Depth 1 · 32 s
Same amount
Cut every half of a bar in two and a half becomes two quarters, then four eighths - the same amount. Multiply top and bottom by the same number, and with the same top, a bigger bottom means smaller parts.
About this video
Different fractions can be exactly the same amount. This short animation shades half of a bar, then cuts every part in two. Now the bar has four parts and two of them are shaded: 2/4. Cut again and it's 4/8. The shaded amount never changed, so 1/2 = 2/4 = 4/8. Fractions like these are called equivalent fractions: different names for the same amount.
Stacking the three bars shows it plainly, and it also shows the rule behind it. Cutting every part in two doubles the number of parts and doubles the number shaded, so multiplying the top and the bottom of a fraction by the same number gives an equivalent fraction: 1/2 with both numbers times 2 is 2/4. Last, the video compares 1/2 with 1/3. They have the same top number, but the bottom of 1/3 is bigger, which means the whole is cut into more parts, so each part is smaller. That's why 1/3 is less than 1/2, even though 3 is more than 2. This video goes with the Same Amount, Different Names lesson of Numbers Level 1 on Knaph.
This video shows depth 1 of Equivalent fractions.
Learn Equivalent fractionsTranscript
- 0:00Half a bar, or two quarters?
- 0:04Cut every part in two. Two quarters, then four eighths. The amount stays the same.
- 0:10Same amount, different names.
- 0:17Multiply the top and the bottom by the same number.
- 0:22Same top number? A bigger bottom means smaller parts.
- 0:28Different fractions, same amount.