Improper fractions, mixed numbers and like fractions · Usually met around P4
Fractions bigger than 1: improper fractions and mixed numbers
As many parts as the bottom number make one whole.
How to do it
Method
As many parts as the bottom number make one whole
74: 4 quarters make 1, 3 left → 1 34
Another way
Count on a number line
44 = 1, 84 = 2: 44 < 74 < 84
In full
A fraction can be bigger than 1. Cut a pizza into 4 equal slices and 4 slices are one whole pizza: 44 = 1, and 84 = 2. With 7 slices you have 74. A fraction whose top is bigger than (or equal to) its bottom is an improper fraction, and it is not less than 1. Of the 7 slices, 4 make one whole and 3 are left, so 74 = 1 34, “one and three quarters”: a mixed number. Its whole-number part is how many wholes the slices make; its fraction part is what is left. Or count squares: 2 full rectangles and 34 of another are 4 + 4 + 3 = 11 quarters, 114, that is 2 34. Or count along a number line: 1 = 44 and 2 = 84, so 74 is between 1 and 2.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Each rectangle is one whole, cut into 3 equal parts. The shaded part is □/3, or as a mixed number □ □/3.
Fill in each box
Show the answer and working
Answer: 5，1，2
3 + 2 = 5 parts are shaded, 53; 3 of them make one whole rectangle and 2 are left: 1 23.
Example 2
108 is bigger than 1.
True or false?
Show the answer and working
Answer: True
1 = 88. A top bigger than the bottom means more than 1; a smaller top means less than 1.
Example 3
Each rectangle is 1, cut into 6 equal parts. The shaded part is □ □/6, that is □/6.
Fill in each box
Show the answer and working
Answer: 2，4，16
Two rectangles are full and the third has 4 parts: 2 46; altogether 6 + 6 + 4 = 16 parts, 166.
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