CBSE Class 7 Maths Chapter Notes for Revision

Key Definitions in Class 7 Maths

Integer

A whole number (not a fractional number) that can be positive, negative, or zero.

Rational Number

A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Simple Equation

An algebraic equation where the highest power of the variable is 1, used to find an unknown value.

Complementary Angles

Two angles whose sum is 90 degrees.

Supplementary Angles

Two angles whose sum is 180 degrees.

Congruent Shapes

Geometric figures that have exactly the same size and shape.

Mean

The average of a set of numbers, calculated by summing all values and dividing by the count of values.

Median

The middle value in a numerically ordered data set. If there are two middle values, it's their average.

Mode

The value that appears most frequently in a data set.

Exponent (or Power)

A number indicating how many times a base number is multiplied by itself.

Must Remember: Key Points for Class 7 Maths

• Integers: Remember the rules for adding, subtracting, multiplying, and dividing positive and negative integers. Product of two negative integers is positive; product of one positive and one negative is negative.
• Fractions & Decimals: Always simplify fractions to their lowest terms. Decimal operations follow place value rules.
• Rational Numbers: Every fraction and integer is a rational number. Operations (addition, subtraction, multiplication, division) for rational numbers are similar to those for fractions.
• Simple Equations: The goal is to isolate the variable. Perform the same operation on both sides of the equation to maintain balance.
• Lines and Angles: Understand types of angles (acute, obtuse, right, straight, reflex), and relationships like vertically opposite, linear pair, alternate interior/exterior, corresponding angles.
• Triangles: The sum of angles in a triangle is always 180°. Exterior angle property: sum of two interior opposite angles. Pythagoras theorem applies only to right-angled triangles.
• Congruence: Criteria for triangle congruence are SSS, SAS, ASA, and RHS. If two triangles are congruent, their corresponding parts (angles and sides) are equal (CPCTC).
• Data Handling: Choose the appropriate measure of central tendency (mean, median, mode) based on the data type and objective.
• Algebraic Expressions: Combine like terms by adding or subtracting their coefficients. Identify terms, factors, and coefficients correctly.
• Exponents & Powers: Memorize the laws of exponents (e.g., a^m a^n = a^(m+n), (a^m)^n = a^(mn), a^0 = 1).
• Perimeter & Area: Differentiate between perimeter (boundary length) and area (surface enclosed). Know formulas for squares, rectangles, triangles, and circles.

Understanding Rational Numbers

Rational numbers are a fundamental concept introduced in Class 7 Maths, expanding your number system beyond integers and fractions. A rational number is defined as any number that can be expressed in the form p/q, where 'p' and 'q' are integers, and 'q' is not equal to zero (q ≠ 0). This definition is crucial because division by zero is undefined.

Key Characteristics:

• Integers are rational numbers: Any integer, say 5, can be written as 5/1, fitting the p/q form. Similarly, -3 can be written as -3/1.
• Fractions are rational numbers: All fractions you've studied previously (e.g., 1/2, 3/4) are directly rational numbers.
• Terminating decimals are rational numbers: Decimals that end, like 0.25, can be written as 25/100 (which simplifies to 1/4).
• Non-terminating repeating decimals are rational numbers: Decimals that go on forever but have a repeating pattern, like 0.333... (which is 1/3), are also rational.

Operations on Rational Numbers:
Performing operations like addition, subtraction, multiplication, and division with rational numbers follows similar rules as those for fractions. When adding or subtracting, you need a common denominator. For example, to add 1/2 and 1/3, you'd convert them to 3/6 and 2/6 respectively, then add the numerators to get 5/6.

Multiplication involves multiplying the numerators together and the denominators together: (p/q) × (r/s) = (p×r)/(q×s). For division, you multiply the first rational number by the reciprocal of the second: (p/q) ÷ (r/s) = (p/q) × (s/r).

Understanding rational numbers is a stepping stone to more advanced topics and is essential for real-world applications involving ratios, rates, and measurements.

Performing Operations on Integers

1. Addition of Integers — If signs are same, add the numbers and keep the common sign. E.g., (-5) + (-3) = -8. If signs are different, subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value. E.g., (-5) + 3 = -2.
2. Subtraction of Integers — To subtract an integer, add its additive inverse (change the sign of the second number and proceed with addition). E.g., 5 - (-3) = 5 + 3 = 8. And (-5) - 3 = (-5) + (-3) = -8.
3. Multiplication of Integers — Multiply the absolute values of the numbers. If signs are same (both positive or both negative), the product is positive. E.g., (-4) × (-2) = 8. If signs are different (one positive, one negative), the product is negative. E.g., (-4) × 2 = -8.
4. Division of Integers — Divide the absolute values of the numbers. Similar to multiplication, if signs are same, the quotient is positive. E.g., (-8) ÷ (-2) = 4. If signs are different, the quotient is negative. E.g., 8 ÷ (-2) = -4. Remember, division by zero is undefined.

Worked Examples: Practicing Class 7 Maths Concepts

• {"title":"Example 1: Solving a Simple Equation","description":"Solve for x: 3x + 7 = 22","solution":"1. Subtract 7 from both sides: 3x + 7 - 7 = 22 - 7 => 3x = 15\n2. Divide both sides by 3: 3x / 3 = 15 / 3 => x = 5\nTherefore, x = 5."}
• {"title":"Example 2: Operations with Rational Numbers","description":"Calculate: (2/3) + (-1/4)","solution":"1. Find a common denominator for 3 and 4, which is 12.\n2. Convert fractions: (2/3) = (2 4) / (3 4) = 8/12. And (-1/4) = (-1 3) / (4 3) = -3/12.\n3. Add the converted fractions: 8/12 + (-3/12) = (8 - 3) / 12 = 5/12.\nTherefore, (2/3) + (-1/4) = 5/12."}

Exam Tip: Avoiding Common Mistakes in Class 7 Maths

Pay close attention to signs when dealing with Integers and Rational Numbers. A single misplaced negative sign can change the entire answer, especially in operations like subtraction and multiplication. When solving equations, always perform the same operation on both sides of the equality to maintain balance. For geometry problems, draw neat diagrams and label them correctly; this often helps visualize the problem and identify relevant properties or theorems. Finally, practice mental math for basic calculations to save time, but for complex problems, show all steps clearly to avoid losing marks even if the final answer is incorrect.

Quick Check: Test Your Knowledge

• Q: What is the sum of -15 and 7? A: -8
• Q: If two angles are supplementary and one angle is 70°, what is the measure of the other angle? A: 110° (180° - 70° = 110°)
• Q: Simplify the algebraic expression: 5x + 3y - 2x + y. A: 3x + 4y
• Q: What is the area of a square with a side length of 8 cm? A: 64 cm² (Area = side × side = 8 × 8 = 64)

Frequently Asked Questions