The bottom number says how many pieces, the top says how many you took
Two numbers, two jobs
A fraction is written as two numbers, one above a line and one below it, like . Each number counts something different. Take a bar cut into 5 equal pieces and color 3 of them: of the bar is colored.
The bottom number is how many equal pieces the whole was cut into, here 5. The top number is how many of those pieces you are talking about, here the 3 you colored. The top number is called the numerator, and the bottom number is called the denominator.
Every piece gets counted for the denominator, so the bottom number is 5. Only the 3 colored pieces count for the numerator.
The bottom counts every piece
Two slips both come from the bottom number. One is writing the fraction upside down, as ; the count of all the pieces always goes at the bottom. The other is counting only the pieces that are not colored and writing . The bottom counts every piece in the whole, colored or not, so it stays 5.
The same two numbers say what is left. 3 of the 5 pieces are colored, so 5 − 3 = 2 are not, and of the bar is plain. The 3 colored fifths and the 2 plain fifths make , the whole bar.
Make one half
Shade more or fewer pieces and the top number changes; cut the bar into more or fewer pieces and the bottom number changes. With 5 pieces no number of shaded pieces is exactly half, so a half needs a different bottom number: , or .
Halves and quarters · A Pizza in Four Equal Slices with One Slice Eaten
QuestionA pizza is cut into 4 equal slices. Sam eats 1 slice. (a) What fraction of the pizza does Sam eat? (b) What fraction of the pizza is left?
1.Draw the pizza as a circle cut into 4 equal slices. Each slice is 14 of the pizza.
The pizza has 4 equal slices. Each slice is 14 of the pizza. 2.(a) Sam eats 1 of the 4 equal slices. He eats 14 of the pizza.
(a) Sam eats 1 of the 4 equal slices. He eats 14 of the pizza. 3.Count the slices that are left: 4 − 1 = 3 slices.
Count the slices that are left: 1, 2, 3. 4.(b) 3 of the 4 equal slices are left, so 34 of the pizza is left. Check: 1 + 3 = 4 slices, which is the whole pizza.
(b) 3 of the 4 equal slices are left, so 34 of the pizza is left.
Answer: (a) 14; (b) 34
Watch out for
- Writing 13 for part (a) because 1 slice is eaten and 3 slices are left. The bottom number counts all the equal slices in the whole pizza, and there are 4 of them.
- Writing 3 for part (b). The 3 is the number of slices left. The question asks for a fraction, so say 3 out of 4 equal slices, which is 34.
Halves and quarters · A Window with Three of Its Four Panes Painted
QuestionA window has 4 equal panes of glass. Dad paints 3 of the panes yellow. (a) What fraction of the window is yellow? (b) How many panes are not yellow?
1.Draw the window with 4 equal panes. Color 3 panes yellow.
The window has 4 equal panes. 3 panes are painted yellow. 2.Count all the equal panes. There are 4. This is the bottom number of the fraction.
Count all the equal panes: 1, 2, 3, 4. The bottom number is 4. 3.Count the yellow panes. There are 3. This is the top number of the fraction.
Count the yellow panes: 1, 2, 3. The top number is 3. 4.(a) 3 of the 4 equal panes are yellow, so 34 of the window is yellow.
(a) 3 of the 4 equal panes are yellow, so 34 of the window is yellow. 5.(b) Count the panes that are not yellow: 4 − 3 = 1. One pane is not yellow, and it is 14 of the window.
(b) 4 − 3 = 1. One pane is not yellow. It is 14 of the window.
Answer: (a) 34; (b) 1 pane
Watch out for
- Writing 43 with the two numbers the wrong way round. The number of all the equal panes, 4, goes at the bottom. The number of yellow panes, 3, goes on top.
- Writing 31 by putting the yellow panes over the panes that are not yellow. The bottom number counts all the panes in the window, yellow or not, so it is 4.
Your turn
1.What fraction is shaded?