Mathematics Q&A for Class 7
47 free answers in Mathematics for Class 7 students, across CBSE, ICSE and State boards. Covers 2 chapters, including Integers, Rational Numbers.
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- MathematicsClass 7All
Main differences between rational and irrational numbers.
Rational and irrational numbers are two distinct types of real numbers. Here are five main differences between them: Definition: Rational Numbers: Rational numbers are numbers that can be expressed as the quotient or fraction b is not equal to zero. In other words, rational numbers are those that can be written as fractions of integers.Irrational Numbers: Irrational numbers cannot be expressed as fractions of integers. They cannot be represented as b are integers. Instead, the
- MathematicsClass 7All
What are geometry basics (Class 7)?
Geometry basics introduce shapes, lines, angles, and figures.Students learn properties of triangles, quadrilaterals, and circles.Diagrams and activities support visual learning.Geometry improves spatial reasoning.It forms the foundation for advanced geometry.
- MathematicsClass 7All
What is surface area and volume Class 7
In Class 7 mathematics (typically for students aged 12-13), surface area and volume introduce students to measuring three-dimensional shapes, building on their earlier understanding of two-dimensional area. Surface area measures the total outer covering of a 3D object in square units (like cm² or m²)—imagine painting the outside of a shape and calculating how much paint you need. Volume measures the three-dimensional space inside an object in cubic units (like cm³ or m&su
- MathematicsClass 7All
What is 1 ➗ 0 and why
1 divided by 0 is undefined in mathematics—it doesn't equal infinity, zero, or any other number. The reason stems from the fundamental definition of division: dividing by zero would require finding a number that, when multiplied by zero, gives you 1, but no such number exists since any number multiplied by zero always equals zero, creating a logical contradiction. The undefined nature of division by zero protects mathematical consistency and prevents paradoxes. If we allowed 1 &
- MathematicsClass 7All
Equilateral Triangle
An equilateral triangle is a triangle where all three sides have equal length and all three interior angles are equal, each measuring 60 degrees (since the sum of angles in any triangle equals 180°, and 180° ÷ 3 = 60°). This special type of triangle possesses numerous symmetrical properties making it mathematically interesting and practically useful. An equilateral triangle has three lines of symmetry (each altitude/median/angle bisector serves as a mirror line), and rotati
- MathematicsClass 7All
What is the product of a rational number and its multiplicative inverse?
The product is always one (1). Formula: (p/q) × (q/p) = 1 (where p ≠ 0) Examples: 3/4 × 4/3 = 12/12 = 1 7/5 × 5/7 = 35/35 = 1 (-2/9) × (-9/2) = 18/18 = 1 Explanation: This is the defining property of multiplicative inverse (reciprocal). The reciprocal is specifically the number that, when multiplied by the original, gives one. <strong
- MathematicsClass 7All
What is the sum of a rational number and its additive inverse?
The sum is always zero (0). Formula: p/q + (-p/q) = 0 Examples: 3/7 + (-3/7) = 0 -5/9 + 5/9 = 0 2/3 + (-2/3) = 0 Explanation: This is the defining property of additive inverse. The additive inverse is specifically the number that, when added to the original, gives zero.
- MathematicsClass 7All
Arrange in ascending order: 2/3, 5/6, 1/2
Step 1: Find LCM(3, 6, 2) = 6 Step 2: Convert all to denominator 6 2/3 = 4/6 5/6 = 5/6 1/2 = 3/6 Step 3: Compare numerators 3/6 < 4/6 < 5/6 Answer in ascending order: 1/2 < 2/3 < 5/6
- MathematicsClass 7All
How do you compare two rational numbers?
There are three methods: Method 1: Cross Multiplication For a/b and c/d: Calculate a × d and b × c If a × d > b × c, then a/b > c/d If a × d < b × c, then a/b < c/d If a × d = b × c, then a/b = c/d Method 2: Same Denominator Convert both to the same denominator (LCM) Compare numerators Method 3: D
- MathematicsClass 7All
Convert 0.454545... (0.4̄5̄) to a rational number.
Step 1: Let x = 0.454545... Step 2: Since 2 digits repeat, multiply by 100 100x = 45.454545... Step 3: Subtract 100x - x = 45.454545... - 0.454545... 99x = 45 Step 4: Solve x = 45/99 Step 5: Simplify (GCD = 9) 45/99 = 5/11 Answer: 0.4̄5̄ = 5/11
- MathematicsClass 7All
Convert 0.666... (repeating) to a rational number.
