EVALUATE VARIABLE EXPRESSIONS INVOLVING RATIONAL NUMBERS WORKSHEET

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 

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.

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