Worksheet on Operations on Rational Expressions provided on our page can be a great resource for students. Rational Expressions Operations Worksheet prevailing is quite flexible and free to use. You can simply solve the various questions provided in the Worksheet to be familiar with various operations like Addition, Subtraction, Multiplication, Division, etc. For any other relevant topic worksheets, you can check our collection of Rational Numbers Worksheets and clear your concerns.

1. Simplify the following rational numbers

(i) (15/8 × 3/5) – (4/5 × -10/8) (ii) (-7/4 × 4/3) + (11/2 × 4/6)

**Solution:**

(i) (15/8 × 3/5) – (4/5 × -10/8)

Given (15/8 × 3/5) – (4/5 × -10/8)

= (15*3/8*5)-(4*-10/5*8)

=(45/40)-(-40/40)

= (45+40)/40

= 85/40

=17/8

(ii) (-7/4 × 4/3) + (11/2 × 4/6)

= (-7*4/4*3)+(11*4/2*6)

= -28/12+44/12

= (-28+44)/12

= 16/12

= 4/3

2. Simplify the following Rational Expressions

(i) (5/2 × 1/5) + (4/3 × 7/2) – (11/8 × 5/3)

(ii) (1/3 × 4/7) – (6/10 × -2/3) + (4/7 × 7/2)

**Solution:**

(i) (5/2 × 1/5) + (4/3 × 7/2) – (11/8 × 5/3)

= (5*1/2*5)+(4*7/3*2)-(11*5/8*3)

= (5/10)+(28/6)-(55/24)

= 5/10+28/6-55/24

= (5*12+28*20-55*5)/120

= (60+560-275)/120

= 345/120

= 23/8

(ii) (1/3 × 4/7) – (6/10 × -2/3) + (4/7 × 7/2)

= (1*4/3*7)-(6*-2/10*3)+(4*7/7*2)

= 4/21-(-12/30)+(28/14)

= 4/21+12/30+28/14

= (40+84+420)/210

= 544/210

= 272/105

3. Find the value of the following and express in standard form

(i) 4/5 ÷ 16/12

(ii) -5 ÷ (-7/17)

**Solution:**

4/5 ÷ 16/12

= 4/5*(12/16)

= 4*12/5*16

= 48/80

= 3/5

Since the rational number 3/5 has no other common factors and the denominator is positive. It is said to be in standard form.

-5 ÷ (-7/17)

= -5*17/-7

= -85/-7

= 85/7

85/7 is in standard form as it has no other common factors and the denominator is positive.

4. By what number should we multiply 14/28 to obtain the product 5/7?

**Solution:**

14/28*x = 5/7

x= (5/7)/(14/28)

= 5/7*28/14

= 10/7

You need to multiply 14/28 with 10/7 to obtain the product 5/7.

5. By what number should we multiply -4/13 so that the product is 24?

**Solution:**

-4/13*x= 24

x = 24/(-4/13)

= 24*13/-4

= 312/-4

= -78

Multiply -4/13 with -78 to obtain the product 24.

6. Cost of a rope is 5 1/3 m is $ 12 1/4. What is Cost Per Meter?

**Solution:**

The cost of a rope is 5 1/3 m is $12 1/4

16/3 m = $49/4

1 m =?

Divide 49/4 with 16/3

= (49/4)/(16/3)

= 49/4*3/16

= (49*3)/(4*16)

= 147/64

= 2 19/64

1 meter of rope costs $ 2 19/64.

7. If 14 trousers of equal size can be prepared from 42 meters of cloth, what is the length of the cloth required for each trouser?

**Solution:**

14 trousers = 42 m

1 trouser = 42/14

= 3m

Therefore, each trouser requires a length of 3m.

8. Divide the sum of 11/5 and -4/7 by the product of -21/7 and 1/-3?

**Solution:**

Sum = 11/5+(-4/7)

=(77-16)/35

= 61/35

Product = -21/7*1/-3

= = -21/-21

= 1

Dividing the sum with the product of given rational numbers we get

= (61/35)/1

= 61/35.

9. Divide the Sum of 45/11 and 5/3 by their difference?

**Solution:**

Sum = (45/11+5/3)

= (45*3+5*11)/33

= (135+55)/33

= 190/33

Difference = (45/11 – 5/3)

= (45*3 – 5*11)/33

= (135 -55)/33

= 80/33

= (190/33)/(80/33)

= 190/33*33/80

= 190/80

= 19/8

10. By what number should -2/3 be multiplied in order to produce 3/4?

**Solution:**

-2/3*x= 3/4

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

= 3/4*3/-2

= (3*3)/(4*-2)

= 9/-8