Step 1: Let x = 0.666... Step 2: Multiply by 10 (one repeating digit) 10x = 6.666... Step 3: Subtract original from multiplied 10x - x = 6.666... - 0.666... 9x = 6 Step 4: Solve for x x = 6/9 = 2/3 Answer: 0.666... = 2/3 Verification: 2 ÷ 3 = 0.666... ✓
- MathematicsClass 7All
How do you convert a terminating decimal to a rational number?
Count the decimal places and use that as the power of 10 in the denominator. Examples: (a) 0.5 1 decimal place 0.5 = 5/10 = 1/2 (b) 0.75 2 decimal places 0.75 = 75/100 = 3/4 (c) 2.125 3 decimal places 2.125 = 2125/1000 = 17/8 (d) 0.008 3 decimal places 0.008 = 8/1000
- MathematicsClass 7All
How do you represent -2/5 on a number line?
Step 1: Identify position -2/5 is negative, so it lies to the LEFT of 0 It's between -1 and 0 Step 2: Divide the segment Divide the space between -1 and 0 into 5 equal parts Each part represents 1/5 Step 3: Mark the point Count 2 parts from 0 towards the left Mark this point as -2/5 Visual: -1 -4/5 -3/5 -
- MathematicsClass 7All
Find five rational numbers between 1/3 and 1/2
Method 1: Common Denominator Convert to same denominator with enough space: 1/3 = 10/30 1/2 = 15/30 Five numbers between 10/30 and 15/30: 11/30, 12/30, 13/30, 14/30, 15/30 Simplified: 11/30, 2/5, 13/30, 7/15, 1/2 Wait, we need numbers BETWEEN 1/3 and 1/2, so: 11/30, 2/5, 13/30, 7/15 (not including 15/30 which equals 1/2) Better answer with more space:</st
- MathematicsClass 7All
How many rational numbers lie between two rational numbers?
Infinitely many rational numbers exist between any two rational numbers. This is called the dense property of rational numbers. Example: Between 1/2 and 1: Using the mean method: (1/2 + 1)/2 = 3/4 (1/2 + 3/4)/2 = 5/8 (3/4 + 1)/2 = 7/8 So: 1/2 < 5/8 < 3/4 < 7/8 < 1 This process can continue forever, finding more numbers each time. General method:</stro
- MathematicsClass 7All
What is the distributive property for rational numbers?
Multiplication distributes over addition. Formula: a × (b + c) = (a × b) + (a × c) Example: 2/3 × (1/4 + 1/5) Method 1 (add first): = 2/3 × (5/20 + 4/20) = 2/3 × 9/20 = 18/60 = 3/10 Method 2 (distribute): = (2/3 × 1/4) + (2/3 × 1/5) = 2/12 + 2/15 = 1/6 + 2/15 = 5/30 + 4/30 = 9/30 = 3/10 Both methods give 3/10 ✓
- MathematicsClass 7All
Simplify: [(2/5) ÷ (3/7)] × (4/9)
Step 1: Solve division first (2/5) ÷ (3/7) = (2/5) × (7/3) = 14/15 Step 2: Multiply by 4/9 (14/15) × (4/9) = (14 × 4)/(15 × 9) = 56/135 Check for simplification: GCD(56, 135) = 1 Already in simplest form. Answer: 56/135
- MathematicsClass 7All
Find the reciprocal of: (a) 7/9 (b) -3 (c) 1
(a) Reciprocal of 7/9: Flip the fraction: 9/7 Verification: 7/9 × 9/7 = 63/63 = 1 ✓ (b) Reciprocal of -3: Write as fraction: -3 = -3/1 Flip: -1/3 Verification: -3 × (-1/3) = 3/3 = 1 ✓ (c) Reciprocal of 1: 1 = 1/1 Flip: 1/1 = 1 Verification: 1 × 1 = 1 ✓
- MathematicsClass 7All
What property is shown by: (2/3 × 4/5) × 1/2 = 2/3 × (4/5 × 1/2)?
This demonstrates the Associative Property of Multiplication. Definition: For any three rational numbers a, b, and c: (a × b) × c = a × (b × c) The grouping of multiplication doesn't matter; the result is the same. Verification: Left side: (2/3 × 4/5) × 1/2 = (8/15) × 1/2 = 8/30 = 4/15 Right side: 2/3 × (4/5 × 1/2) = 2/3 × (4/10) = 2/3 × 2/5
- MathematicsClass 7All
Divide: (5/6) ÷ (10/9)
Step 1: Convert to multiplication by reciprocal (5/6) ÷ (10/9) = (5/6) × (9/10) Step 2: Multiply (5 × 9)/(6 × 10) = 45/60 Step 3: Simplify (GCD = 15) 45/60 = 3/4 Answer: 3/4