Fractions

Ratio and Proportion

Work and time

More topics and problems to be added

Fractions

Arrange the following fractions in increasing order

Increasing order means smallest to largest

Fractions can be compared using different methods. In this example we are going to change all of them to the same denominator

The denominators are 3, 4 and 5

LCM of 3, 4 and 5 is 60

Change each given fraction to an equivalent fraction so that each of the denominators is 60

Ratio and Proportions

If A : B = 2 : 3 and B : C = 4 : 5 what is A : C?

Let’s try and understand what makes this problem tricky.

What if the problem said

If A : B = 2 : 3 and B : C = 3 : 4 what is A : C?

Most students will get this one right as they can see a ‘bridge’ between the 'B's…both 'B's are 3 and therefore we can get rid of 'B'

Therefore, A : C = 2 : 4 (which can be simplified to 1 : 2 but that’s not the point)

The idea is, we need the same number on both the 'B's to eliminate them.

The problem does not have the same number on the two 'B's

But wait…can’t we change both Bs to the same number by adjusting the A and the C? Good idea! Let’s do it…

The Bs are 3 and 4 whose LCM is 12, therefore let’s change the Bs to 12 (pretty much like you do in equivalent fractions)

A : B = 2 : 3 = ? : 12

Now this is the same as asking

so the answer is 8

Therefore, A : B is also 8 : 12

Similarly, B : C = 12: 15

Work and time

John can do a piece of work in 4 days when he works on his own. Betty takes 6 days to do the same work when working on her own. If they work together, how many days it would take them to finish the work?

Note: The answer is NOT 5 days! (It has to less than 4 days which is what John alone takes to finish the work)

In 1 day John can finish of the work

In 1 day, Betty can finish of the work

Together working, in 1 day they can finish

of the work

of the work is completed in 1 day

Therefore, the whole work will be completed in