### Question Description

Find the average of 3/8, 2/5 and 2 3/4 and write the solution as a mixed number

## Explanation & Answer

3/8, 2/5, 2 3/4

The third number 2 3/4 is a mixed number, let us go ahead and convert it into a fraction.

2 3/4 = (2*4 + 3)/4 <Multiply the whole number by the bottom number and add by the top number>

= (8 + 3)/4 <Evaluate inside the parenthesis with order of operations>

= 11/4

So now we can replace the mixed number with its improper fraction

3/8, 2/5, 2 3/4

3/8, 2/5, 11/4 <2 3/4 is replaced with 11/4>

Then to find the average, we would find the total sum of all of your fractions and divide the sum by the count of the number of fractions. After these steps, check if the fraction can be reduced. And if the result is still an improper fraction, we would convert it back to a mixed fraction.

*ADD FRACTIONS FIRST:*

* 3/8 + 2/5 + 11/4 <When adding fractions, we must find the common denominator>*

*Common denominator is 40*

* (3/8)*(5/5) + (2/5)*(8/8) + (11/4)*(10/10) <Apply common denominator>*

*15/40 + 16/40 + 110/40*

* (15 + 16 + 110)/40 <With the denominators all the same, we can add all numerators>*

141/40

*THEN DIVIDE BY THE COUNT FOR THE NUMBER OF FRACTIONS*

* (141/40) / 3 <We were given a count of three fractions, meaning we divide by 3>*

(141/40) * (1/3) <Division is the same as multiplying by the divisor's reciprocal>

141/120 <Multiply in both the numerator and denominator>

CHECK IF THE FRACTION CAN BE REDUCED

141/120

Common factor of 141 and 120 is 3, meaning we divide the numerator and denominator by 3

(141/3)/(120/3) <Top and bottom numbers are divided by their common factor.>

47/40

IS THE RESULT AN IMPROPER FRACTION? IF YES, THEN CONVERT BACK TO A MIXED FRACTION

Is 47/40 an improper fraction? YES

47/40 <40 goes into 47, one time. Meaning the quotient is 1, with a remainder of:

47 - (1*40) = 7 >

1 7/40

**SOLUTION: 1 7/40**