Arithmetic Expressions - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Arithmetic expressions are the grammar of calculation. A sentence like 'double the sum of 8 and 5' must become 2 x (8 + 5), not 2 x 8 + 5. This chapter trains students to read a problem carefully, build the expression correctly, and evaluate it in a disciplined order.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Expression versus equation

An expression has numbers and operations, such as 18 - 3 x 4. An equation says two expressions are equal, such as 18 - 3x = 6.

Order matters

Multiplication and division are done before addition and subtraction unless brackets change the order. Brackets are not decoration; they control meaning.

Word phrases

Phrases like 'sum of', 'difference between', 'product of', and 'quotient of' indicate operations. Words such as 'twice', 'thrice', and 'half' create multipliers or divisions.

3. Rules and formulas to remember

• Operation order: Brackets -> division/multiplication -> addition/subtraction. Work from left to right within the same priority.
• Distributive idea: a x (b + c) = a x b + a x c. Useful for mental arithmetic and simplification.
• Expression from phrase: twice the sum of a and b = 2 x (a + b). Brackets preserve the intended meaning.

4. Worked examples

Example 1: Evaluate 45 - 5 x 6 + 12.

Do multiplication first: 5 x 6 = 30. Then 45 - 30 + 12 = 15 + 12 = 27.

Example 2: Evaluate (45 - 5) x (6 + 12).

Brackets first: 45 - 5 = 40 and 6 + 12 = 18. Product = 40 x 18 = 720.

Example 3: Write '9 less than the product of 7 and 8' as an expression.

Product of 7 and 8 is 7 x 8. 9 less than it gives 7 x 8 - 9.

Example 4: A notebook costs Rs. 35 and a pen costs Rs. 12. Write the cost of 4 notebooks and 5 pens.

4 x 35 + 5 x 12 = 140 + 60 = Rs. 200.

5. Activity corner

Give students expression cards and word cards. They must match '3 x (12 + 5)' with 'three times the sum of 12 and 5'. Then ask them to create a different sentence for the same expression.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Solving left to right without priority Fix: Use the operation order each time.
• Mistake: Ignoring brackets Fix: Evaluate every bracket before operating outside it.
• Mistake: Writing 'less than' in the wrong order Fix: 9 less than 40 is 40 - 9, not 9 - 40.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Evaluate 72 / 8 + 5 x 3.
2. Evaluate 6 x (14 - 9) + 11.
3. Write 'five more than twice 13'.
4. Write 'half of the sum of 18 and 26'.
5. A ticket costs Rs. 75. Write the cost of 6 tickets after a Rs. 40 discount on the total.
6. Why are brackets needed in word problems?

9. Answer key

1. Evaluate 72 / 8 + 5 x 3. Answer: 24.

2. Evaluate 6 x (14 - 9) + 11. Answer: 41.

3. Write 'five more than twice 13'. Answer: 2 x 13 + 5.

4. Write 'half of the sum of 18 and 26'. Answer: (18 + 26) / 2.

5. A ticket costs Rs. 75. Write the cost of 6 tickets after a Rs. 40 discount on the total. Answer: 6 x 75 - 40 = Rs. 410.

6. Why are brackets needed in word problems? Answer: They show which operation must happen first.

10. Quick revision

• Main themes: order of operations, brackets, numerical expressions, word-to-expression translation.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.