Using an efficient method for division
🎯 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.
💡 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
2. $56$ children arrange themselves in teams of $4$. How many teams do they make?
👀 Show answer
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
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
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
6. Copy this calculation and find the missing digit.
👀 Show answer
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
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
🧠 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.