Question

Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1. Can their sum equal 1? Can their sum be greater than 1? Explain.

Answer 1

Yes, the sum can be equal to 1.

Yes, the sum can be greater than 1.

Explanation:

Given:

Two different fractions with same denominator. The two fractions are less than 1.

Case 1:

Sum equal to 1:

When two different fractions with same denominator are added, then we add their numerators and divide the sum by their common denominator.

Now, for the sum to be equal to 1, the sum of the numerators should be equal to that of the common denominator.

Example:

Consider two fractions
`(1)/(3)\ and\ (2)/(3)`. Now, addition of these fractions is given as:

`(1)/(3)+(2)/(3)=(1+2)/(3)=(3)/(3)=1`

Thus, addition of two different fractions with same denominator can be equal to 1.

Case 2:

Sum greater than 1:

When two different fractions with same denominator are added, then we add their numerators and divide the sum by their common denominator.

Now, for the sum to be greater than 1, the sum of the numerators should be greater than that of the common denominator.

Example:

Consider two fractions
`(8)/(10)\ and\ (9)/(10)`. Now, addition of these fractions is given as:

`(8)/(10)+(9)/(10)=(8+9)/(10)=(17)/(10)=1.7>1`

Thus, addition of two different fractions with same denominator can be equal be greater than 1.