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NCERT Class 6 · Mathematics Based on NCERT Class 6 Mathematics textbook · Free CBSE study kit

Chapter Notes

**GANITA PRAKASH — CLASS 6 MATHS KEY POINTS**

**Prime Numbers:** Exactly 2 factors (1 and itself) — examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Number 1 is neither prime nor composite.

**Composite Numbers:** More than 2 factors — examples: 4, 6, 8, 9, 10, 12, 15, 20.

**HCF (Highest Common Factor):** Largest number dividing two or more numbers. Example: HCF of 12 and 18 is 6.

**LCM (Least Common Multiple):** Smallest number that is a multiple of two or more numbers. Example: LCM of 4 and 6 is 12.

**Perimeter Formula:**

• Rectangle: 2(length + width)

• Square: 4 × side

• Any shape: sum of all sides

**Fractions:** Part of whole (numerator/denominator). Equivalent fractions: 1/2 = 2/4 = 3/6.

**Decimals:** Another way to write fractions using a decimal point. Example: 0.5 = 1/2.

**Ratio:** Comparison of two quantities using ':' (like 2:3 means 2 parts to 3 parts).

**Symmetry:** Shape divided into two identical mirror-image parts by a line of symmetry.

**Integers:** Positive (+), negative (−), and zero. Used for temperature, heights, losses/gains.

**Diagrams to Remember:** Number line showing integers; prime number sieve; symmetrical shapes.

**Don't Confuse:** Perimeter (outside distance) ≠ Area (inside space). HCF (smallest common) ≠ LCM (largest common).

MCQs — 10 Questions with Answers

Q1. Which of these is a prime number?

  • A. 2 ✓
  • B. 4
  • C. 6
  • D. 8

Answer: A — 2 has exactly two factors (1 and 2), making it prime; all others are composite numbers with more than 2 factors.

Q2. What is the HCF of 12 and 18?

  • A. 2
  • B. 6 ✓
  • C. 12
  • D. 36

Answer: B — 6 is the largest number that divides both 12 and 18 exactly (12÷6=2, 18÷6=3).

Q3. The LCM of 4 and 6 is ___.

  • A. 2
  • B. 12 ✓
  • C. 24
  • D. 4

Answer: B — 12 is the smallest number that both 4 and 6 divide into (4×3=12, 6×2=12).

Q4. What is the perimeter of a square with side length 5 cm?

  • A. 5 cm
  • B. 10 cm
  • C. 20 cm ✓
  • D. 25 cm

Answer: C — Perimeter of square = 4 × side = 4 × 5 = 20 cm.

Q5. Which fraction is equivalent to 1/2?

  • A. 2/3
  • B. 3/6 ✓
  • C. 2/5
  • D. 3/4

Answer: B — 3/6 = 1/2 because when you divide both numerator and denominator by 3, you get 1/2.

Q6. A shape has a line of symmetry. This means ___.

  • A. It has four equal sides
  • B. One side is longer than the other
  • C. Both sides of the line are mirror images ✓
  • D. It is always a circle

Answer: C — A line of symmetry divides a shape so that both halves are identical mirror images of each other.

Q7. Which number is NOT an integer?

  • A. −5
  • B. 0
  • C. 3.5 ✓
  • D. 7

Answer: C — Integers include all whole numbers (positive, negative, zero) but not decimal or fractional numbers like 3.5.

Q8. If the perimeter of a rectangle is 20 cm and its length is 6 cm, what is its width?

  • A. 4 cm ✓
  • B. 6 cm
  • C. 8 cm
  • D. 10 cm

Answer: A — Using perimeter = 2(length + width), we get 20 = 2(6 + width), so width = 4 cm.

Q9. In a ratio of boys to girls is 3:2 in a class, if there are 9 boys, how many girls are there?

  • A. 3 girls
  • B. 6 girls ✓
  • C. 12 girls
  • D. 18 girls

Answer: B — If 3 parts = 9 boys, then 1 part = 3, so 2 parts (girls) = 6 girls.

Q10. Which of the following numbers has exactly 3 factors?

  • A. 6
  • B. 9 ✓
  • C. 10
  • D. 12

Answer: B — 9 has factors 1, 3, and 9 (exactly 3 factors); 6 has 1,2,3,6 (4 factors); 10 has 1,2,5,10 (4 factors); 12 has 1,2,3,4,6,12 (6 factors).

Flashcards

What is a prime number?

A number with exactly 2 factors: 1 and itself (like 2, 3, 5, 7, 11).

What does HCF stand for?

Highest Common Factor — the largest number that divides two or more numbers exactly.

What does LCM stand for?

Least Common Multiple — the smallest number that is a multiple of two or more numbers.

Define perimeter.

The total distance around the boundary of any 2D shape, found by adding all side lengths.

What is a fraction?

A way to show part of a whole, written as numerator ÷ denominator (like 1/2 or 3/4).

What is symmetry?

When a shape looks the same on both sides of a line, like a butterfly's wings are mirror images.

What are integers?

All whole numbers including positive numbers, negative numbers, and zero (...−2, −1, 0, 1, 2...).

What is the difference between a composite and prime number?

A prime number has exactly 2 factors; a composite number has more than 2 factors.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator (for example, 1/4 = 0.25).

What is a line of symmetry?

An imaginary line that divides a shape into two identical parts that are mirror images of each other.

Important Board Questions

What is a prime number? Give two examples. [1 mark]

A prime number has exactly 2 factors (1 and itself). Examples: 2, 3, 5, 7, 11, etc.

Find the HCF of 15 and 20 using the division method or by listing factors. [2 marks]

List all factors of 15 (1, 3, 5, 15) and 20 (1, 2, 4, 5, 10, 20). The highest common factor is 5.

Your mother is making a cake recipe that requires 3/4 cup of sugar. If she wants to make double the recipe, how much sugar does she need? Explain using fractions. [3 marks]

Double of 3/4 means 2 × (3/4) = 6/4 = 1½ cups. Show that multiplying a fraction by 2 doubles the amount.

Draw and label a rectangle with length 8 cm and width 5 cm. Calculate its perimeter and explain what perimeter means in your own words. Then, name at least two line(s) of symmetry in this rectangle. [5 marks]

Perimeter = 2(length + width) = 2(8+5) = 26 cm. Explain that perimeter is the total distance around the outside. A rectangle has 2 lines of symmetry (one horizontal through the middle, one vertical through the middle).

True or False: The LCM of 6 and 9 is 18. Give a reason for your answer. [2 marks]

Check if 18 is the smallest number divisible by both 6 and 9. (18÷6=3, 18÷9=2). Yes, this is true because no smaller common multiple exists.

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