Question

the sum of three mixed numbers is 22 1/20. two of the numbers are 8 1/2 and 5 1/4. what is the third number?

Answer 1

make all mixed number improper fractions first...

rule: a b/c=(ac+b)/c

22 1/20=8 1/2+5 1/4+n

441/20=17/2+21/4+n make all have a common denominator of 20

441/20=170/20+105/20+20n/20 multiply both sides by 20

441=170+105+20n combine like terms

441=275+20n subtract 275 from both sides

166=20n divide both sides by 20

n=166/20 and we can convert this back to a mixed number...

n=(160+6)/20

n=8+6/20

n=8 3/10

Answer 2

To do this we need to calculate:

`22 (1)/(20) - 8 (1)/(2) - 5 (1)/(4)`

`= (441)/(20) - (17)/(2) - (21)/(4)`
Then we need to convert these to all have a common denominator:

`= (441)/(20) - (170)/(20) - (105)/(20)`

`= (441-170-105)/(20)`

`= (166)/(20)`

`= 8 (6)/(20)`

`= 8 (3)/(10)`