Start by counting the pieces
Cut a paper strip into eight equal pieces. Colour two pieces blue and another three yellow. How many pieces have you coloured altogether?
Count them: two blue pieces and three yellow pieces make five pieces.
Each piece is one eighth of the strip. We can write the story as 2/8 + 3/8 = 5/8.
The bottom number stays 8 because the whole strip still has eight equal pieces. We have counted more pieces; we have not changed their size.
Try it yourself
Draw two identical strips and split each into four equal pieces. Each piece is called a quarter.
- Colour three quarters of the first strip.
- Colour two quarters of the second strip.
- Count all the coloured quarters. There are five.
Four quarters fill one whole strip. The fifth quarter is left over. So 5/4 means one whole and one quarter, also written 1 1/4.
A fraction can be bigger than one whole. Keep using the same size of piece as you count.
Make the pieces the same size
What about 1/2 + 1/4? A half and a quarter are different-sized pieces of the same whole. We need matching pieces before we count them together.
- Draw a strip and colour half of it.
- Split the whole strip into four equal pieces. Your coloured half now covers two quarters.
- Colour one more quarter. Three of the four pieces are now coloured.
That gives us 1/2 + 1/4 = 3/4.
The same idea works with thirds and sixths. Split each third into two equal pieces: one third becomes two sixths. Add one more sixth and you have three sixths, which cover half the strip.
Does your answer fit the picture?
Go back to the picture when an answer looks strange. Adding another piece should give you more than you started with.
For example, half a strip plus a quarter must cover more than half a strip. An answer of one third would be too small.
Check three things: are you using the same-sized whole, are the pieces equal, and have you counted the pieces correctly?