Question

Change each mixed number into an equal improper fraction a. 1 7/16, b. 11 5/9, c. 30 5/9, d. 10 10/13, e. 24 3/5, f. 129 1/2

Answer 1

We need to convert the following fractions into improper fraction.

a.
`1 (7)/(16)`, b.
`11 (5)/(9)`, c.
`30 (5)/(9)`

d.
`10 (10)/(13)`, e.
`24 (3)/(5)`, and f.
`129 (1)/(2)`

We know that an improper fraction is a fraction in which the numerator is greater than the denominator.

Now, to convert a mixed fraction, say
`a(b)/(c)` into improper fraction as,
`a(b)/(c)=(a* c+b)/(b)`

Now, let us consider each part one by one.

a.
`1 (7)/(16)`

`1(7)/(16)=(16*1+7)/(16) =(23)/(16)`

b.
`11 (5)/(9)`

`11(5)/(9)=(11*9+5)/(9) =(104)/(9)`

c.
`30 (5)/(9)`

`30(5)/(9)=(30*9+5)/(9) =(275)/(9)`

d.
`10 (10)/(13)`

`10(10)/(13)=(10*13+10)/(13) =(140)/(13)`

e.
`24 (3)/(5)`

`24(3)/(5)=(24*5+3)/(5) =(123)/(5)`

f.
`129 (1)/(2)`

`129(1)/(2)=(129*2+1)/(2) =(259)/(2)`

Answer 2

a)

`(23)/(16)`

b)

`(104)/(9)`

c)

`(275)/(9)`

d)

`(140)/(13)`

e)

`(103)/(5)`

f)

`(259)/(2)`

Explanation:

" A fraction in which the numerator is greater than the denominator "

We have to change each of the mixed fraction into improper fraction:

We know that the mixed fraction is converted into fraction as:

`a(b)/(c)=(a* c+b)/(c)`

a)

`1(7)/(16)` could be written as:

`=(1* 16+7)/(16)\\\\=(16+7)/(16)\\\\=(23)/(16)`

b)

`11(5)/(9)`

`=(11* 9+5)/(9)\\\\=(99+5)/(9)\\\\=(104)/(9)`

c)

`30(5)/(9)`

`(30* 9+5)/(9)\\\\=(270+5)/(9)\\\\=(275)/(9)`

d)

`10(10)/(13)`

`(10* 13+10)/(13)\\\\=(130+10)/(13)\\\\=(140)/(13)`

e)

`24(3)/(5)\\\\=(24* 5+3)/(5)\\\\=(100+3)/(5)\\\\(103)/(5)`

f)

`129(1)/(2)\\\\\\=(19* 2+1)/(2)\\\\=(258+1)/(2)\\\\=(259)/(2)`