I need help with this fraction problem: 3 1/4 + 5 1/8 = ?

[Angelwngs27]

I'm doing this fraction problem that is the following:

3 1/4 + 5 1/8 = ?

Can anyone explain how to get the answer to this problem?

 

[stapel]

I'm doing this fraction problem that is the following:

3 1/4 + 5 1/8 = ?

Can anyone explain how to get the answer to this problem?

Which way is your instructor expecting you to proceed? Will you be (a) adding the whole-number parts and the fractional parts separately or (b) converting the mixed numbers to improper fractions, adding, and then converting back? (Whatever method your instructor or textbook used is probably the way to go.)

When you reply, please show your efforts so far (or else specify the method you're using, and that you're asking for lesson instruction first). Thank you!

 

[Angelwngs27]

This is how I got the answer I got...

I turned the mixed fractions into improper fractions that I found turned into 13/8 + 41/8. I then multiplied 13 by 2 to even the fraction out. So, I got 13 x 2 = 26/8. So, I then did 26/8 + 41/8 = 67/8. I then divided 67 by 8, and got 8 3/8. It says in the answer key in the back that, that is the correct answer. But my friend is the one that told me to multiply 13 by 2. Why exactly did I need to do that to get the correct answer?:wink:

 

[stapel]

I turned the mixed fractions into improper fractions that I found turned into 13/8 + 41/8.

The first mixed number was:

. . . . .$\displaystyle 3\, \dfrac{1}{4}$

This converts as:

. . . . .$\displaystyle \dfrac{3\, \cdot\, 4\, +\, 1}{4}\, =\, \dfrac{12\, +\, 1}{4}\, =\, \dfrac{13}{4}$

Where did the "8" come from? (The other mixed number was converted correctly.)

Please show all of your steps. Thank you!

 

[MaxWong]

The first mixed number was:

. . . . .$\displaystyle 3\, \dfrac{1}{4}$

This converts as:

. . . . .$\displaystyle \dfrac{3\, \cdot\, 4\, +\, 1}{4}\, =\, \dfrac{12\, +\, 1}{4}\, =\, \dfrac{13}{4}$

Where did the "8" come from? (The other mixed number was converted correctly.)

Please show all of your steps. Thank you!

It is simply because 13/4 = 26/8 to make the question easier.

 

[Vanice]

I'm doing this fraction problem that is the following:

3 1/4 + 5 1/8 = ?

Can anyone explain how to get the answer to this problem?

1. Add the fractions first
1 1
4 + 8
2.Find the LCD which will be the denominator of the final answer. The LCD is 8
3. Do the following LCD divided by denominator x numerator
So 8 divided 4 x 1 is 2
So 8 divided 8 x 1 is 1
2+1=3
So the answer is 3/8 but wait add the numbers 3+5=8 so the most final is 8 3/8 (simplify if necessary)

 

[AngleWyrm]

I'm doing this fraction problem that is the following:
3 1/4 + 5 1/8 = ?

Converting the mixed fractions into pure fractions:
\(\displaystyle
3 \frac{1}{4} = ( 3 \times \frac{4}{4} ) + \frac{1}{4} = \frac{3\times4 + 1}{4} = \frac{13}{4} \\
5 \frac{1}{8} = ( 5 \times \frac{8}{8} ) + \frac{1}{8} = \frac{5\times8 + 1}{8} = \frac{41}{8} \\
\)
The common denominator between them:
\(\displaystyle \frac{1}{4} \times \frac {1}{8} = \frac{1}{4 \times 8} = \frac{1}{32}\\
\)
Adding our newfound apple baskets to apple baskets:
\(\displaystyle \\ \frac{13 \times 8}{4 \times 8} + \frac{41 \times 4}{8 \times 4} = \frac{104 + 164}{32} = \frac {268}{32} \\
\)
Most efficient Greatest Common Denominator alogrithm is the Euclidean algorithm
\(\displaystyle 268 / 32 = 8 \times 32 + 12 \\
32 / 12 = 2 \times 12 + 8 \\
12 / 8 = 1 \times 8 + 4 \\
8 / 4 = 2 \times 4 + 0 \)
No remainder ends the process with 8 as the solution to Greatest Common Denominator

Simplifying our fraction, 32/8 gives us a divisor of 4
$\displaystyle \frac {268/4}{32/4} = \frac{67}{8} = \frac{8 \times 8 + 3}{8} = 8 \frac{3}{8}$

 

[tangaloomaflyer]

Converting the mixed fractions into pure fractions:
\(\displaystyle
3 \frac{1}{4} = ( 3 \times \frac{4}{4} ) + \frac{1}{4} = \frac{3\times4 + 1}{4} = \frac{13}{4} \\
5 \frac{1}{8} = ( 5 \times \frac{8}{8} ) + \frac{1}{8} = \frac{5\times8 + 1}{8} = \frac{41}{8} \\
\)
The common denominator between them:
\(\displaystyle \frac{1}{4} \times \frac {1}{8} = \frac{1}{4 \times 8} = \frac{1}{32}\\
\)
Adding our newfound apple baskets to apple baskets:
\(\displaystyle \\ \frac{13 \times 8}{4 \times 8} + \frac{41 \times 4}{8 \times 4} = \frac{104 + 164}{32} = \frac {268}{32} \\
\)
Most efficient Greatest Common Denominator alogrithm is the Euclidean algorithm
\(\displaystyle 268 / 32 = 8 \times 32 + 12 \\
32 / 12 = 2 \times 12 + 8 \\
12 / 8 = 1 \times 8 + 4 \\
8 / 4 = 2 \times 4 + 0 \)
No remainder ends the process with 8 as the solution to Greatest Common Denominator

Simplifying our fraction, 32/8 gives us a divisor of 4
$\displaystyle \frac {268/4}{32/4} = \frac{67}{8} = \frac{8 \times 8 + 3}{8} = 8 \frac{3}{8}$

This is is a great insight and the GCD algorithm is very handy

in this case though it would be easier to make 13/4 into 26/8 and then add the numerators

67/8 simplifies to 8 and 3/8ths