Division of 2-digit numbers
🎯 In this topic you will
- Estimate the size of an answer when a number up to 100 is divided by a one-digit number.
- Divide a number up to 100 by a one-digit number accurately.
- Decide whether to round up or round down after division in order to give a sensible answer to a problem.
🧠 Key Words
- division
- divisor
- remainder
- round up / round down
Show Definitions
- division: A mathematical operation that splits a number into equal parts.
- divisor: The number by which another number is divided.
- remainder: The amount left over when a number cannot be divided equally.
- round up / round down: A decision made after calculation to increase or decrease a number to the nearest sensible whole value.
Division in Everyday Life 🧮
T hink about when you use division in your everyday life. For example, when organising a party for 45 people, you may need one paper plate for each person. If paper plates come in packs of 8, you need to work out how many packs are required.
Making Sense of the Answer 🤔
Y ou need to develop strategies to divide 45 by 8 and then decide what the answer means in real life. This helps you work out whether you should round your answer up or down so that everyone has what they need.
💡 Quick Math Tip
Estimate first: Before dividing, round the number to a nearby multiple of the divisor. This gives you a quick idea of the size of the answer and helps you check whether your final result makes sense.
❓ EXERCISES
1. How many weeks are equivalent to $35$ days?
👀 Show answer
2. A shop sells cards in packs of $6$. Magda buys some of these packs. She buys $30$ cards. How many packs does Magda buy?
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3. Complete these calculations.
a. $98 \div 7$
b. $64 \div 4$
c. $96 \div 8$
d. $84 \div 6$
👀 Show answer
b. $64 \div 4 = 16$
c. $96 \div 8 = 12$
d. $84 \div 6 = 14$
4. Two sets of calculations which have different properties are mixed together.
$20 \div 3 \quad 23 \div 3 \quad 25 \div 3 \quad 14 \div 3 \quad 7 \div 3$
a. Sort the calculations into two sets.
b. Write one more example for each set.
👀 Show answer
The other set gives answers with remainders: $20 \div 3$, $23 \div 3$, $25 \div 3$, $14 \div 3$, $7 \div 3$. An extra example is $10 \div 3$.
5. $60$ people go for a walk. They need to cross a lake by boat. Each boat can take $9$ people. What is the least number of boats needed to take all of the people across the lake?
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6. $27$ apricots are put in bags. Each bag holds $6$ apricots. How many full bags are there?
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7. Zac and Sarah calculated $75 \div 5$. Zac used repeated subtraction and Sarah used a number line. Whose method do you prefer? Explain your reason.
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🧠 Think like a Mathematician
Each of these numbers gives a remainder of $1$ when it is divided by $4$.
a. Investigate other numbers that have a remainder of $1$ when divided by $4$. Put the numbers in order and look at the pattern of the ones digits, for example $5, 9, 13$.
What do you notice about the pattern?
b. What about other remainders? You could choose numbers that have a remainder of $2$ or $3$ when divided by $4$, or numbers that have a remainder of $1$ when divided by $5$.
Write about the patterns you find.
- You will show you are specialising when you find solutions to the problem.
- You will show you are generalising when you recognise patterns in your results.
- If you explain your results, you will show you are convincing.
👀 show answer
- a. Numbers that give a remainder of $1$ when divided by $4$ follow the form $4n+1$, such as $5, 9, 13, 17, 21$. The ones digits repeat in the pattern $1, 5, 9, 3, 7$.
- b. Numbers with remainder $2$ follow $4n+2$ and end in digits like $2, 6, 0, 4, 8$. Numbers with remainder $3$ follow $4n+3$. For division by $5$ with remainder $1$, numbers follow $5n+1$ and the ones digits repeat every five numbers.
- In all cases, numbers with the same remainder form a repeating pattern because the divisor stays constant.