Question

Higher Order Thinking 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

1) Gathering the data

2) Since we don't know exactly their numerators we can write, for instance, two fractions with the same bottom number and lesser than 1:

`\begin{gathered} (1)/(4),\text{ }(3)/(4) \\ (1)/(4)+(3)/(4)=(4)/(4)=1 \\ (2)/(4)+(3)/(4)=(5)/(4)=1.25 \\ (1)/(5)+(3)/(5)=(4)/(5)=0.8 \end{gathered}`

2) Hence, we can conclude that the sum can be equal to 1, greater than 1, and lesser than 1. That'll depend on the numerator, and the fractions Leah can pick.

3) So, they can be less, equal to, and greater than 1.