A second fold changes the labels
Fold a paper strip in half and shade one half. Fold it again so the whole strip has four equal sections. The shaded area now covers two sections.
You can describe that same area as 1/2 or 2/4. These are equivalent fractions: different written fractions with the same value. Folding did not add or remove any shaded paper.
Try it yourself
Draw two identical strips and shade half of each. Leave the first in two equal parts. Divide the second into six equal parts, keeping its shaded area unchanged.
Each original half becomes three smaller pieces. There are six pieces in the whole and three selected pieces: 1/2 = 3/6. Both strips cover exactly the same length.
Smaller pieces, same amount
Draw a strip with three equal pieces and colour two of them. You have coloured 2/3 of the strip.
- Cut each of the three pieces in half.
- The strip now has six equal pieces altogether.
- The coloured part now covers four of those pieces.
The same coloured amount is now called 4/6. That is why 2/3 and 4/6 are equivalent fractions: they name the same share of the same whole.
Both numbers doubled because every piece was split in two. The amount of colour stayed the same.
Join pieces back together
You can also join small pieces together. Draw eight equal pieces and colour six. That shows 6/8.
- Put the eight pieces into pairs. There are four pairs.
- The six coloured pieces make three coloured pairs.
- Three of the four pairs are coloured, so the same amount is 3/4.
Writing a fraction with smaller numbers like this is called simplifying. You have not made the share smaller; you have given it a simpler name.
In the same way, four of eight pieces cover half the strip. So 4/8 and 1/2 name the same amount.