Eduki

Working with rational coefficients is similar to what we do with integers. If the rational coefficients are given in terms of fractions and not decimals then we have to make the denominators of the fraction the same by multiplying. For example,

𝑥/2 + 𝑥/3

What is the common multiple of 2 and 3 which we can get? There are many answers such as 6, 12, 18, etc. But the lowest one is 6. (Remember Lowest common multiple?)

(𝑥 x 3)/(2 x 3) + (𝑥 x 2)/(3 x 2)

=3𝑥/6 + 2𝑥/6 

=5𝑥/6 

It can also be said that when 𝑥/2 and 𝑥/3 are added it becomes the same as 5/6 times 𝑥.  

When one of the operating coefficients is rational and the other is an integer, the LCM is the denominator of the coefficient expressed as a ratio and the integer is supposed to have a denominator as the coefficient. 

Problems relating percentages

If 40 has to be decreased by 8 percent, 8 percent of 40 is calculated at first and then the quantity is deducted from 40. 

That is 40-8% of 40

= 40-(8/100) x 40

=  40-0.08x40

=  40 x (1-0.08)

=  40 x 0.92

This shows that when a number is decreased or increased by a certain percentage, it can be found by multiplying the given number with a particular factor. If a number has to increase by 5 percent then, it should be multiplied by 1+0.05 or 1.05 and if it decreases by 5 percent then it should be multiplied by 1-0.05 or 0.95. Here the number 0.05 is found by dividing the given percentage 5 by 100. 

What happens when 70𝑥 is increased by 30%?

= 70𝑥 + 30% of 70𝑥

= 70𝑥 + (30/100) x 70𝑥

= 70𝑥 + 21𝑥

= 91𝑥