method based on terms, which also explains why the rule works. This post walks through that method with numbers, covers the rules for brackets, and ends with a practice routine.
What does the Class 7 Arithmetic Expressions chapter cover?
NCERT's Class 7 mathematics book, Ganita Prakash, comes in two parts; Part 1 was first published in April 2025 and the current copy is marked "Reprint 2026-27". Chapter 2, Arithmetic Expressions, covers:
Simple expressions and comparing them by reasoning instead of calculating
Brackets, which specify the order of operations
Terms, and how they decide the order when there are no brackets
Swapping and grouping terms (the commutative and associative properties of addition)
Removing brackets, including the sign change after a minus
The distributive property
Why do expressions need rules at all?
The chapter compares brackets to punctuation. "Shalini sat next to a friend with toys" means something different once you add a comma. In the same way, 30 + 5 × 4 could be read two ways. In the book, Mallesh has 30 marbles and Arun has 5 bags of 4, so the right reading multiplies first: 30 + 20 = 50. Purna, adding first, gets 140.
With brackets, the meaning is clear: 30 + (5 × 4). Work out what is inside brackets before anything else.
What are terms, and how do they decide the order?
The book defines terms as the parts of an expression separated by a "+" sign. To find them:
Rewrite every subtraction as adding the inverse: 83 − 14 becomes 83 + (−14).
Split at each "+". A product such as 6 × 5 is a single term, because it has no "+" inside.
Evaluate each term.
Add the terms, in any order.
Worked example 1 (from the book). 48 − 10 × 2 + 16 ÷ 2
As a sum of terms: 48 + (−10 × 2) + (16 ÷ 2)
Terms: 48, −20 and 8
Value: 48 − 20 + 8 = 36
Worked example 2 (from the book). 5 × (3 + 2) + 7 × 8 + 3
Brackets first: 5 × 5 = 25
Next term: 7 × 8 = 56
Add: 25 + 56 + 3 = 84
Worked example 3. 23 − 2 × 4 + 16
Terms: 23, −2 × 4 and 16, so 23, −8 and 16
Value: 23 − 8 + 16 = 31
Because terms can be added in any order, step 4 lets you choose an easy order. For −7 + 10 + (−11), the book shows that every order gives −8.
How do you remove brackets after a minus sign?
The chapter's rule: when you remove brackets that have a minus sign in front, the sign of every term inside changes.
Worked example 4 (from the book). Irfan buys biscuits for ₹15 and dal for ₹56 and pays ₹100. His change is 100 − (15 + 56) = 100 − 71 = ₹29. Without brackets this becomes 100 − 15 − 56 = 85 − 56 = 29. The answer matches. Writing 100 − 15 + 56 instead gives 141, which the book calls absurd.
Worked example 5 (from the book). 500 − (250 − 100) = 500 − 150 = 350. Removing the brackets gives 500 − 250 + 100 = 350. The −100 inside becomes +100.
When the brackets have a plus sign in front, nothing changes: 28 + (35 − 10) = 28 + 35 − 10 = 53.
How does the distributive property help?
The book's example: two friends each order a ₹43 cutlet and a ₹24 rasgulla. The total is 2 × (43 + 24), which equals 2 × 43 + 2 × 24 = 86 + 48 = ₹134. Multiplying a bracket means multiplying every term inside.
Worked example 6. Use it for mental maths: 12 × 98 = 12 × (100 − 2) = 1200 − 24 = 1176.
Do extra brackets help students?
Researchers have tested this. Gunnarsson, Sönnerhed and Hernell (2016) studied 169 Swedish students aged 12 to 13 and compared expressions like a − b × c with versions such as a − (b × c), where the brackets are not needed. Their data did not support using such brackets to stop students attaching the middle number to the first operation. A larger online study of 528 students by Ngo and colleagues (2023) found students were more accurate when the multiplication sat on the left of an expression than on the right, and extra brackets improved accuracy only when the multiplication was in the middle.
The lesson for you is that the position of a multiplication can pull you into working left to right. Splitting into terms protects you wherever the multiplication sits.
Which mistakes cost the most marks?
Working strictly left to right. 30 + 5 × 4 is 50, not 140.
Not flipping signs. 500 − (250 − 100) is not 500 − 250 − 100.
Distributing to one term only. 2 × (43 + 24) is not 2 × 43 + 24.
Losing the minus with a term. In 23 − 2 × 4, the term is −8.
Skipping the check. Estimate first; a change bigger than what you paid is a warning sign.
How should you practise this week?
Day 1: Split ten expressions into terms before evaluating any of them.
Day 2: Write a shopping story for 100 − (35 + 42) and for 3 × (20 + 15).
Day 3: Remove brackets in six expressions, three with a minus in front, and check each by evaluating both forms.
Day 4: Start the book's "Expression Engineer" puzzle: use four 4s to make every number from 1 to 10 (the book goes up to 20).
Day 5: Use the distributive property to do 15 × 99, 25 × 104 and 8 × 47 in your head.
If you want to check where an answer went wrong, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer. Turning subtraction into adding the inverse comes from integers in Class 6, and the same rules carry over to expressions using letter-numbers in Class 7.
Write the cost of your family's last restaurant bill as one expression with brackets, then work it out by splitting it into terms.
