Fractions and Rational Numbers

Introduction to Fractions and Rational Numbers

• A fraction represents a part of a whole.
• It consists of two parts: a numerator and a denominator.
• The numerator is the top number, and the denominator is the bottom number.

Multiplying Fractions

• To multiply fractions, multiply the numerators together and the denominators together: (a/b) * (c/d) = (ac) / (bd)
• When multiplying fractions, simplify them first if possible by canceling common factors in the numerators and denominators.

Visual Representation of Fractions

• A square divided into four equal parts, with one part shaded, represents the fraction 1/4.
• Adding 1/4 + 1/4 equals 2/4, which can be simplified to 1/2.

Examples of Fraction Operations

• Calculate "half of 20": (1/2) * 20 = 10
• Calculate "two-thirds of 42": (2/3) * 42 = 28

Exercise 2.1 - Question 1 (MCQ)

Part 1

• Multiply 5/3 and 12/25.
• Simplify first: 3 divides into 12 to get 4, and 5 divides into 25 to get 5.
• (5/3) * (12/25) = 4/5

Part 2

• Multiply 2 4/7, 2 3/4, and 1 2/5.
• Convert each mixed fraction to an improper fraction:
  • 2 4/7 = 18/7
  • 2 3/4 = 11/4
  • 1 2/5 = 7/5
• Multiply the improper fractions: (18/7) * (11/4) * (7/5)
• Simplify: Cancel the 7s and simplify 18/4 to 9/2. The result is (9 * 11) / (2 * 5) = 99/10
• Convert the improper fraction 99/10 to a mixed fraction: 9 9/10

Part 3

• Multiply 15/32 and 12/25.
• Simplify first: 3 divides into 12 to get 3, and 5 divides into 25 to get 5.
• (15/32) * (12/25) = 9/40

Exercise 2.1 - Question 2 (Solving Problems)

Part 1

• Multiply 16 and 5/3.
• (16) * (5/3) = 80/3

Part 2

• Multiply 3 4/5 and 6 3/7.
• Convert to improper fractions: 3 4/5 = 19/5, 6 3/7 = 45/7
• Multiply: (19/5) * (45/7) = 171/7

Part 3

• Multiply 7/8 and 6.
• (7/8) * 6 = 21/4

Part 4

• Multiply 3/4 and 5/8.
• (3/4) * (5/8) = 15/32

Part 5

• Multiply 15/21 and 26/52.
• Simplify: (15/21) * (26/52) = 5/14

Part 6

• Multiply 100/75 and 35/42.
• Simplify to: (100/75) * (35/42) = 7/9

Part 7

• Multiply 3 1/3, 1 2/5, and 1 1/14.
• Convert to improper fractions: 3 1/3 = 10/3, 1 2/5 = 7/5, 1 1/14 = 15/14
• Multiply: (10/3) * (7/5) * (15/14) = 5

Part 8

• Multiply 2 1/3, 1 1/2, and 1 1/6
• Convert to improper fractions: 7/3 * 3/2 * 7/6
• Multiply: 49/12
• Convert to mixed fraction: 4 1/12

Part 9

• (2 1/7) * (1 3/46)*(1 5/18) * (5/7)
• Covert to improper fractions: 15/7 * 49/46 * 23/18 * 5/7
• Simplify and multiply: 25/12

Part 10

• (2 1/3) * (1 1/2) + (1 2/3) * (2 2/3)
• Covert to improper fractions: 7/3*3/2 + 5/3+8/3
• Solve the equation 143/18 = 7 17/18

Part 11

• (5 1/3 * 4 1/2) - ( 3 1/4 * 1 5/6)
• Covert to improper fractions: 16/3 * 9/2 - 13/4 * 11/6
• Multiply and find common denominator to solve: 25/12 = 18 1/12

Exercise 2.1 - Question 3 (Missing Number)

Part 1

• Find the missing number when: 4/5 + x = 4
• Solve the missing value, therefore x = 1/4

Part 2

• Solve the equation: 12 - 2 ¾ = x/4
• Solve for missing variable, therefore x = 37

Part 3

• Solve the equation: (9 3/8) - (2 1/8) = X * (1 ¼)
• The missing number is 7

Exercise 2.1 - Question 4

Part 1

• Find 1/10 of 11/17: (1/10) of (11/17)
• Mutiply and solve: 11/170

Part 2

• Find 3/6 of 12m: (3/6) of (12)
• Multiply and solve: 6m

Part 3

• Find 1/10 of 13/36: (1/10) of (13/36)
• Multiply and solve: 13/360

Part 4

• Find quarter of one rupee: (1/4) of (1)
• Solve: 0.25 Rupees or 25 Paisa

Part 5

• Find quarter of 1000: (1.4) of (1000)
• Solve: 250

Part 6

• Find 3/4 of 5/27 (3/4) * (5/27)
• Solve and multiply: 5/36

Part 7

• Find 9/10 of 100/99 (9/10) * (100/99)
• Simplify and solve: 10/11

Learn about fractions, numerators, and denominators. We will also cover multiplying fractions, simplification, and visual representation. Examples of fraction operations are provided, including calculating fractions of whole numbers. Exercise 2.1 - Question 1 (MCQ) is also discussed.