**Interpret quotients of rational numbers by describing real-world contexts :**

In mathematics, a rational number is any number that can be expressed in the form p/q where "q" is not equal to zero.

The quotient of the rational number p/q is nothing but the result that we get when we divide "p" by "q".

The rules for the sign of quotient are summarized below.

Let p and q be rational numbers.

**Example 1 : **

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.

**Example 2 : **

Over 5 months, Carlos wrote 5 checks for a total of $323.75 to pay for his cable TV service. His cable bill is the same amount each month. What was the change in Carlos’s bank account each month to pay for cable?

**Solution :**

**Step 1 :**

Use a negative number to represent the withdrawal from his account each month

**Step 2 : **

Find -323.75 / 5

**Step 3 : **

Determine the sign of the quotient.

The quotient will be negative because the signs are different.

**Step 4 :**

Divide.

-323.75 / 5 = -64.75

Hence, Carlos withdrew $64.75 each month to pay for cable TV.

**Example 3 : **

Maya wants to divide a 3/4 -pound box of trail mix into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can Maya fill ?

**Solution : **

**Step 1 : **

To get answer for the above question, we have to divide 3/4 by 1/12.

That is, we have to find the value of (3/4) / (1/12).

**Step 2 : **

Determine the sign of the quotient.

The quotient will be positive, because the signs of both numerator (3/4) and denominator (1/12) are same.

**Step 3 : **

Write the complex fraction as division :

(3/4) / (1/12) = (3/4) ÷ (1/12)

**Step 4 : **

Rewrite the above division as multiplication by taking the reciprocal of the second fraction.

(3/4) ÷ (1/12) = (3/4) x (12/1)

**Step 5 : **

Simplify

(3/4) x (12/1) = (3/1) x (3/1)

(3/4) x (12/1) = 9

Hence, Maya can fill 9 bags of trail mix.

After having gone through the stuff given above, we hope that the students would have understood "Interpret quotients of rational numbers by describing real-world contexts".

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