Rational Systems Theory

In this section we will study about rational system theory. Rational system is one of the important topic is mathematical number system. Rational system is used for represents the rational numbers. For example, if the distance of 3 km to the right of a place was denoted by 3, then the distance of 5 km to the left of the same place could be denoted by -5. Let us start our study about rational system theory.

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Solved problems for rational systems theory:

Solved problem 1: A restaurant bought `12 2/3` pounds of rice. They used `6 1/3` pounds of it. How much rice is left?

Solution:

Find how much rice is left by subtracting `6 1/3` from `12 2/3` .

Subtract. Remember to subtract whole numbers from whole numbers and fractions from fractions.

` 12 2/3 - 6 1/3 = 6 1/3`

This answer is in simplest form.

There are` 6 1/3` pounds of rice left.

Answer: There are `6 1/3` pounds of rice left.

Solved problem 2: A piece of land is 5 miles wide. It is `2 1/8` times as long as it is wide. How long is the piece of land?

Solution:

The piece of land is 2 1/8 times 5 miles long.

Multiply:

` 2 1/8` * 5 =?

Write   `2 1/8 ` as an improper fraction.

`2 1/8 = ((2 * 8) + 1)/8 = 17/8`

Write 5 as an improper fraction.

`5 = 5/1`

Multiply the numerators and multiply the denominators.

17/8 * 5/1 = (17 * 5)/(8 * 1) = 85/8

Simplify the product.

`85/8 = 10 5/8`

The piece of land is `10 5/8` miles long.

Answer: The piece of land is `10 5/8` miles long.

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Unsolved problems for rational systems theory:

Unsolved problem 1: Kyle's cat weighs 6 pounds. Kyle's dog weighs `1 1/2 ` times as much as his cat. How much does Kyle's dog weigh?

Unsolved problem 2: Ismail rode his bike for `3 1/10` miles on Wednesday. On Thursday, he biked 5 times as far as on Wednesday. How many miles did Ismail bike on Thursday?

Solutions for rational systems theory:

Solution 1: Kyle's dog weighs 9 pounds.

Solution 2: Ismail biked `15 1/2` miles on Thursday.