**Evaluate variable expressions involving rational numbers worksheet:**

Here we are going to see, some practice questions on evaluating variable expressions involving rational numbers.

(1) Evaluate the following rational expression

(20/c) - 8 - 9 z use c = 5 and z = 7

(2) Evaluate the following rational expression

(-n/9) - 9 + 5 h use n = 27 and h = -8

(3) Evaluate the following rational expression

(a/3) - (b/6) + (c/12) use a = 6, b = -7 and c = -9

(4) Evaluate the following rational expression

(4/a) ÷ (9/b) use a = 9 and b = 36

**Question 1 :**

Evaluate the following rational expression

(20/c) - 8 - 9 z use c = 5 and z = 7

**Solution :**

= (20/c) - 8 - 9 z

Now we have to apply c = 5 and z = 7 in the given rational expression

= (20/5) - 8 - 9 (7)

= 4 - 8 - 63

= 4 - 71

= -67

Hence the answer for the variable expression is -67.

**Question 2 :**

Evaluate the following rational expression

(-n/9) - 9 + 5 h use n = 27 and h = -8

**Solution :**

= (-n/9) - 9 + 5 h

Now we have to apply n = 27 and h = -8 in the given rational expression

= (-27/9) - 9 + 5(-8)

= -3 - 9 - 40

= -12 - 40

= -52

Hence the answer for the variable expression is -52.

**Question 3 :**

Evaluate the following rational expression

(a/3) - (b/6) + (c/12) use a = 6, b = -7 and c = -9

**Solution :**

= (a/3) - (b/6) + (c/12)

Now we have to apply a = 6, b = -7 and c = -9 in the given rational expression

= (6/3) - (-7/6) + (-9/12)

= (2/1) + (7/6) - (9/12)

In order to combine the above fractions, we have check whether the denominator of the above fractions are same.

Since the denominators are not same, we have to take L.C.M

L.C.M (6, 12) = 12

= (2/1) x (12/12) + (7/6) x (2/2) - (9/12)

= (24/12) + (14/12) - (9/12)

= (24 + 14 - 9)/12

= (38 - 9)/12

= 31/12

Hence the answer for the variable expression is 31/12.

**Example 4 :**

Evaluate the following rational expression

(4/a) ÷ (9/b) use a = 9 and b = 36

**Solution :**

= (4/a) ÷ (9/b)

Now we have to apply a = 9 and b = 36 in the given rational expression

= (4/9) ÷ (9/36)

= (4/9) x (36/9)

Multiplying the numerators we get

= (4 x 36)/(9 x 9)

= 144/81

Simplifying the numerator and denominator by 3, we get

= 48/27

= 16/9

Hence the answer for the variable expression is 16/9.

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