Question

Tegan bought 1 1/6 metres of ribbon. She needs 2/5 meters to wrap her brothers present and 3/4 meters to wrap her sister's present. Did she buy enough ribbon?

Answer 1

Yes, Tegan buys enough ribbon.

Explanation:

Given:

Length of ribbon bought by Tegan =
`(11)/(6)` =
`1.83` meters

Ribbon needed to wrap her brother's present =
`(2)/(5)` meters

Ribbon needed to wrap her sister's present =
`(3)/(4)` meters

Let the length of ribbon needed for wrapping be 'x' meters

So,

⇒
`x=(2)/(5) +(3)/(4)`

⇒ Taking LCD of
`5` and
`4` that is
`20`.

⇒
`x=((2* 4)+(3* 5))/(20)`

⇒
`x=(8+15)/(20)`

⇒
`x=(23)/(20)` meters

Comparing
`(23)/(20)` and
`(11)/(6)`.

LCD of
`20` and
`6` is
`60`.

Now equating the denominators.

⇒
`(23* 3)/(20* 3) = (69)/(60)` and ⇒
`(11* 10)/(6* 10) =(110)/(60)`

Now we can compare the above like fractions.

⇒
`(69)/(60)` <
`(110)/(60)`

Shortcut:

We can directly compare the factions by cross multiplying.

⇒
`(23)/(20) \ \ \ \ \ \ \ \ \ (11)/(6)`

⇒
`23* 6` ,
`20* 11`

⇒
`138` and
`220`

⇒
`138` <
`220`

Then

⇒
`(23)/(20)` <
`(11)/(6)`

She has enough ribbon to wrap the presents as ribbon bought by Tegan is greater in length than the ribbon used.