Formally speaking, a rational number is a number of the fractional (ratio) form a/b , where a and b are integers and b ≠ 0. The collection of all rational numbers is denoted by ℚ.

**Rational
Numbers**

Even after
coining integers, one could not relax! 10÷5 is no doubt fine, giving the answer
2 but is 8÷5 comfortable? Numbers between numbers
are needed. 8÷5 seen as 1.6, is a number between 1 and 2. But, where does (–3)÷4
lie? Between 0 and –1. Similarly, where do you find – 12/5
on the number line? Between –2 and –3. Thus, a ratio made by dividing an integer
by another integer is called a **rational number**. (Remember, we should not divide
by zero!)

Formally
speaking, a rational number is a number of the fractional (ratio) form ** a/b** , where

Since operations
on rational numbers demand a basic knowledge of operations on fractions, let us
recall through an exercise some of the basic ideas related to fractions.

** **

__Recap Exercise__

**1.The simplest form of 125/200 is _________.**

**Solution:** 125/200 = [125 ÷ 25] / [200 ÷
25] = 5/8

**[Answer: 5/8]**

**2. Which of the following is not an equivalent
fraction of 8/12 ?**

**(A) 2/3 **

**(B) 16/24 **

**(C) 32/60 **

**(D) 24/36 **

**[Answer: (C) 32/60]**

**Solution:**

∴ 32 / 60 is not an equivalent fraction of 8 / 12.

**3.Which is bigger: 4/5 or 8/9 ? **

**Solution:**

LCM of 5 and 9 = 45

**4.Add the fractions:3/5 + 5/8 + 7/10
**

**Solution:**

LCM of 5, 8, 10 = 5 × 2 × 4

= 40

3/5 + 5/8 + 7/10 = [ (3 × 8) + (5 × 5) + (7 × 4) ] / 40

= [24 + 25 + 28] / 40

= 77 / 40 = 1 (37/40)

**5.Simplify: **

**Solution:**

1/8 – (1/6 – 1/4) = 1/8 – { [(1 × 2) − (1 × 3) ] / 12 }

= 1/8 – ( [2−3] / 12 )

= 1/8 – ( − 1/12 )

= 1/8 + 1/12 = [(1 × 3) + (1 × 2)] / 24

= [3 + 2] / 24 = 5 / 24

**6. Multiply: **

**Solution:**

2 (3/5) × 1 (4/7) = (13/5) × (11/7) = 143/35 = 4 (3/35)

**7.Divide: 7/36 by 35/81 **

**Solution:**

7/36 ÷ 35/81 = 7/36 × 81/35 = 9/20

**8. Fill in the boxes: **

**Solution:**

28/44 = [28 ÷ 4] / [44 ÷ 4] = 7 / 11

7/11 = 28 / 44 = 42 / 66 = 70 / 110 = 77 / 121

** 42** / 66 = 70 /

**9. In a city 7/20 of the population are women and 1/4 are children. Find
the fraction of the fraction of the population of men.**

**Solution:**

Let the total population = 1

Population of men = Total population − Women − Children

= 1 – 7/20 – 1/4 = 20/20 – 7/20 – 5/20

= [20 – 7 – 5] / 20 = 8/20 = 2/5

∴ Population of men = 2/5

**10. Represent (1/2 – 1/4) by a diagram.**

**Solution:**

** **

**Try these**

**1. Is the number –7 a rational
number? Why?**

**Solution:**

Yes

– 7 is a rational number. Because – 7 = −14 / 2 = *p* / *q*

**2. Write any 6 rational
numbers between 0 and 1.**

**Solution:**

1/2, 1/3, 1/4, 1/5, 1/6, 1/7

** **

**Note**

The word ‘ratio’ in Math refers to the comparison of the sizes of
two different quantities of any kind. For example, if there is one teacher for every
20 students in a class, then the ratio of teachers to students is 1:20. Ratios are
often written as fractions and so 1:20 = 1/20. For this reason, numbers
in the fractions form are called rational numbers

Tags : Numbers | Chapter 1 | 8th Maths , 8th Maths : Chapter 1 : Numbers

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