**Dividing rational numbers worksheet :**

Worksheet on dividing rational numbers is much useful to the students who would like to practice problems on division of rational numbers.

1. Divide 2/3 by -7/6

2. Divide -2 by 8/3

3. Divide 9/5 by 3

4. A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent ?

**Problem 1 : **

Divide 2/3 by -7/6

**Solution :**

**Step 1 : **

Take the reciprocal of the second rational number.

-7/6 ---- reciprocal ----> -6/7

**Step 2 : **

Multiply the first rational number 2/3 by -6/7

(2/3) x (-6/7)

**Step 3 : **Simplify

(2/1) x (-2/7)

**Step 4 : **Multiply

(2/1) x (-2/7) = -4/7 Positive times negative equals negative

Hence, 2/3 ÷ -7/6 = -4/7

**Problem 2 : **

Divide -2 by 8/3

**Solution :**

**Step 1 :**

Take the reciprocal of the second rational number.

8/3 ---- reciprocal ----> 3/8

**Step 2 : **

Multiply the first rational number 2 by 3/8

(-2) x (3/8)

**Step 3 : **Simplify

(-1) x (3/4)

**Step 4 : **Multiply

(-1) x (3/4) = -3/4 Positive times negative equals negative

Hence, -2 ÷ 8/3 = -3/4

**Problem 3 : **

Divide 9/5 by 3

**Solution :**

**Step 1 :**

Take the reciprocal of the second rational number.

3 ---- reciprocal ----> 1/3

**Step 2 : **

Multiply the first rational number 9/5 by 1/3

(9/5) x (1/3)

**Step 3 : **Simplify

(3/5) x (1/1)

**Step 4 : **Multiply

(3/5) x (1/1) = 3/5 Positive times positive equals positive

Hence, 9/5 ÷ 3 = 3/5

**Problem 4 : **

A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent ?

**Solution :**

To find how far she should travel in each descent, we have to divide 100 by 5.

**Step 1 :**

Take the reciprocal of the divisor 5.

5 ---- reciprocal ----> 1/5

**Step 2 : **

Multiply 100 by 1/5

(100) x (1/5)

**Step 3 : **Simplify

(20) x (1/1)

**Step 4 : **Multiply

(20) x (1/1) = 20

Hence, she should travel 20 feet in each descent.

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

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