Question

Ryan is 4 1/2 ft. tall. He is 3 in. taller than his sister Lizzie. She is 3/4 of a foot taller than her sister Emma. How tall is Emma ?

Answer 1

`3(1)/(12)` ft tall

Explanation:

We must follow the indications:

Ryan is 4 1/2 ft. tall.

Ryan =
`4(1)/(12) ft`

He is 3 in. taller than his sister Lizzie. to find how tall is Lizzie we need to substract 3 inches from the height of Ryan, but we can only substract the quantities if they are in the same units.

Thus we convert the 3 inches to feet, since we 1 feet = 12 inches:

`(1)/(4) feet=3inches`

so the height of lizzie:

`4(1)/(12)ft-(1)/(4)ft\\ \\`

we convert the first mixed number to fraction by multiplying 4 by 12 and adding the numerator 1:

`4(1)/(12)=(4*12+1)/(12)=(49)/(12)`

the subtraction becomes:

`(49)/(12)ft-(1)/(4)ft\\ \\=(49*4-12*1)/(12*4)\\ \\=(196-12)/(48)\\\\=(184)/(48)\\ \\=(46)/(12) \\`

`=(23)/(6)`

Lizzie is 23/6 ft tall.

She is 3/4 of a foot taller than her sister Emma, thus we must substract 3/4 from the height of Lizzie to find the height of Emma:

`(23)/(6)ft-(3)/(4)ft\\ \\=(23*4-6*3)/(6*4)\\ \\=(92-18)/(24)\\ \\=(74)/(24)\\ \\=(37)/(12)\\ \\=3(1)/(12)`

Emma is
`3(1)/(12)` ft tall.