Division as sharing
Theory
Division as sharing is a Year 3 maths skill: splitting a total into equal groups to find how many are in each group. This page explains what \(14 \div 2 = 7\) means, how to share step by step, how division and multiplication form a fact family, and what happens when there are leftovers. Curriculum: VC2M3N05 / AC9M3N04.
Division as sharing means splitting a total into a set number of equal groups to find how many are in each group. When you share equally, every group gets the same amount.
The sharing symbol is \(\div\). The sentence \(14 \div 2 = 7\) means \(14\) shared into \(2\) equal groups is \(7\) in each group. The total is what you start with, the number of groups is how many you share into, and the answer is how many are in each group.
Sharing is joined to multiplication. Because \(2 \times 7 = 14\), you know \(14 \div 2 = 7\). This is called a fact family. Sometimes a total will not share evenly and a few are left over.
Division as sharing has no formula, but these facts help you share and check.
How to share a total into equal groups
- Read the numbers. Find the total to share and the number of groups to share it into.
- Deal one to each group. Give one to every group, then go around again, and keep going until none are left.
- Count one group. Count how many are in a single group. That is the answer. Check it with a multiplication fact.
If some are left and there are not enough to give one more to every group, stop. Those are left over (the remainder).
| \(16 \div 4\) | \(=\) | \(4\) |
| \(\text{check: } 4 \times 4\) | \(=\) | \(16\) |
There are \(4\) strawberries in each bowl.
| \(21 \div 3\) | \(=\) | \(7\) |
| \(\text{check: } 3 \times 7\) | \(=\) | \(21\) |
Each table gets \(7\) textas.
| \(4 \times 3\) | \(=\) | \(12\) |
| \(14 - 12\) | \(=\) | \(2\) |
Each child gets \(3\), with \(2\) left over.
| \(24 \div 2\) | \(=\) | \(12\) |
| \(24 \div 3\) | \(=\) | \(8\) |
Shared among more friends means fewer each: \(12\) then \(8\).
Common pitfalls
Frequently asked questions
What is division as sharing?
Division as sharing means splitting a total into a set number of equal groups to find how many are in each group. For example, \(14\) shared into \(2\) equal groups is \(7\) in each group.
How do you share a number into equal groups?
Deal one to each group at a time, like dealing cards, until none are left. Then count how many are in one group. That is how many each group gets.
What does 14 divided by 2 mean?
It means \(14\) shared equally into \(2\) groups. Each group gets \(7\), so \(14 \div 2 = 7\). The \(2\) is the number of groups and the \(7\) is how many are in each group.
How is division related to multiplication?
They are a fact family. Because \(2 \times 7 = 14\), you know \(14 \div 2 = 7\). You can use a multiplication fact you already know to check a sharing answer.
What happens when a number cannot be shared equally?
Some are left over. When \(14\) is shared among \(4\) children, each gets \(3\) and \(2\) are left over, because \(4 \times 3 = 12\) and \(14 - 12 = 2\). The leftover is called the remainder. If fewer are left than there are groups, they cannot go round again, so they stay left over.
Does sharing among more groups give more or less each?
Fewer each. The same total shared among more groups means each group gets less. \(24\) shared among \(2\) is \(12\) each, but \(24\) shared among \(3\) is only \(8\) each.