Fractions on a Number Line

For Elementary Students

Whole Numbers on a Number Line

You already know how to show whole numbers on a number line:

0 ─── 1 ─── 2 ─── 3 ─── 4 ─── 5

But what about numbers between 0 and 1? That's where fractions come in!

Fractions Fill the Gaps

Fractions are numbers that go between whole numbers.

Think about it like this: If whole numbers are the big marks on a ruler, fractions are all the little marks in between!

Halves on a Number Line (1/2)

To show halves, divide each space into 2 equal parts.

0 ───────── 1/2 ───────── 1

1/2 is exactly halfway between 0 and 1.

Fourths on a Number Line (1/4, 2/4, 3/4)

To show fourths (quarters), divide the space from 0 to 1 into 4 equal parts.

0 ─── 1/4 ─── 2/4 ─── 3/4 ─── 1
            (1/2)

Notice: 2/4 is the same spot as 1/2! (They're equivalent fractions.)

Thirds on a Number Line (1/3, 2/3)

To show thirds, divide from 0 to 1 into 3 equal parts.

0 ──── 1/3 ──── 2/3 ──── 1

Each piece is one third of the way from 0 to 1.

Placing a Fraction

Example: Show 3/4 on a number line.

Step 1: Draw a line from 0 to 1

Step 2: Divide it into 4 equal parts (because the denominator is 4)

Step 3: Count 3 parts from 0 (because the numerator is 3)

      start  count 3
        ↓     → → →
0 ─── 1/4 ─── 2/4 ─── 3/4 ─── 1
                       ↑
                     here!

Answer: 3/4 is at the third mark.

For Junior High Students

Fractions Beyond 1

Fractions can be greater than 1 — they go past the whole number 1!

Example: Show 5/4 on a number line.

0 ─── 1/4 ─── 2/4 ─── 3/4 ─── 1 ─── 5/4 ─── 6/4 ─── 7/4 ─── 2
            (1/2)         (4/4)  (1¼)  (1½)  (1¾)  (8/4)

5/4 is the same as 1¼ (one and one fourth).

Mixed Numbers on a Number Line

Mixed numbers like 1½ can be shown too.

Example: Place 2⅓ on a number line.

0 ─── 1 ─── 2 ─── 2⅓ ─── 2⅔ ─── 3
                   ↑
                 here

2⅓ is just past 2, one-third of the way to 3.

Comparing Fractions Using a Number Line

A number line makes it easy to see which fraction is larger.

Example: Which is bigger: 2/5 or 3/5?

0 ─── 1/5 ─── 2/5 ─── 3/5 ─── 4/5 ─── 1
               ↓       ↓
             smaller  larger

3/5 is farther right, so 3/5 > 2/5.

Example: Which is bigger: 1/3 or 1/4?

0 ──── 1/4 ──── 1/3 ──── 1/2 ──── 1
        ↓        ↓
      smaller  larger

1/3 is farther right, so 1/3 > 1/4.

Why? When you cut something into fewer pieces (3 instead of 4), each piece is bigger!

Equivalent Fractions on a Number Line

Equivalent fractions land on the same point.

Example: 1/2, 2/4, and 3/6 are all equivalent.

Number line for halves:
0 ─────────── 1/2 ─────────── 1

Number line for fourths:
0 ─── 1/4 ─── 2/4 ─── 3/4 ─── 1
               ↑
          same spot!

Number line for sixths:
0 ── 1/6 ── 2/6 ── 3/6 ── 4/6 ── 5/6 ── 1
                    ↑
               same spot!

All three fractions are at the same location: halfway between 0 and 1.

Distance on a Number Line

The distance from one fraction to another can be found by subtracting.

Example: What's the distance from 1/4 to 3/4?

0 ─── 1/4 ─── 2/4 ─── 3/4 ─── 1
       ↓               ↓
     start            end
       ←─────────→
         2/4 = 1/2

Distance: 3/4 - 1/4 = 2/4 = 1/2

Benchmark Fractions

Some fractions are useful as benchmarks (reference points):

You can estimate other fractions by comparing to these!

Example: "Is 5/8 closer to 1/2 or 1?"

0 ──── 1/4 ──── 1/2 ──── 5/8 ──── 3/4 ──── 1
                         ↑

5/8 is between 1/2 and 3/4, closer to 1/2.

Fractions with Different Denominators

To show fractions with different denominators on one number line, find a common division.

Example: Show 1/2, 1/3, and 1/6 together.

Use sixths (since 6 is divisible by 2 and 3):

0 ── 1/6 ── 2/6 ── 3/6 ── 4/6 ── 5/6 ── 1
             ↑      ↑
            1/3    1/2

• 1/6 = 1/6
• 1/3 = 2/6
• 1/2 = 3/6

Real-Life Number Lines

• Measuring cups (1/4 cup, 1/2 cup, 3/4 cup markings)
• Rulers (fractions of an inch: 1/2", 1/4", 1/8")
• Timelines (showing parts of an hour, day, year)

Practice