2 1/4 inches + 5 3/4 inches + 8 1/2 inches:
First, to start solving this problem, we will have to add the whole numbers first. The whole numbers are the...whole numbers in front of the fraction. In this case, the whole numbers would be 2, 5, and 8. So, we have to add those three numbers up (2 + 5 + 8) to get the answer which is 15.
[tex]15 + \frac{1}{4} + \frac{3}{4} + \frac{1}{2} [/tex]
Second, now we have to find the least common denominator (LCD) of the three denominators. The denominators are the bottom number of the fraction. This case the denominators would be 4, 4, and 2.To find the LCD, we will have to list the multiples of each denominator and find the first common one.
Multiples of 4: 4
Multiples of 4: 4
Multiples of 2: 2, 4
Since 4 appears in the multiples of each denominator, 4 is our LCD.
Third, since only one fraction needs their denominator changed (the other two fractions already carry the denominator of 4), we have to multiple each number by whatever gets us 4. Remember, whatever you do to the bottom, do to the top.
[tex]15 + \frac{1}{4} + \frac{3}{4} + \frac{1\times2}{2\times2} = 15 + \frac{1}{4} + \frac{3}{4} + \frac{2}{4} [/tex]
Fourth, since all of our denominators are the same, we can now combine our numerators (join the denominators) and add them all up.
[tex]15 + \frac{1+3+2}{4} = 15 + \frac{6}{4} [/tex]
Fifth, we now need to convert 6/4 into a mixed fraction. To find the mixed fraction form of 6/4, we will need to divide the denominator (4) by the numerator (6) and then write any remainder above the denominator.
Mixed fraction: [tex]15 + 1 \frac{2}{4} = 16 \frac{2}{4} [/tex]
Sixth, we can simplify 2/4 down some more. To do so, we need to find the greatest common factor of the numerator and denominator, then divide the GCF by them. To find the GCF, we list all of the factors of them and find the first common one.
Factors of 2: 1, 2
Factors of 4: 1, 2, 4
The GCF is 4.
Seventh, we can now divide both our numerator and denominator by our recently found GCF which was 2.
[tex]2 \div 2 = 1 \\ 4 \div 2 = 2[/tex]
Answer in fraction form: [tex]\fbox {16 1/2 inches}[/tex]
Answer in decimal form: [tex]\fbox {16.5 inches}[/tex]
