# Upper and lower boundary mixed

If you have a calculation such as (atimesb)-c and you need to know the possible limits of the upper boundary and lower boundary

Apply the separate rules for each operation
and apply BIDMAS

(see our section on BIDMAS)

Example

The following formula has been corrected to 1 D.P.

(23.7times31.3)-16.8

What are the upper and lower boundaries of this calculation?

First find the upper and lower boundary of 23.7 to 1 D.P.

23.7 to one decimal place

23.ul7 underline the digit (1^(st) decimal place).

23.ul7\0 look next door

0      5 or more raises the score. So 23.65 would raise to 23.7.

0       four or less just ignore 23.7499 it would ignore and stay at 23.7.

This is simplified to 23.75

So the upper and lower boundary of 23.7 is 23.75 and 23.65.

Now find the upper and lower boundary of 31.3 to 1 D.P.

31.3 to 1 D.P.

31.ul3 underline the digit (1^(st)decimal point).

31.ul3\0 look next door

0      5 or more raises the score. So 31.25 would raise to 31.3.

0       four or less just ignore 31.3499 it would ignore and stay at 31.3.

This is simplified to 31.35

So the upper and lower boundary of 31.3 is 31.35 and 31.25.

Now find the upper and lower boundary of 16.8 to 1 D.P.

16.8 to 1 D.P.

16.ul8 underline the digit (1^(st)decimal point).

16.ul8\0 look next door

0      5 or more raises the score. So 16.75 would raise to 16.8.

0       four or less just ignore 16.8499 it would ignore and stay at 16.8.

This is simplified to 16.85

So the upper and lower boundary of 16.8 is 16.85 and 16.75.

Summary

Upper and lower boundary of 23.7 is 23.75 and 23.65

Upper and lower boundary of 31.3 is 31.35 and 31.25

Upper and lower boundary of 16.8 is 16.85 and 16.75

i - So the upper boundary is(23.7times31.3)-16.8 to 1 D.P.

NOTE:

Multiplication use the maximum boundary of each

Subtraction use the biggest difference between the two

This would be:

 (23.75 xx 31.35) - 16.75 Big xx Big - Small

Applying BIDMAS.

744.56-16.75=727.81 to 2 D.P.

ii - The lower boundary is (23.7times31.3)-16.8 to 1 D.P.

NOTE:

Multiplication use the minimum boundary of each

Subtraction use the smallest difference between the two

This would be:

 (23.65 xx 31.25) - 16.85 Small xx Small - Big

Applying BIDMAS.

739.06-16.85=722.21 to 2 D.P.

Answer: The upper and lower boundary of this calculation is 727.81 and 722.21.