Class 7 – Mathematics
Master 30 Class 7 Mathematics topics covering integers, rational numbers, decimals, algebra, equations, proportion, percentages, simple interest, commercial mathematics, geometry, mensuration, symmetry, statistics, probability and multi-concept problem solving.
🔢 Integers, Rational Numbers and Decimals
Multiplication and Division of Integers
Integers can be multiplied and divided using sign rules. The sign of the answer depends on whether the two integers have the same or different signs.
(+6) × (+4) = 24
(−6) × (−4) = 24
(−6) × (+4) = −24
(−24) ÷ (−6) = 4
Calculate: (−8) × 7 and (−54) ÷ 9.
Same signs → positive answer.
Different signs → negative answer.
Understanding Rational Numbers
A rational number is a number that can be written in the form p/q, where p and q are integers and q is not zero.
3/5, −7/4, 8/3 and 5 are rational numbers.
5 can be written as 5/1.
Write −3, 7 and 0 as rational numbers with denominator 5 where possible.
The denominator of a rational number cannot be zero.
Representing Rational Numbers on the Number Line
Rational numbers can be represented on a number line by dividing the space between consecutive integers into equal parts.
To represent 3/4, divide the interval from 0 to 1 into four equal parts and mark the third division from zero.
Represent 1/2, −3/4 and 5/4 on a number line.
Negative rational numbers appear to the left of zero.
Comparing and Ordering Rational Numbers
Rational numbers can be compared by converting them to equivalent fractions with a common denominator or by using their positions on a number line.
Compare 2/3 and 3/4.
2/3 = 8/12
3/4 = 9/12
Therefore, 3/4 > 2/3.
Arrange 1/2, 3/5 and 2/3 in ascending order.
A common denominator makes fraction comparison easier.
Performing Operations on Rational Numbers
Rational numbers can be added, subtracted, multiplied and divided using fraction rules.
2/3 + 1/6 = 4/6 + 1/6 = 5/6
2/3 × 3/5 = 2/5
Calculate 3/4 − 1/6 and simplify your answer.
For addition and subtraction, first obtain a common denominator.
Multiplying and Dividing Decimal Numbers
Decimal numbers follow the usual multiplication and division rules, with careful attention to decimal-place values.
2.5 × 4 = 10
7.2 ÷ 3 = 2.4
Calculate 3.6 × 2.5 and 8.4 ÷ 0.7.
Place value is essential when working with decimal numbers.
🔠 Algebra and Linear Equations
Understanding Algebraic Terms and Coefficients
An algebraic expression contains terms separated by addition or subtraction signs. A coefficient is the numerical factor multiplying a variable.
In 5x + 3y − 7:
Terms → 5x, 3y, −7
Coefficient of x → 5
Coefficient of y → 3
Identify the terms and coefficients in 8a − 4b + 9.
In x, the coefficient of x is 1.
Combining Like and Unlike Algebraic Terms
Like terms contain the same variables raised to the same powers. Unlike terms have different variable parts.
5x + 3x = 8x
4a + 2b cannot be combined because they are unlike terms.
Simplify: 7x + 4y + 3x − 2y.
Only like terms can be combined by adding or subtracting coefficients.
Adding and Subtracting Algebraic Expressions
Algebraic expressions are added or subtracted by grouping and combining corresponding like terms.
(3x + 4) + (2x + 5)
= 3x + 2x + 4 + 5
= 5x + 9
Simplify (7x + 5) − (3x + 2).
When subtracting an expression, carefully change the signs of the terms inside the second bracket.
Solving Multi-Step Linear Equations
Multi-step equations require more than one mathematical operation to isolate the unknown variable.
3x + 5 = 20
3x = 15
x = 5
Solve: 4x − 7 = 21.
Maintain equality by performing equivalent operations correctly.
💰 Proportion, Percentage and Commercial Mathematics
Understanding Direct Proportion
Two quantities are in direct proportion when they increase or decrease together at a constant ratio.
