Question

How do you simplify `2 1/10+(1 2/7+ 4 9/10)`?

Answer 1

`=580/70`

Explanation:

Simplifying the given expression including mixed numbers is

determined by changing mixed numbers into fractions then

adding the fractions.

Mixed numbers is changed into fractions by:

`color(red)(a c/d=(a xx d + c)/d)`

Changing the mixed numbers into fractions:

`2 1/10 =color(red)((2 xx 10 + 1 )/10=21/10)`

`1 2/7 =color(red)((1 xx 7 + 2 )/7= 9/7 )`

`4 9/10 = color(red)((4 xx 10 + 9)/10= 49/10)`
`" "`

Adding the fractions is determined by computing the common denominator `G.C.D(7 , 10)`

Common denominator is determined by computing the prime factorization and choosing the greatest common factors.

`10=2 xx 5 xx 1`
`7 = 7 xx 1`

Denominator is:
`G.C.D(7 , 10) = 2 xx 5 xx 7 xx 1 =70`

`2 1/10+(1 2/7+4 9/10)`

`= color(red)(21/10) + color(red)(9/7) + color(red)(49/10)`

`=(21 xx 7)/70 + (9 xx 10)/70 + (49 xx 7)/70`

`=(147 + 90 + 343)/70`

`=580/70`