First fractions · Usually met around P3
Fractions on a number line
Count the spaces, not the tick marks.
How to do it
Method
Count the spaces, not the tick marks
0 to 1 in 4 equal spaces: 3 along is 34; 2 = 84
Another way
Count from the nearest whole
2 = 84, one space left is 74
In full
Cut the stretch from 0 to 1 on a number line into equal spaces: each space is one part of 1. With 4 spaces each is 14, and 3 spaces to the right of 0 is 34. Count the spaces, not the tick marks: 3 small ticks between 0 and 1 make 4 equal spaces. Past 1, keep counting: the 5th space is 54, which is 1 and 14 more. Whole numbers can be fractions too: 1 = 44, and 2 is two lots of 44, which is 84. Another way: find the nearest whole number first, then count spaces left or right from it: 74 is 1 space left of 2 (= 84).
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
On the number line each whole is cut into 2 equal spaces. The arrow points to □/2.
Show the answer and working
Answer: 3
Each space is 12, and the arrow is 3 spaces from 0: 32. Or count 1 spaces on from 1.
Example 2
On the number line, 179 is to the right of 1.
True or false?
Show the answer and working
Answer: True
1 = 99. A fraction with a top bigger than 9 is right of 1; smaller, left of 1.
Example 3
Start at 0 and jump 14 to the right each time: jump 1 lands on 14, jump 2 on 24, jump 3 on 34… Going on like this, jump 20 lands on □/4.
Show the answer and working
Answer: 20
Each jump adds 1 to the top: after jump 20 the top is 20 × 1 = 20, so 204.
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