Help with Adding Fractions

The problem is:

Esteban is 63 1/8 inches tall. Haley is 59 5/8 inches tall. How much taller is Esteban than Haley? Write in simplest form.

The work I done so far:

63 1/8 - 59 5/8

= 63 1/8 + (-59 5/8)

= 4 6/8

= 4 3/4

It's a multiple choice problem and the choices are:

A. 4 1/2 in.

B. 4 1/4 in.

C. 3 3/4 in.

D. 3 1/2 in.

Re: Help with Adding Fractions

Quote:

Originally Posted by

**Nadeshiko** The problem is:

Esteban is 63 1/8 inches tall. Haley is 59 5/8 inches tall. How much taller is Esteban than Haley? Write in simplest form.

The work I done so far:

63 1/8 - 59 5/8

= 63 1/8 + (-59 5/8)

= 4 6/8

= 4 3/4

It's a multiple choice problem and the choices are:

A. 4 1/2 in.

B. 4 1/4 in.

C. 3 3/4 in.

D. 3 1/2 in.

This is why I don't like mixed fractions. Simply put, in line 2 you added 5/8 when you should have subtracted it.

There are two ways to handle this. The first is to simply write the difference in terms of whole numbers and fractions, which is what you were trying to do. It reads like this:

(63 + 1/8) - (59 + 5/8) = (63 - 59) + (1/8 - 5/8) = 4 - 1/2 = 3 + 1/2

The other way is to write the whole thing in terms of fractions. It's a bit trickier but works a lot better.

$\displaystyle \left ( 63 + \frac{1}{8} \right ) - \left ( 59 + \frac{5}{8} \right ) = \left ( \frac{63 \cdot 8}{8} + \frac{1}{8} \right ) - \left ( \frac{59 \cdot 8}{8} + \frac{5}{8} \right )$

which again works out to be 3 + 1/2.

-Dan

Re: Help with Adding Fractions

Hello, Nadeshiko!

Quote:

$\displaystyle \text{Esteban is }63\tfrac{1}{8}\text{ inches tall.}$

$\displaystyle \text{Haley is }59\tfrac{5}{8}\text{ inches tall.}$

$\displaystyle \text{How much taller is Esteban than Haley?}$

$\displaystyle \text{The work I did so far:}$

. . $\displaystyle 63\tfrac{1}{8} - 59\tfrac{5}{8} \;=\; 63\tfrac{1}{8}+ (-59\tfrac{5}{8}) \;=\; 4\tfrac{6}{8}\;\;{\color{red}??}$

Do you see what you did?

You subtracted the whole numbers: .$\displaystyle 63 - 59 \:=\:4$

Then you *added* the fractions: .$\displaystyle \tfrac{1}{8}\,{\color{red}+}\,\tfrac{5}{8} \:=\:\tfrac{6}{8}$

You have: .$\displaystyle (63 + \tfrac{1}{8}) - (59 + \tfrac{5}{8})$

. . . . . . . $\displaystyle =\;63 + \tfrac{1}{8} - 59 - \tfrac{5}{8}$

. . . . . . . $\displaystyle =\;(63-59) + (\tfrac{1}{8} - \tfrac{5}{8})$

. . . . . . . $\displaystyle =\;4 + (\text{-}\tfrac{4}{8})$

. . . . . . . $\displaystyle =\;4 - \tfrac{1}{2}$

. . . . . . . $\displaystyle =\;3\tfrac{1}{2}$

Re: Help with Adding Fractions

Another way:

$\displaystyle 63\frac{1}{8}- 59\frac{5}{8}= 62+ \frac{8}{8}+ \frac{1}{8}- 59\frac{5}{8}= 62\frac{9}{8}- 59\frac{5}{8}= (62- 59)+\left(\frac{9- 5}{8}\right)= 3\frac{4}{8}= 3\frac{1}{2}$