GoalReview fractions: equal parts, fractions of a set, comparing, number lines and fractions equal to one half.
New words
unit fraction · a fraction with 1 on top, such as 1/4fraction of a set · a part of a group, found by sharing the group equallyequivalent · equal in amount even if written differently
Explanation
A fraction names equal parts of a whole. The bottom number tells how many equal parts there are, and the top number tells how many we take. A unit fraction has 1 on top. A bigger bottom number makes smaller parts, so 1/2 > 1/3 > 1/4. To find a fraction of a set, divide into equal groups. For 3/4 of 12 apples, 12 ÷ 4 = 3 in a group, and 3 groups make 3 × 3 = 9. When the bottom numbers are the same, the bigger top number is the greater fraction: 5/8 > 3/8. On a number line from 0 to 1, cut into equal spaces, fractions farther right are greater. The fractions 2/4, 3/6 and 4/8 are all equal to 1/2.
Worked examples
Find 3/4 of 12 apples. There are 4 equal baskets, so each basket has 12 ÷ 4 = 3 apples. Three baskets have 3 × 3 = 9 apples.
Compare 3/8 and 5/8: both bars are cut into eighths, and 5 parts are more than 3 parts, so 5/8 > 3/8.
Which fraction is at point A? The line from 0 to 1 has 6 equal spaces. A is 4 spaces from 0, so A is at 4/6.
Class activity
Fraction strips. Cut paper strips of the same length: one left whole and others cut into halves, thirds, fourths, sixths and eighths. Lay them in a stack and find three pairs of strips that show equal amounts, like 2/4 and 4/8. Then put the unit fractions in order from the greatest to the least.
Practice
1
What fraction of the bar is shaded?
5 of 6 equal parts are shaded, so 5/6.
2
Find 3/4 of 20.
20 ÷ 4 = 5, and 3 × 5 = 15. So 3/4 of 20 is 15.
3
Which fraction is greater, 4/6 or 5/6?
5/6 is greater, because both are sixths and 5 parts are more than 4 parts.
4
Write two fractions that are equal to 1/2.
For example 2/4 and 4/8 (or 3/6). The top number is half of the bottom number.
5
What fraction is shown at point B on the number line?
B is 5 spaces from 0 and each space is 1/8, so B is at 5/8.
