Fractions on a Number Line

Use three steps. First, use the denominator to divide the space from 0 to 1 into equal parts. Second, mark each equal part with a tick. Third, count from 0 using the numerator. For 3/4, divide 0 to 1 into 4 equal parts, then count 3 marks from 0. The point you land on is 3/4.

The denominator tells you how many equal parts to divide the space between 0 and 1. A denominator of 4 means 4 equal parts. A denominator of 8 means 8 equal parts, so each part is smaller and the tick marks are closer together.

An improper fraction is greater than or equal to 1, so the number line must extend past 1. For example, 7/4 equals 1 3/4, so it sits between 1 and 2. Divide each whole into fourths, then count 7 fourths from 0.

Fractions farther to the right on a number line are larger. For example, 1/3 is left of 1/2, so 1/3 is less than 1/2. Plotting both fractions on the same line makes the comparison visible.

The fraction exactly in the middle of 0 and 1 is 1/2. The midpoint splits the distance into two equal parts. The midpoint between 0 and 1/2 is 1/4, because it is half of one half.

Equivalent fractions land on the same point. For example, 1/2, 2/4, and 3/6 all mark the exact same location halfway between 0 and 1. The labels look different, but the value is the same.