# Fractions and Mixed Numbers: Average of 1 1/2, 1/3, 2 1/3, 3 1/4, 5, 5 2/3 and 6 5/7

## Workout for Average of 1 1/2, 1/3, 2 1/3, 3 1/4, 5, 5 2/3 & 6 5/7

**Example Problem**

Find the sum between 1 1/2, 1/3, 2 1/3, 3 1/4, 5, 5 2/3 and 6 5/7.

**Step by step workout**

step 1 Input values:

11/2, 1/3, 21/3, 31/4, 5, 52/3, 65/7

Total count = 7

step 2 Convert the mixed numbers to corresponding fractions form , if any.

Fraction form = (whole number x denominator) + numerator/denominator

11/2 = (( 1 x 2 ) + 1)/2=3/2

21/3 = (( 2 x 3 ) + 1)/3=7/3

31/4 = (( 3 x 4 ) + 1)/4=13/4

52/3 = (( 5 x 3 ) + 2)/3=17/3

65/7 = (( 6 x 7 ) + 5)/7=47/7

step 3 Convert the whole numbers to corresponding fractions form, if any.

, 5 = 5/1

step 4 Arrange all the numbers as fractions.

3/2+1/3+7/3+13/4+5/1+17/3+47/7

step 5 Compare all denominators of the fractions, if they are not same, find the LCM (least common multiple) for all denominators. 84 is the LCM for 2 , 3 , 3 , 4 , 1 , 3 , 7 .

step 6 Multiply LCM 84 with each numerators and denominators

= (3 x 84)/(2 x 84)+(1 x 84)/(3 x 84)+(7 x 84)/(3 x 84)+(13 x 84)/(4 x 84)+(5 x 84)/(1 x 84)+(17 x 84)/(3 x 84)+(47 x 84)/(7 x 84)

step 7 Simply the above expression to have same denominators for all fractions.

=(3 x 42)/84+(1 x 28)/84+(7 x 28)/84+(13 x 21)/84+(5 x 84)/84+(17 x 28)/84+(47 x 12)/84

=126/84+28/84+196/84+273/84+420/84+476/84+564/84

=126 + 28 + 196 + 273 + 420 + 476 + 564/84

step 8 Add all numerators and rewrite it in a single form.

=2083/84

step 9 Divide the sum by total count of fractions.

= 2083/84รท 7

= 2083/84x1/7

=2083/588

__Fraction Form:__

11/2+1/3+21/3+31/4+5+52/3+65/7= 2083/588

__Decimal Form:__

11/2+1/3+21/3+31/4+5+52/3+65/7= 3.54

2083/588 is the average of fractions and whole numbers 1 1/2, 1/3, 2 1/3, 3 1/4, 5, 5 2/3 and 6 5/7.