Sharing and Partition up to 99

Sharing, also called partition division, is one of the two main ways to think about division. In a sharing problem, you already know the total amount and the number of equal groups you need to make. Your job is to figure out how many items end up in each group. For example, if you share 18 counters equally among 3 friends, you are asking: "If I split 18 into 3 equal groups, how many does each friend get?" This is written as the division statement \( 18 \div 3 = 6 \).

Sharing problems up to 99 use the same idea as smaller numbers, just with bigger totals and, sometimes, two-digit divisors or two-digit answers. The key skill is dealing out items evenly, one round at a time, until every group has the same amount.

It helps to compare sharing with its partner idea, grouping. In a sharing problem, you know the number of groups and need to find the group size. In a grouping problem, it is the opposite: you know how many go in each group and you need to find the number of groups you can make. Both approaches can lead to the same division statement, but the story behind the numbers is different, so reading the problem carefully matters.

Follow these steps whenever you see a sharing or partition problem:

1. Find the total number of items being shared.
2. Find the number of equal groups (people, boxes, plates, and so on).
3. Share the items one at a time, round by round, across every group.
4. Count how many items landed in one group once the sharing is finished.
5. Write the result as a division statement, such as \( 18 \div 3 = 6 \).

Suppose 18 counters need to be shared equally among 3 friends. Dealing them out one at a time, round after round, each friend ends up with the same amount:

Each friend receives 6 counters, so \( 18 \div 3 = 6 \). Notice this matches the related multiplication fact \( 3 \times 6 = 18 \), which is why sharing and multiplication facts are always closely linked.

Sharing problems up to 99 often involve two-digit totals. Suppose a teacher has 84 stickers to share equally among 7 classes. Instead of drawing 84 dots, it is easier to think in equal bars, each bar representing one class's share:

Each class receives 12 stickers, giving the division statement \( 84 \div 7 = 12 \). Writing this out formally connects to division statements up to 99, where the total, the number of groups, and the group size are always organized the same way.

Not every total shares out perfectly. If you tried to share 20 counters among 3 friends, each friend would get 6, and 2 counters would be left over because \( 3 \times 6 = 18 \), not 20. That leftover amount is called the remainder. Sharing problems that do not divide evenly are covered in more depth in remainders from division up to 99, but it is useful to notice while practicing equal sharing that some totals split perfectly and others leave a remainder behind.

• Draw or imagine the groups first, then deal items out one at a time rather than guessing the answer.
• Check your answer by multiplying the group size by the number of groups to see if you get back the original total.
• For larger two-digit totals, look for friendly facts (such as multiples of 10) to share out in bigger, faster rounds.
• Always read the problem carefully to decide whether you are sharing (finding group size) or grouping (finding number of groups).

Related lessons

• Math 2