Class 7 Arithmetic Expressions
Understand expressions, compare them intelligently, work with terms and brackets, and use mathematical properties to simplify calculations based on NCERT Ganita Prakash Grade 7 Part I.
What are Arithmetic Expressions?
An arithmetic expression is a mathematical phrase made using numbers and operations such as addition, subtraction, multiplication, and division. An expression has a definite numerical value. In this chapter, students learn to read, compare, and evaluate expressions without brute calculation, understand terms and brackets, rearrange and group terms using the commutative and associative properties, remove brackets accurately, and apply the distributive property for efficient mental mathematics.
Simple Expressions & Values
Every mathematical phrase evaluates to a definite value. Explore operations, values, and equivalent expressions.
13 plus 2 (Sum of 13 and 2)
20 minus 4 (Difference of 20 and 4)
12 times 5 (Product of 12 and 5)
18 divided by 3 (Quotient of 18 by 3)
Expression Builder: Construct & Evaluate
Comparing Expressions: Using =, <, and >
We compare expressions based on their numerical values: $10 + 2 > 7 + 1$ (since $12 > 8$), and $13 - 2 < 4 \times 3$ (since $11 < 12$).
Ascending Order of Expressions (Textbook Page 25)
Reading and Evaluating Complex Expressions
Resolving ambiguities through punctuation in math: the power of brackets and mathematical terms.
Consider: “Shalini sat next to a friend with toys.” (The friend has the toys).
Versus: “Shalini sat next to a friend, with toys.” (Shalini has the toys).
Just as commas eliminate ambiguity in English, brackets and terms eliminate ambiguity in arithmetic!
Example 4: Mallesh Brought 30 Marbles; Arun Brought 5 Bags of 4 Marbles
Expression: 30 + 5 × 4
(30 + 5) × 4 = 35 × 4 = 140 (INCORRECT)
Arun didn't bring 35 bags of 4 marbles!30 + (5 × 4) = 30 + 20 = 50 (CORRECT)
Arun has 20 marbles. Mallesh has 30. Total = 50!Brackets enclose the product term (5 × 4). Evaluate inside brackets first (20), then add to 30.
Terms in Expressions: Converting Subtraction to Inverses
Textbook Definition: Terms are the parts of an expression separated by a ‘+’ sign. Subtraction is treated as adding the additive inverse: $83 - 14 = 83 + (-14)$. The terms are $83$ and $-14$.
Note: Products like 4 × 6 stay together as a single term because they contain no ‘+’ sign.
Swapping and Grouping: Commutative & Associative Laws
When an expression is written as a sum of terms, changing the order or grouping of terms does not alter the final value.
Term 1 + Term 2 = Term 2 + Term 1
Example 6 (Madhu's Drone): 6m up and 4m down: 6 + (−4) = 2. Swapping: (−4) + 6 = 2. Swapping preserves the sum even with negative numbers!
(Term 1 + Term 2) + Term 3 = Term 1 + (Term 2 + Term 3)
In (−7) + 10 + (−11): grouping first two gives (3) + (−11) = −8. Grouping last two gives (−7) + (−1) = −8. Both yield −8.
Manasa took 5 minutes to add a list and got 11,749, then realized she forgot 9,055. Due to the associative property, she does NOT restart: she simply computes $11,749 + 9,055 = 20,804$!
Hat and Shoes: Wear hat first or shoes first → identical outcome (Commutative!).
Socks and Shoes: Wear shoes first then socks → uncomfortable and absurd (Non-commutative!).
Writing Expressions from Stories (10 Scenarios)
Convert everyday situations into precise mathematical expressions:
Mallika spends ₹25 every day for lunch at school from Monday to Friday (5 school days). Which expression gives her total weekly lunch expenditure?
Irfan bought a packet of biscuits for ₹15 and toor dal for ₹56. He gave a ₹100 note to the shopkeeper. How much change will he receive?
Four friends ordered 4 dosas at ₹23 each and tipped the waiter ₹5. If the number of friends later increases to 7 friends ordering 7 dosas with the same ₹5 tip, what is the total cost?
33 children are playing in a circle. When the teacher calls '5', Ruby observes students forming groups of 5. If the teacher had called '4', what expression describes the grouping of the 33 children?
Raghu had four 2 kg packets of rice. He bought 100 kg more from the wholesale market and packed all of it into 2 kg packets. How many 2 kg packets does he have in total?
Queen Alia gave 100 gold coins each to Princess Elsa and Princess Anna. Elsa doubled her coins in business, while Anna spent half her coins on jewellery. How many coins do both have together?
The market in Begur operates all 7 days of the week. Rahim supplies 9 kg each day and Shyam supplies 11 kg each day. How many kg of mangoes do they supply in a week?
Binu earns ₹20,000 every month. Each month she spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses. What is her total savings by the end of one year (12 months)?
A snail climbs 3 cm up a 10 cm post each day, and slips down 2 cm each night. On which day does it reach the delicious treat on top of the 10 cm post?
Melvin reads a 2-page story every day except on Tuesdays and Saturdays (he reads on 5 days a week). How many stories does he read in 8 weeks?
Removing Brackets & The Distributive Property
Sign-flipping rules for brackets preceded by minus, and distributing multiplication across sums.
Rule: Minus outside flips +40 to −40 and +3 to −3
Common Pitfall: 200 − 40 + 3 = 163 (WRONG)
The Distributive Property: Multiplication Over Addition & Subtraction
The multiple of a sum is equal to the sum of the multiples: $a \times (b + c) = a \times b + a \times c$.
