Lesson 13: Fraction Games

Property

To create the largest possible quotient from a set of numbers for the expression $W \div \frac{1}{d}$:

• Use the largest available number for the whole number dividend ($W$).
• Use the next largest available number for the denominator of the unit fraction divisor ($d$).

To create the smallest possible quotient:

• Use the smallest available number for the whole number dividend ($W$).
• Use the next smallest available number for the denominator of the unit fraction divisor ($d$).

Examples

Given the numbers 3, 4, and 5 to fill in the blanks for $W \div \frac{1}{d}$:

• To make the largest quotient: Use the largest number (5) for $W$ and the next largest (4) for $d$.

• To make the smallest quotient: Use the smallest number (3) for $W$ and the next smallest (4) for $d$.

Explanation

This skill challenges you to use your understanding of division to create expressions with the greatest or least possible value. To get the largest result when dividing a whole number by a unit fraction, you need to start with the largest whole number and divide it into the smallest possible fractional pieces. Smaller fractional pieces have larger denominators. To get the smallest result, you should start with the smallest whole number and divide it into the largest possible fractional pieces (which have smaller denominators).