For example, a pizza is divided into 8 equal parts, and one part is taken out, thus the fraction representing the taken out part is 1/8 as one part is taken out of 8 equal parts. 1/8 part of the pizza can be represented in many forms such as:

- One-Eighth
- 1/8
- 1 by 8

The remaining parts collectively will be 7/8 of the pizza as of now; there are only 7 pieces left. Similarly, if we take three parts of this pizza then the fraction representing the taken part will be 3/8 and if 2 pieces are taken out, they will be 2/8 of the entire pizza. It can be simplified and written as 1/4.

- For the Addition of fractions and multiplication of fractions, commutative and associative properties are true.
- Fractional multiplication gives 1, and the identity element is 0.
- The multiplicative inverse property reciprocates the fraction. That is, a/b is b/a, where a and b are non-zero numbers.
- The distributive property of multiplication over addition holds true for fractions.

- 2/9, 3/9, 5/9, 9/9, 4/9 (Here, the denominators of all the fractions are the same, that is, 9).
- 3/10, 7/10, 1/10, 9/10, 6/10 (Here, the denominators of all the fractions are the same, that is, 10).
- 1/7, 2/7, 4/7, 5/7, 7/7, 8/7.
- 1/2, 7/2, 6/2, 5/2, 9/2.
- 7/5, 1/5, 4/5, 3/5.

- 9/2, 1/6, 5/4, 7/3 (Here, the denominator of all the fractions is different).
- 1/2, 1/4, 2/3, 5/6, 8/9 (Here, the denominator of all the fractions is different).
- 3/8, 2/3, 3/5, 2/7.
- 1/9, 2/7, 3/4, 2/5, 3/2.
- 4/2, 1/6, 2/3, 7/5.

(4 × 2) / (12 × 2) = 8/24

Equivalent fraction by division with the same number, here, both numerator and denominator are divisible by 4, dividing by 4:

(4 ÷ 4) / (12 ÷ 4) = 1/3

88/42 = 44/21

Therefore, the reduced fraction becomes 44/21.

4/5 + 7/3 = (12 + 35)/15

= 47/15

1/2 – 3/5 = (5-6)/10

= -1/10

Flipping the fraction after division sign and changing the sign to multiplication sign:

35/20 × 10/7

Reducing the fractions:

7/4 × 10/7 = 70/28 = 10/4 = 5/2

Therefore, the answer is 5/2.

- Convert the decimal into p/q form where q = 1.
- Now multiply the numerator and denominator by 10 till the numerator becomes a whole number from decimals. For example, if there are two numbers after the decimal point, multiply and divide by 100.
- Now, simplify the fraction obtained.

**Example: Convert 0.8 into a fraction.**
**Solution:**

- Convert into p/q form ⇢ 0.8/1
- Multiply 10/10 ⇢ 0.8/1 × 10/10
- Simplifying fraction ⇢ 8/10 = 4/5.

5 ÷ 13 = 0.38461538

0.38461538 × 100 = 38.461538 %

(3 × 2)/(39 × 2)

= 6/78

Equivalent fraction by division with the same number, here, both numerator and denominator are divisible by 3, dividing by 3:

(3 ÷ 3)/(39 ÷ 3)

= 1/13

Fraction of student that like cricket = 1 – 1/3

= (3 – 1)/3

= 2/3rd students like cricket.

Number of students that like cricket = 2/3 × 90

= (2 × 30)

= 60

Suger needed for half the recipe = 1/2 of 3/4

Required sugar = 1/2 × 3/4 = 3/8

And the least common multiple of 6 and 8 is 24,

5/6 = 20/24,

and 7/8 = 21/24

5/6 + 7/8 = 20/24 + 21/24 = 41/24

1 hour = 1/24 days

8 hours = 1/24 × 8 days

8 hours = 8/24 = 1/3 days

Given: Length = 3/4 meter and Breadth = 1/2 meter

Area = (3/4) × (1/2) = 3/8

Ram drove 5/8 of 1 = 5/8 unit and

again he drove 1/4 of 1 = 1/4 unit

Total distance covered till now = 1/4 + 5/ 8 = 7/8

Remaining distance = 1 – 7/8 = 1/8

Students who take bus = 5/6 of the total students

⇒ Students who take bus = 5/6 × 300 = 250 students

Thus, students who don’t take the bus = 300 – 250 = 50 students

Red marbles = 1/3 × x = x/3

and Blue marbles = 1/4 × x = x/4

Thus, red marbles + blue marble = x/3 + x/4 = (3x+4x)/12 = 7x/12

So, 7x/12 of the marbles are red or blue.

Green marbles = x – 7x/12 = 5x/12

Given jar has 5 green marbles,

⇒ 5x/12 = 5

⇒ x = 12

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