MathIsland · We are all mathematicians.
Fractions
Explain why dividing the same whole into more equal parts makes each part smaller.
Start with the picture
Read both how the whole is divided and how many parts are taken.
Check with another example
1. Which is larger, 1/4 or 1/8 of equally sized bars?
- 1/8
- 1/4
- Equal: both are one part
My reason
2. Which quantity equals 1/2?
- 2/4
- 1/4
- 2/3
My reason
3. For equally long ribbons, which portion is longer: 3/8 or 1/4?
- 1/4
- They are equal
- 3/8
My reason
Explain in your own words
Why is 1/4=2/8? Explain the amount in the picture rather than just multiplying top and bottom by two.
Answers and reasons
1. 1/4
Yes. One quarter contains two eighths.
2. 2/4
Split each half in two: the same half is now two quarters.
3. 3/8
Yes. Since 1/4=2/8, three eighths is longer. The wholes have the same length.
Halving each quarter makes eight equal pieces. The original quarter becomes two pieces without changing its amount.