APPLYING RATIONAL NUMBER OPERATIONS

In this section, you will 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 number.

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    

So, 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

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

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