EVALUATE VARIABLE EXPRESSIONS INVOLVING RATIONAL NUMBERS WORKSHEET

Evaluate Variable Expressions Involving Rational Numbers Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on evaluating variable expressions involving rational numbers. 

Evaluate Variable Expressions Involving Rational Numbers Worksheet - Problems

Problem 1 :

Evaluate the following rational expression.

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

Problem 2 :

Evaluate the following rational expression.

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

Problem 3 :

Evaluate the following rational expression.

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

Problem 4 :

Evaluate the following rational expression.

(4/a) ÷ (9/b) use a = 9 and b = 36 

Evaluate Variable Expressions Involving Rational Numbers Worksheet - Solutions

Problem 1 :

Evaluate the following rational expression.

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

Solution :

  =  (20/c) - 8 - 9z

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

So, the value of the given expression is -67.

Problem 2 :

Evaluate the following rational expression.

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

Solution :

  =  (-n/9) - 9 + 5h

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

So, the value of the given expression is -52.

Problem 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

So, the value of the given expression is 31/12.

Problem 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

So, the value of the given expression is 16/9.

After having gone through the stuff given above, we hope that the students would have understood how to evaluate variable expressions involving rational numbers. 

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