Fractions on the Number Line
A number line shows fractions not just as shapes, but as exact physical lengths and locations measured from 0.
Prerequisites: What You Need First
You should know these two topics well before placing fractions on the number line:
Locating 73 → 7 pieces of 13
Draw whole rectangles divided into 3 equal pieces (13 each):
3 + 3 + 1 = 7 pieces of 13 → 73 = 213 (2 wholes + 1 piece)
Between 2 and 3: It has passed 2 wholes, and advanced 1 piece towards 3.
Since 73 contains 2 full wholes (63 = 2), we first advance from 0 straight to 2.
Divide the space between 2 and 3 into 3 equal pieces (13 each) and advance 1 piece forward.
Example: 25 → 2 pieces of 15
Draw 1 whole bar divided into 5 equal parts, and shade 2 parts:
• It couldn't reach 1 whole yet, so it is strictly between 0 and 1.
• If we divide the space between 0 and 1 into 5 equal parts, we get pieces of 15.
Example: 64 → 6 pieces of 14
Draw 2 wholes divided into 4 equal pieces each (4 pieces in Whole 1 + 2 pieces in Whole 2):
4 + 2 = 6 pieces of 14 → 64 = 124 (1 whole + 2 pieces)
Between 1 and 2: It has passed 1 whole, and advanced 2 pieces towards 2.
Since 64 contains 1 full whole (44 = 1), we first advance from 0 straight to 1.
Divide the space between 1 and 2 into 4 equal pieces (14 each) and advance 2 pieces forward.
Example: 345 — "This is Much Easier!"
Why is 345 much easier? Because the whole number is already given:
3 wholes + 4 pieces of 15
We jump straight to 3 wholes, divide the space between 3 and 4 into 5 equal parts, and advance 4 pieces forward.
Since the whole number 3 is already given in 345, we first advance from 0 straight to 3.
Divide the space between 3 and 4 into 5 equal pieces (15 each) and advance 4 pieces forward.
🎯 Teacher's Key Observation: "A value very close to 4!" Notice that 345 lands right next to 4, because 45 is only 15 away from the next complete whole.