Vegetable cutlet costs ₹43; rasgulla costs ₹24. For 2 friends:
2 × (43 + 24) = 2 × 43 + 2 × 24 = 86 + 48 = ₹134
Scouts: 4 rows of 5; Guides: 3 rows of 5.
(4 + 3) × 5 = 4 × 5 + 3 × 5 = 20 + 15 = 35 children
Rewrite: (100 − 3) × 25
= 100 × 25 − 3 × 25 = 2500 − 75 = 2425
Step-by-Step Expression Solver
Expression Engineer!
Use operations and brackets as engineering tools to hit target values.
Construct expressions using exactly three 3s with +, −, ×, ÷ and brackets:
A snail climbs 3 cm during daytime and slips 2 cm at night. The post is 10 cm high. Why does it reach the top on day 8 and not day 10?
Manasa spent 5 minutes adding a long list of numbers and got 11,749. She realized she forgot to include 9,055. Does she need to add the entire list from scratch?
Evaluate: 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10 in two different ways.
Using exactly three 3s and arithmetic operations (+, −, ×, ÷) and brackets, create expressions for 2, 3, 4, and 12.
Whenever Jasoda subtracts 9, she subtracts 10 and adds 1 (e.g. 36 − 9 = 26 + 1 = 27). Explain why this works using brackets.
Explain how a grid with two rows of (5 yellow + 3 blue) tiles can be represented by 2 × (5 + 3) and 2 × 5 + 2 × 3.
Common Mistakes in Arithmetic Expressions
Critical traps to watch out for when parsing, evaluating, and removing brackets:
Expressions describe physical contexts. 30 + 5 × 4 has two terms: 30 and (5 × 4). Evaluate each term first to get 30 + 20 = 50, rather than blindly adding 30 + 5.
In 100 − (15 + 56), both 15 and 56 must be subtracted: 100 − 15 − 56. Writing 100 − 15 + 56 is a common blunder that results in 141.
In 2 − 10 + 4 × 6, the terms are 2, −10, and 4 × 6. 4 and 6 are factors within a single term, not separate terms.
a − b ≠ b − a, and (a − b) − c ≠ a − (b − c). For example, 16 − (8 − 3) = 11, while (16 − 8) − 3 = 5. Only addition of terms is associative.
3 × (6 + 7) = 3 × 6 + 3 × 7 = 39. A common error is writing 3 × 6 + 7 = 25.
When a plus sign precedes the brackets, signs inside DO NOT change: 28 + (35 − 10) = 28 + 35 − 10 = 53.
In 500 − (250 − 100), the term −100 becomes +100 upon removing the bracket: 500 − 250 + 100 = 350.
On day 8 morning, the snail climbs 3 cm from 7 cm and reaches the 10 cm top. It does not slip back at night because it has already reached the goal!
An expression like 13 + 2 is a phrase with a value (15). It has no equals sign until you equate it to its value or another expression.
Smart comparisons (like 113 − 25 vs 112 − 24) can be solved instantly by noting both numbers are shifted by 1.
Practice Questions & Solutions (24 Questions)
What is the value of the arithmetic expression 13 + 4?
Which of the following expressions has a value of 12?
Fill in the blank to make the expressions equal: 13 + 4 = ___ + 6
What are the terms of the expression 13 − 2 + 6 when subtractions are converted to additions?
How many terms are in the expression 5 + 6 × 3?
Which property of addition states that swapping terms does not change the sum (Term 1 + Term 2 = Term 2 + Term 1)?
Evaluate the expression 30 + 5 × 4 without brackets by first evaluating its terms.
What is the value of 5 × (3 + 2) + 7 × 8 + 3?
When removing brackets preceded by a minus sign in 200 − (40 + 3), which expression is correct?
Remove the brackets from 500 − (250 − 100). What does it become?
Using the Distributive Property, expand 3 × (6 + 7).
Use mental math and the distributive property to evaluate 97 × 25.
Without calculating, which is greater: 1023 + 125 or 1022 + 128?
Without calculating, compare 113 − 25 and 112 − 24.
Arrange these expressions in ascending order: (a) 67 − 19, (b) 67 − 20, (c) 35 + 25, (d) 5 × 11, (e) 120 ÷ 3.
Why is 5 × 4 + 3 NOT equal to 5 × (4 + 3)?
Which of the following pairs has the same value: (a) 16 − (8 − 3) and (b) (16 − 8) − 3?
In 'Tinker the Terms', if 53 + (−16) = 37, what is 53 + (−15)?
Add brackets to make this statement true: 34 − 9 + 12 = 13
Using only reasoning of terms, which expression is equal to 93 + 37 × 44 + 76?
Compare without evaluating: (76 − 53) × 88 ___ 88 × (53 − 76)
Using the numbers 2, 3, 5, operators + and −, and brackets, what is the SMALLEST integer value you can produce?
In the Three 3s challenge, which expression correctly uses exactly three 3s to equal 4?
Fill in the blank using the distributive property: (17 − 9) × 7 = 17 × 7 − ___ × 7
Key Takeaways: Arithmetic Expressions
The core mathematical principles established in NCERT Ganita Prakash Grade 7 Part I:
Every arithmetic expression evaluates to a single numerical value. Expressions can be compared using =, <, and >.
Terms are parts separated by ‘+’. Subtractions are additions of negative inverses ($a - b = a + (-b)$).
Adding terms in any order or grouping yields the same sum: a + b = b + a (commutative) and (a + b) + c = a + (b + c) (associative).
A minus sign before brackets flips every sign inside ($a - (b + c) = a - b - c$); a plus sign keeps signs identical.
$a \times (b + c) = a \times b + a \times c$. The multiple of a sum is equal to the sum of the multiples.
Expressions can often be compared by observing term-by-term differences without computing full arithmetic totals.