**Applying rational number operations :**

In this section, we are going to learn how rational number operations (addition, subtraction, multiplication and division) can be applied to solve real world problems.

**Example 1 : **

Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?

**Solution : **

**Step 1 : **

Use positive numbers to represent the distance Malachi hiked.

**Step 2 : **

Find 2.5 + 1.5.

Let us use the real number line to add 2.5 and 1.5.

**Step 3 : **

Start at 2.5.

**Step 4 : **

Move 1.5 units to the right because the second addend is positive.

The result is 4.

Malachi hiked 4 miles.

**Example 2 : **

The temperature on an outdoor thermometer on Monday was 5.5 °C. The temperature on Thursday was 7.25 degrees less than the temperature on Monday. What was the temperature on Thursday ?

**Answer : **

**Step 1 : **

Find 5.5 - 7.25.

**Step 2 :**

Start at 5.5.

**Step 3 :**

Move |7.25| = 7.25 units to the left, because we are subtracting a positive numbe

The result is -1.75.

The temperature on Thursday was -1.75 °C.

**Example 3 : **

The science teacher is filling her new fish aquarium. The aquarium holds 40 gallons. If she fills the aquarium 4/5 of the way full, how many gallons will she need?

**Solution :**

If 4/5 of the aquarium is filled, then 1/5 th of the aquarium to be filled to make it full. Because 5 - 4 = 1.

To find number of gallons, we have to multiply 40 by 1/5.

**Step 1 : **Multiply 40 by 1/5

40 x 1/5

**Step 2 : **Simplify

8 x 1/1

**Step 3 : **Multiply

8 x 1/1 = 8

Hence, the science teacher needs 8 gallons to make the aquarium full.

**Example 4 :**

Cooper's bird feeder holds 9/10 of a cup of birdseed. Cooper is filling the bird feeder with a scoop that holds 3/10 of a cup. How many scoops of birdseed will Cooper put into the feeder?

**Solution : **

**Step 1 : **

To get answer for the above question, divide the total amount of birdseed by the size of each scoop.

That is, we have to find the value of (9/10) / (3/10).

**Step 2 : **

Determine the sign of the quotient.

The quotient will be positive, because the signs of both numerator (9/10) and denominator (3/10) are same.

**Step 3 : **

Write the complex fraction as division :

(9/10) / (3/10) = (9/10) ÷ (3/10)

**Step 4 : **

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

(9/10) ÷ (3/10) = (9/10) x (10/3)

**Step 5 : **

Simplify

(9/10) x (10/3) = (3/1) x (1/1)

(9/10) x (10/3) = 3

Hence, Cooper will put 3 scoops of birdseed into the feeder

After having gone through the stuff given above, we hope that the students would have understood "Applying rational number operations".

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