Question

What’s the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21 e. 7⁄11 and 9⁄121 f. 1⁄2, 3⁄18, and 4⁄9

Answer 1

Imagine a cake. OK? Now divide the cake in 2 equal pieces, each one is ½ of the cake.
Now divide each piece in 2 halves; each one is ¼ of the cake. Witch is largest? 1:2=0,5; 1:4=0,25. 0,5>0,25.

5:6=0,83333
29:36=0,80555
0,83>0,80 so 5/6 is the largest.

Do this for each group.

a.5/6
b.5/8
c.19/45
d.13/14
e.7/11
f.1/2

Answer 2

a.
`(5)/(6)`,

b.
`(5)/(12)`,

c.
`(19)/(45)`,

d.
`(13)/(14)`,

e.
`(7)/(11)`,

f.
`(1)/(2)`

Explanation:

(a)

`(5)/(6)\text{ and }(29)/(36)`

Making denominator common.

`(5* 6)/(6* 6)\text{ and }(29)/(36)`

`(30)/(36)\text{ and }(29)/(36)`

Now compare the numerators.

`30>29`

`(30)/(36)>(29)/(36)`

`(5)/(6)>(29)/(36)`

Therefore
`(5)/(6)` is largest fraction.

(b)

`(5)/(12)\text{ and }(3)/(8)`

Making denominator common.

`(5* 2)/(12* 2)\text{ and }(3* 3)/(8* 3)`

`(10)/(24)\text{ and }(9)/(24)`

Now compare the numerators.

`10>9`

`(10)/(24)>(9)/(24)`

`(5)/(12)>(3)/(8)`

Therefore
`(5)/(12)` is largest fraction.

(c)

`(2)/(5)\text{ and }(19)/(45)`

Making denominator common.

`(2* 9)/(5* 9)\text{ and }(19)/(45)`

`(18)/(45)\text{ and }(19)/(45)`

Now compare the numerators.

`18<19`

`(18)/(45)<(19)/(45)`

`(2)/(5)<(19)/(45)`

Therefore
`(19)/(45)` is largest fraction.

Similarly,

(d)

`(5)/(7)\text{ and }(13)/(14)\text{ and }(19)/(21)`

By making denominator common, we get

`(30)/(42)\text{ and }(39)/(42)\text{ and }(38)/(42)`

By comparing the numerators, we get 39 is greatest therefore
`(13)/(14)` is largest fraction.

(e)

`(7)/(11)\text{ and }(9)/(121)`

By making denominator common, we get

`(77)/(121)\text{ and }(9)/(121)`

By comparing the numerators, we get 77 is greatest therefore
`(7)/(11)` is largest fraction.

(d)

`(1)/(2)\text{ and }(3)/(18)\text{ and }(4)/(9)`

By making denominator common, we get

`(9)/(18)\text{ and }(3)/(18)\text{ and }(8)/(18)`

By comparing the numerators, we get 9 is greatest therefore
`(1)/(2)` is largest fraction.