If 2 notebooks cost ₹40, then at the same price:
4 notebooks cost ₹80.
Doubling the number of notebooks doubles the cost.
If 5 kg of rice costs ₹300, find the cost of 8 kg at the same rate.
In direct proportion, the ratio of corresponding quantities remains constant.
Understanding Inverse Proportion
Two quantities are inversely proportional when an increase in one produces a corresponding decrease in the other so that their product remains constant.
If 4 workers complete a suitable fixed task in 6 days, the total is 4 × 6 = 24 worker-days.
At the same work rate, 8 workers would require 24 ÷ 8 = 3 days.
If 6 machines complete a fixed job in 10 hours at equal rates, how long would 12 such machines take?
For inverse proportion, one quantity increases while the other decreases proportionally.
Calculating Percentage Increase and Decrease
Percentage change compares the amount of increase or decrease with the original value.
A price increases from ₹200 to ₹250.
Increase = ₹50
Percentage increase = (50 ÷ 200) × 100 = 25%
A number decreases from 500 to 400. Find the percentage decrease.
Percentage change is calculated relative to the original value.
Understanding Simple Interest
Simple interest is interest calculated only on the original principal for a given rate and period of time.
Principal = ₹2,000
Rate = 5% per year
Time = 2 years
SI = (2000 × 5 × 2) ÷ 100
= ₹200
Find the simple interest on ₹5,000 at 6% per year for 3 years.
Simple Interest = (Principal × Rate × Time) ÷ 100
Solving Discount and Marked-Price Problems
The marked price is the displayed price of an item. A discount is the reduction offered on that price.
Marked Price = ₹1,000
Discount = 20%
Discount amount = ₹200
Selling Price = ₹800
A bag marked at ₹1,500 is sold at a 10% discount. Find its selling price.
Selling Price = Marked Price − Discount Amount.
📐 Lines, Angles and Triangles
Understanding Pairs of Angles
Angles can form different relationships depending on their positions and measures. Common pairs include adjacent, vertically opposite, complementary and supplementary angles.
35° and 55° are complementary because their sum is 90°.
120° and 60° are supplementary because their sum is 180°.
Find the complement of 42° and the supplement of 115°.
Vertically opposite angles are equal.
Exploring Transversals and Parallel Lines
A transversal is a line that intersects two or more lines at distinct points. When it crosses parallel lines, special angle relationships are formed.
Corresponding angles are equal.
Alternate interior angles are equal.
Interior angles on the same side are supplementary.
Draw two parallel lines crossed by a transversal and identify a pair of corresponding angles.
These standard relationships depend on the intersected lines being parallel.
Understanding the Angle-Sum Property of Triangles
The sum of the three interior angles of any triangle is always 180°. This property can be used to find an unknown angle.
Angles = 50°, 60° and x
50° + 60° + x = 180°
x = 70°
Two angles of a triangle are 45° and 75°. Find the third angle.
Interior angles of a triangle always total 180°.
Understanding Exterior Angles of Triangles
An exterior angle of a triangle is formed when one side of the triangle is extended. Its measure equals the sum of the two non-adjacent interior angles.
Remote interior angles = 50° and 60°.
Exterior angle = 50° + 60° = 110°
Two remote interior angles are 45° and 70°. Find the corresponding exterior angle.
An exterior angle equals the sum of its two remote interior angles.
Exploring Congruence of Triangles
Two triangles are congruent when they have exactly the same shape and size. Their corresponding sides and angles are equal.
SSS — Side-Side-Side
SAS — Side-Angle-Side
ASA — Angle-Side-Angle
RHS — Right angle-Hypotenuse-Side
Draw two triangles having sides 4 cm, 5 cm and 6 cm. What do you observe?
Equal corresponding measurements establish congruence only when they satisfy an appropriate congruence condition.
Understanding Triangle Inequality
For three positive lengths to form a triangle, the sum of any two side lengths must be greater than the third side.
