Chris, Fergus and Graeme play a game. Chris and Fergus each choose a decimal and Graeme tries to find the decimal that is half-way between Chris’ and Fergus’ decimals on the number line.
If Chris chooses 0.12 and Fergus chooses 0.012, what decimal should Graeme choose?
Solution
Graeme should choose 0.066.
Here is how you can check the answer.
0.12 – 0.066 = 0.054.
0.066 – 0.012 = 0.054.
So then 0.12 and 0.012 are both 0.054 away from 0.066. That means that 0.066 is half-way between 0.12 and 0.012.
But is there a rule for finding halves? You might know that to find the half-way point of two whole numbers you add then and divide by 2. So to find half-way between 5 and 11 we work out (5 + 11)/2 = 16/2 = 8.
The same thing happens for 5 and 10. (5 + 10)/2 = 15/2 = 7½, and 7½ is half-way between 5 and 10.
The same thing works for decimals. How do we get the half-way point of 0.12 and 0.012? Just add them and divide by 2. So we get (0.12 + 0.012)/2 = (0.132)/2 = 0.066, as Graeme had already discovered.
Extension
What decimal lies half-way between 0.34 and 0.244?
You might also like to play this game with two friends.