Section C: Summary Fraction and Decimal Operations

Section Summary

We played games with fractions and decimals, trying to make the largest or smallest number with given digits. Let’s use the numbers 1, 3, 5, and 6. What is the smallest sum of two fractions we can make with these numbers? We want to use the smaller numbers, 1 and 3, for the numerators and the larger numbers, 5 and 6, for the denominators. This gives two possibilities, $\frac{1}{6} + \frac{3}{5}$ and $\frac{1}{5} + \frac{3}{6}$ . The expression $\frac{1}{5} + \frac{3}{6}$ has the smaller value which makes sense since we want the larger numerator, which means more equal pieces, to go with the larger denominator which makes those pieces smaller.

The smallest difference we can make with these numbers is $\frac{3}{6} - \frac{1}{5}$ which is a little smaller than $\frac{3}{5} - \frac{1}{6}$ . Finally, the largest product we can make is $\frac{6}{3} \times \frac{5}{1}$ or $\frac{5}{1} \times \frac{6}{3}$ which both have the value $\frac{30}{3}$ or 10.