Sides 4 cm, 5 cm and 7 cm can form a triangle because:
4 + 5 > 7
4 + 7 > 5
5 + 7 > 4
Can 2 cm, 3 cm and 6 cm form a triangle? Explain.
Check the sum of the two shorter sides against the longest side.
Constructing Triangles from Given Measurements
Triangles can be constructed accurately when sufficient measurements of sides and angles are provided.
To construct a triangle with sides 5 cm, 6 cm and 7 cm:
1. Draw one side of 7 cm.
2. Draw an arc of radius 5 cm from one endpoint.
3. Draw an arc of radius 6 cm from the other endpoint.
4. Join the intersection point to both endpoints.
Construct a triangle with sides 4 cm, 5 cm and 6 cm.
Check that the given side lengths satisfy the triangle inequality.
📏 Mensuration and Symmetry
Calculating Area of Parallelograms
The area of a parallelogram is determined by its base and corresponding perpendicular height.
Base = 8 cm
Height = 5 cm
Area = 8 × 5 = 40 cm²
Find the area of a parallelogram with base 12 cm and height 7 cm.
Area of parallelogram = Base × Perpendicular Height.
Calculating Area of Circles
The area of a circle measures the region enclosed by its circumference. It depends on the square of its radius.
Radius = 7 cm
Area = π × 7²
Using π = 22/7:
Area = 154 cm²
Find the area of a circle with radius 14 cm using π = 22/7.
Area of circle = πr².
Understanding Circumference Applications
Circumference is the distance around a circle. It is useful when calculating circular boundaries, wheels, tracks and other round objects.
Radius = 7 cm
Circumference = 2 × 22/7 × 7
= 44 cm
Find the circumference of a circular object with radius 14 cm.
Circumference = 2πr = πd.
Exploring Reflection and Rotational Symmetry
A figure has reflection symmetry when one half is the mirror image of the other. A figure has rotational symmetry when it matches itself after a rotation of less than 360°.
A square has 4 lines of symmetry and rotational symmetry of order 4.
Determine the lines of symmetry and rotational order of a rectangle.
The order of rotational symmetry tells how many times a shape matches itself during one complete turn.
📊 Statistics and Probability
Organising Data Using Grouped Frequency Tables
Grouped frequency tables organise larger numerical data sets into class intervals and record how many observations fall within each group.
Marks | Frequency
0–10 | 3
10–20 | 5
20–30 | 8
30–40 | 4
Collect the heights of 20 students and organise them into suitable class intervals.
Use clear, non-overlapping class intervals so each observation belongs to one group.
Understanding Mean, Median and Mode
Mean, median and mode are measures used to describe the centre or typical value of a data set.
Data: 2, 3, 3, 5, 7
Mean = 20 ÷ 5 = 4
Median = 3
Mode = 3
Find the mean, median and mode of:
4, 5, 6, 6, 7, 8, 6.
Mean → arithmetic average
Median → middle value after ordering
Mode → most frequent value
Understanding Experimental Probability
Experimental probability is estimated from the results of repeated experiments rather than only from theoretical reasoning.
A coin is tossed 50 times and gives 28 heads.
Experimental probability of heads = 28/50 = 14/25.
Roll a die 30 times and record how often 6 appears. Use the results to calculate its experimental probability.
Experimental Probability = Number of times event occurs ÷ Total number of trials.
🧠 Mathematical Reasoning and Problem Solving
Solving Multi-Concept Mathematical Problems
Many real mathematical problems require more than one concept. Successful problem solving involves identifying relevant information, choosing suitable operations, completing the calculations and checking whether the result is reasonable.
A school bag has a marked price of ₹1,200 and a discount of 15%.
Discount = 15% of ₹1,200 = ₹180
Selling price = ₹1,200 − ₹180 = ₹1,020
If a student pays ₹1,500:
Change = ₹1,500 − ₹1,020 = ₹480
A circular garden has radius 7 m. Find its circumference using π = 22/7. If fencing costs ₹50 per metre, calculate the total fencing cost.
Understand → Plan → Calculate → Check → Present the answer with the correct unit.