How we can estimate a fraction

[navdeep_bajwa]

How you can Estimate 11/30 of 6/20 of 120
I did not understood the method shown in Manhattan guide

Is this correct
Add 3 to 30 makes 33 so 11/33 =1/3 now subtract 3 from 20 so 6/17=1/2.9
So approx product is 1/3* 1/3 and actual product is 1/3 * a value greater than 1/3(1/2.9) so actual will be greater than 1/3

[esledge]

To estimate a fraction (I'll use 9/52 for an example), you have options:

A) You could round the denominator to a round number, such that (1/that denominator) is an easily recognized decimal. So 9/52 would round to 9/50, and since 1/50 = 0.02, 9/50 = 0.18.

B) You could round the denominator to a multiple of the numerator, so that you can reduce both top and bottom to something recognizable. So 9/52 would round to 9/54 = 1/6, which you should memorize as 16.6% (or you should quickly recall that 1/6 is half of 1/3 or half of 33.3%).

How you can Estimate 11/30 of 6/20 of 120
I did not understood the method shown in Manhattan guide

In your example, there are two fractions. Before rounding either one or both of them, first see whether you can cancel between them:

11/30 * 6/20 (6 is a factor of both 6 and 30, so cancel that!)
=11/5 * 1/20
=11/100

In this particular case, I think no fraction estimation is really necessary, since 100 is such a nice denominator.
11/100 = 0.11

Maybe the estimation comes in at the calculation of 11/100 of 120. Since 0.11 is a little more than 1/10, the answer will be a little more than 1/10 of 120, or a little more than 12.

[pritesh.suvarna]

One more approach could be an extension of what navdeep mentioned.

11/30 approx. = 1/3 (since we add 3 to 30)
6/20 approx. = 1/3 (we can remove 2 from 20)

1/3*1/3 = 1/9 = 0.11

Ans = 0.11 (120)

Thanks
Pritesh

[Ben Ku]

I think Emily's comment that before you round, make you try canceling common factors. Whereas canceling common factors do not change the value of the expression, rounding always changes the expression; rounding is less accurate.

In regard to rounding, it is helpful to make a note of how you're rounding, and make sure you compensate for it.

In Pritesh's explanation I would revise it and say
11/30 approx. = less than 1/3 (since we add 3 to 30)
6/20 approx. = greater than 1/3 (we can remove 2 from 20)

Here we can see that our approximations compensate for each other.

Hope that helps.