Groups, Sharing and Halves
Primary 2 · Mathematics
Groups, Sharing and Halves
Lesson 2 of 3
12 min
Let's begin
It is break time. Keza has 12 sweets in her pocket and 3 friends waiting beside her.
She wants to share the sweets so that nobody feels cheated. Everyone must get the same number. How can Keza be sure she is being fair?
Keza does not guess. She goes round and round, giving one sweet to each friend each time.
Round 1: one sweet each. She has given away 3. She has 9 left.
Round 2: one sweet each. She has given away 6. She has 6 left.
Round 3: one sweet each. She has given away 9. She has 3 left.
Round 4: one sweet each. She has given away 12. She has 0 left.
Now count what one friend is holding. Each friend went round 4 times, so each friend has 4 sweets.
That is fair sharing. Everybody got 4.
The sign ÷ means shared into equal groups. We read it as divided by.
What Keza did looks like this:
12 ÷ 3 = 4
Read it out loud: twelve divided by three equals four. It means 12 sweets shared into 3 equal groups gives 4 in each group.
The first number is what you started with. The second number is how many groups you shared it into. The answer is how many each group gets.
Mugisha has 10 bananas. He shares them equally between 2 baskets.
One for this basket, one for that basket... round and round until the bananas are finished. Each basket ends up with 5 bananas.
10 ÷ 2 = 5
Now Mutesi has 20 Frw. She shares it equally among her 5 little cousins.
Give 1 Frw to each cousin, again and again. After 4 rounds the money is gone. Each cousin holds 4 Frw.
20 ÷ 5 = 4
Notice something: when you share into more groups, each group gets less. Share 20 Frw among 5 cousins and each gets 4 Frw. Share the same 20 Frw among only 2 cousins and each gets 10 Frw. More friends, smaller pieces!
You never have to wonder if you were right. Just put the groups back together.
Keza said 12 ÷ 3 = 4. Is that true? She has 3 friends, holding 4 sweets each. Count them all up:
4 + 4 + 4 = 12. Yes! She started with 12, so her answer was correct.
And you already know a quicker way to add equal groups. It is times!
3 × 4 = 12. Correct again.
Sharing and times are opposite jobs, like putting on your shoes and taking them off.
Always check. It takes five seconds and it saves you from a wrong answer.
Sometimes things do not share out evenly.
Habimana has 13 sweets and 3 friends. He goes round and round. Each friend gets 4 sweets... and there is 1 sweet left in his hand.
He cannot give it to one friend, because then that friend would have more than the others. That would not be fair.
The piece left over has a name: the remainder. You will do much more with remainders in P3. For now, just know this: if you share fairly and something is still in your hand, you have not made a mistake.
Tip
Deal it out like cards. Never try to guess the answer to a sharing question. Put out one thing for each group, then go round again, and again, until your hand is empty. Then count what just one group has. That number is your answer.
Use stones or bottle tops if you like. Deal them out, then tap Show answer to check.
10 ÷ 5 = ?
Answer: 2. Ten stones shared into 5 groups gives 2 in each group. Check: 5 × 2 = 10. Correct!
Share 15 sweets equally among 3 friends. How many does each friend get?
Answer: 5 sweets. 15 ÷ 3 = 5. Check: 3 × 5 = 15. Correct!
20 ÷ 2 = ?
Answer: 10. Check: 2 × 10 = 20. Correct!
Uwase pours 18 beans equally into 2 cups. How many beans are in one cup?
Answer: 9 beans. 18 ÷ 2 = 9. Check: 2 × 9 = 18. Correct!
Byiringiro has 16 pencils. He gives 2 pencils to each friend until they are all gone. How many friends got pencils?
Answer: 8 friends. Count in twos until you reach 16: 2, 4, 6, 8, 10, 12, 14, 16. That is 8 jumps. So 16 ÷ 2 = 8.
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