Halving Odd Numbers

Halving Odd Numbers
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Halving Odd Numbers example Summary

  • Odd numbers are not in the two times table and will not make a whole number when we halve them.
  • We separate our odd number into the previous even number, plus one.
  • 5 = 4 + 1
  • We halve the even number, 4, to make 2.
  • We halve the remaining one, to make   1 / 2.
  • Half of 5 is 2 and a half.
To halve an odd number: subtract one, halve it and then add a half.

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Halving Odd Numbers Example

  • 7 is an odd number, which we will halve.
  • First we subtract 1 to get an even number.
  • 7 – 1 = 6.
  • We then find half of 6, which is 3.
  • We add one half to 3 to get our answer.
  • 3 +   1 / 2 = 3   1 / 2.
  • Half of 7 is 3 and a half.

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Halving Odd Numbers Interactive Question Generator

Halving Odd Numbers Worksheet and Answers

Halving Odd Numbers

Odd numbers cannot be halved to give a whole number. We will look at methods we can use for teaching halving odd numbers.

In our first example of halving odd numbers, we are asked to halve the number five. We’ll start by looking at the method of division by sharing. We can represent the number five with five counters. We want to halve it, which means that we want to share it equally across two groups.

We can easily halve four of the counters by placing two in each group, since 4 is even. However, there is one counter remaining in the middle. If we put this whole counter in either of the groups, we would not have shared five equally.

The only way that we can share this last counter equally is to split it in half.

Each half can then be placed in each group. Each group contains 2    1 / 2   counters.

Therefore, half of 5 is 2  1 / 2  .

teaching halving odd numbers with counters, halve of 5 is 2 and a half

When first introducing halving odd numbers and teaching halving to your child, you could show this easily with plasticine or food, tearing the last item in half.

Starting again with our five counters, we can develop a method to work out halving an odd number mentally.

sharing five counters into two equal parts

We found that it was easy to halve the counters when the number was even.

We were able to halve four of the counters easily. So, we can begin by subtracting 1 from our odd number.

Subtracting one from every odd number will always give us an even number.

  • Step 1: Subtract 1

the first step of our method for halving the odd number, 5

5 – 1 = 4

Now that we have an even number, we can easily halve it.

  • Step 2: Halve it

dividing the even number 4 equally into two parts to halve it

4 ÷ 2 = 2

We have easily divided the four counters into two groups.

Now, we must remember that one counter that we previously subtracted.

  • Step 3: Add  1 / 2

example of halving odd numbers, half of 5 is two and a half

The ‘1’ that we originally subtracted must also be halved. Half of 1 is    1 / 2.

So, we must add this on to the 2.

2 +  1 / 2 = 2  1 / 2

Half of 5 is 2  1 / 2.

Another way of thinking of this is that we were able to partition the 5 into 4 + 1.

Half of 4 is 2

Half of 1 is    1 / 2

2 +  1 / 2 = 2 1 / 2

Now we’ll look at another example of halving odd numbers where we will use our three steps.

We are asked to find half of 7.

We can work out this example of halving an odd number by partitioning 7 into 6 + 1.

We do this in the following three steps.

halving the odd number 7 by partitioning

  • Step 1: Subtract 1

7 – 1 = 6

We subtracted 1 to give us an even number to halve.

  • Step 2: Halve it

6 ÷ 2 = 3

  • Step 3: Add    1 / 2

3 +    1 / 2 = 3   1 / 2

We add  1 / 2   because this is half of the ‘1’ that we originally subtracted.

We worked this out by partitioning the 7 into 6 + 1. This partitioning method is the easiest to do mentally when teaching your child to halve odd numbers.

First, we halved the 6.

Half of 6 is 3

Next, we halved the 1.

Half of 1 is    1 / 2

Finally, we added these together.

3 +  1 / 21 / 2