1 A student incorrectly tried to add the fractions 15 and 23

1. A student incorrectly tried to add the fractions 1/5 and 2/3 by adding the numerators and the denominators. The procedure was shown as: (1/5)+(2/3)=(1+2)/(5+3)=(3/8). Write the fractions (1/5), (2/3), and (3/8) in order from smallest to largest.

Now take any two other fractions, add the numerators and the denominators, and then write the fractions in order from smallest to largest. Do you see a pattern? If so, explain it.

If not, try a few more examples until you find a pattern. Discuss with your classmates.

Solution

1. Write the fractions (1/5), (2/3), and (3/8) in order from smallest to largest.

To check for the smallest an biggest fraction multiply the denominator by a commona number so that all denominators become sam: 5*3*8 = 120

So, 1/5 = 24/120   ; 2/3 = 80/120 ; 3/8 = 45/120

Out of the three frcations we can arrange them in oredr of thier numerator:

24/120 , 45/120 , 80/120 -----> 1/5 , 3/8 , 2/3

take any two other fractions, add the numerators and the denominators, and then write the fractions in order from smallest to largest:

1/4 , 2/5 ---> add = (1+2)/(4+5) = 3/9 = 1/3

Make the denomiator same: 15/60 , 24/60 , 20/60

Smalltes to largest : 15/60 , 20/60 , 24/60 ---> 1/4 , 1/3 , 2/5

So, we find the 1st fraction , then the added result and then the 2nd fraction appear in the order

This pattern is being followed for both above cases