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Using an efficient method for division

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visibility 155update 5 months agobookmarkshare

🎯 In this topic you will

I will learn how to make a sensible guess when dividing a two-digit number by a one-digit number.
I will learn how to divide numbers up to 100 by a one-digit number.
I will learn how to decide whether to round my answer up or down after dividing to solve a real problem.

🧠 Key Words

dividend
divisor
quotient
remainder

Show Definitions

dividend: The number that is being divided in a division calculation.
divisor: The number you divide by in a division calculation.
quotient: The result or answer you get when one number is divided by another.
remainder: The amount left over when a number cannot be divided evenly.

Using Division to Solve Problems

Y ou can use division to help solve real-life problems. For example, if 224 players enter a seven-a-side football competition, dividing 224 by 7 tells you how many teams have entered the competition.

📘 Worked example

Calculate $75 \div 4$.

Estimate. $40 \div 4 = 10$ and $80 \div 4 = 20$, so the answer is between 10 and 20 and closer to 20.

Split $75$ into $40 + 35$.

There are ten fours in forty and eight fours in thirty-five with a remainder of 3.

Answer:

$18\ r3$

Using the estimate, write 1 to show ten fours, and write 3 next to the 5 to show that you carry 30 over.

There are eight fours in thirty-five with a remainder of 3.

💡 Quick Math Tip

Estimate before you divide: First divide nearby friendly numbers (like 40 and 80 instead of 75). This helps you check whether your final answer makes sense and tells you if it should be closer to the lower or higher estimate.

❓ EXERCISES

1. Parveen needs $28$ balloons. A shop sells balloons in packs of $5$. How many packs does Parveen need to buy?

👀 Show answer

$28 \div 5 = 5$ remainder $3$, so Parveen must buy $6$ packs.

2. $56$ children arrange themselves in teams of $4$. How many teams do they make?

👀 Show answer

$56 \div 4 = 14$, so they make $14$ teams.

3. A carton of orange juice fills $6$ cups. Erik wants to fill $50$ cups with orange juice. How many cartons does Erik need?

👀 Show answer

$50 \div 6 = 8$ remainder $2$, so Erik needs $9$ cartons.

4. A group of friends earn $\$96$ by washing cars. They share the money equally. They get $\$8$ each. How many friends are in the group?

👀 Show answer

$96 \div 8 = 12$, so there are $12$ friends.

5. Correct the errors in these calculations.

$86 \div 3$ is shown as $22$

$57 \div 3$ is shown as $52$

Discuss with your partner how the errors may have happened.

👀 Show answer

$86 \div 3 = 28$ remainder $2$. $57 \div 3 = 19$. The errors come from incorrect place value handling.

6. Copy this calculation and find the missing digit.

👀 Show answer

The missing digit is $7$.

a. What is the highest remainder possible when you divide by $3$?

b. What is the highest remainder possible when you divide by $4$?

c. Make a general statement comparing the divisor and the remainder.

👀 Show answer

a. $2$ b. $3$ c. The remainder is always less than the divisor.

8. Petra has two strips of card. Each strip is $24$ centimetres long. One strip is divided into $3$ equal parts. The other strip is divided into $4$ equal parts. Petra uses the two strips to make this shape. What is the total length of Petra’s shape?

👀 Show answer

Each part is $8$ cm and $6$ cm. The total length is $48$ cm.

🧠 Think like a Mathematician

Imagine you have a set of number cards from $0$ to $9$.

Use 4 different cards to make division sentences like this:

$\square \square \div \square = \square$

Find all the possible solutions.

👀 Show Answers

Each division must use four different digits, so no digit can be repeated.
The two-digit number must be exactly divisible by the one-digit divisor.
The remainder must be $0$ for the sentence to be correct.
For example, $84 \div 6 = 14$ works because all digits $8,4,6,1$ are different.
Try starting with easy divisors like $2$, $3$, $4$, and $5$ to make sure you find all possible solutions.

📘 What we've learned

We learned how to estimate answers when dividing a two-digit number by a one-digit number.
We practiced dividing numbers up to $100$ by a one-digit number, sometimes with a remainder.
We learned that a division result can be written as $\text{quotient remainder}$, for example $18\ r3$.
We learned how to decide whether to round up or round down after division to solve real-life problems correctly.
We understood that the remainder is always less than the divisor.

Using an efficient method for division

🎯 In this topic you will

🧠 Key Words

Using Division to Solve Problems

💡 Quick Math Tip

❓ EXERCISES

🧠 Think like a Mathematician

📘 What we've learned

Related Past Papers

Related Tutorials

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