**Evaluate numerical expressions involving rational numbers :**

Here we are going to see learn how to evaluate numerical expressions involving rational numbers.

Based on the signs in the given question we have to perform the operations

(i) Addition

(ii) Subtraction

(iii) Multiplication

(iv) Division

If we have mixed signs in an expression, then we have to choose which operation to be done first based on the BODMAS or PEMDAS rule.

Let us see some examples based on the above concept.

**Example 1 :**

Find 1/4 of 3/5

**Solution :**

= 1/4 of 3/5

= (1/4) x (3/5)

= 3/20

**Example 2 :**

Evaluate 4/9 **÷ **5

**Solution :**

= (4/9) **÷ **5

= (4/9) ÷ (5/1)

= (4/9) x (1/5)

= 4/45

**Example 3 :**

Evaluate 0.9 + 0.2 ÷ 2

**Solution :**

= 0.9 + 0.2 ÷ 2

Based on the "BODMAS" or "PEMDAS" rule, first we have to perform division.

= 0.9 + **(0.2 ÷ 2)**

**= 0.9 + 0.1**

**= 1.0**

**Example 4 :**

Evaluate (4/5) x (1/2) - (1/5)

**Solution :**

= (4/5) x (1/2) - (1/5)

Based on the "BODMAS" or "PEMDAS" rule, first we have to perform multiplication.

= (4/5) x (1/2) - (1/5)

**= (4/10) - (1/5)**

**In order to subtract the above fractions, we have to make the denominators same. For that let us take L.C.M**

**= (4/10) - (1/5) x (2/2)**

**= (4/10) - (2/10)**

**= (4 - 2)/10**

**= 2/10**

** = 1/5**

**Example 5 :**

Evaluate (3/4) ÷ (1/2) - 1

**Solution :**

= (3/4) ÷ (1/2) - 1

Based on the "BODMAS" or "PEMDAS" rule, first we have to perform division.

= (3/4) x (2/1) - 1

**= (6/4) - 1**

Simplifying 6 and 4, we get (3/2) - 1

**In order to subtract the above fractions, we have to make the denominators same. For that let us take L.C.M**

**= (3/2) - (1/1) x (2/2)**

**= (3/2) - (2/2)**

**= (3 - 2)/2**

**= 1/2**

**Example 6 :**

Evaluate (1/2) x (4/5) + 1

**Solution :**

= (1/2) x (4/5) + 1

Based on the "BODMAS" or "PEMDAS" rule, first we have to perform multiplication.

= (1/2) x (4/5) + 1

**= (4/10) + 1**

Simplifying 4 and 10, we get (2/5) + 1

**In order to subtract the above fractions, we have to make the denominators same. For that let us take L.C.M**

**= **(2/5) + (1/1) x (5/5)

**= (2/5) + (5/5)**

**= (2 + 5)/5**

**= 7/5**

After having gone through the stuff given above, we hope that the students would have understood "Evaluate numerical expressions involving rational numbers".

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