Division
🎯 In this topic you will
- Estimate the size of an answer before carrying out a calculation.
- Divide whole numbers up to $1000$ by one-digit whole numbers.
- Divide whole numbers up to $1000$ by two-digit whole numbers.
🧠 Key Words
- dividend
- divisor
- quotient
- remainder
Show Definitions
- dividend: The number that is being divided in a division calculation.
- divisor: The number by which the dividend is divided.
- quotient: The result obtained when one number is divided by another.
- remainder: The amount left over when a number cannot be divided exactly.
Checking Answers with Estimation
In this section you will learn how to divide larger numbers. Before doing the exact calculation, it is useful to estimate the answer so that you can check whether your final answer is reasonable.
❓ EXERCISES
1. Pablo estimates the answer to all these calculations is $30$.
$598 \div 21$
$914 \div 34$
$564 \div 14$
$342 \div 13$
Do you agree? Explain your answer.
👀 Show answer
$914 \div 34 \approx 26.9$ (about $27$)
$564 \div 14 \approx 40.3$ (not close to $30$)
$342 \div 13 \approx 26.3$ (about $26$)
Pablo is incorrect because not all answers are close to $30$.
2.
a. Calculate $765 \div 7$
b. Divide $297$ by $11$
c. Find the value of $874$ divided by $38$
👀 Show answer
b. $297 \div 11 = 27$
c. $874 \div 38 = 23$
3. Parveen and Ingrid both calculate $493$ divided by $7$.
Parveen says, “The answer is $70$ remainder $3$.”
Ingrid says, “The answer is $70\frac{3}{7}$.”
Who is correct? Explain your answer.
👀 Show answer
4. Here are two calculation cards $A$ and $B$.
What is the difference between $A$ and $B$?
👀 Show answer
$B = 374 \div 11 = 34$
Difference $= 42 - 34 = 8$.
5. Use factors to work out these calculations.
a. $924 \div 12$
b. $960 \div 15$
c. $882 \div 18$
👀 Show answer
b. $960 \div 15 = 64$
c. $882 \div 18 = 49$
6. Eggs are put in boxes. Each box holds $12$ eggs.
A farmer has $684$ eggs. How many boxes does he need to pack his eggs?
👀 Show answer
7. Mandy says, “I can work out $825 \div 15$ by dividing by $10$ and then dividing by $5$.”
Do you agree with Mandy? Explain your answer.
👀 Show answer
8. Use the numbers from the circles to copy and complete the two number sentences.
👀 Show answer
$306 \div 34 = 9$
9.
a. Find the missing digits.
b. Write the answer as a mixed number.
👀 Show answer
10. A meal in a restaurant costs the same for each person.
For $11$ people the meal costs $\$297$. What is the cost for each person?
👀 Show answer
11. Work out the value of the missing digit.
a. $39\Box \div 6 = 65$ remainder $3$
b. $76\Box \div 9 = 84$ remainder $8$
👀 Show answer
b. $764 \div 9 = 84$ remainder $8$ → missing digit $4$
🧠 Think like a Mathematician
Choose any four digits.
Arrange them to make a division calculation:
□ □ □ $\div$ □
Work out the answer.
Try other arrangements using the same four digits.
Follow-up Questions:
👀 show answer
- 1: The largest answer happens when the three-digit number is as large as possible and the divisor is as small as possible. For example, using digits $9, 8, 7, 2$: $987 \div 2 = 493.5$, which is much larger than most other arrangements.
- 2: The smallest answer happens when the three-digit number is as small as possible and the divisor is as large as possible. For example, using digits $9, 8, 7, 2$: $278 \div 9 \approx 30.9$, which is much smaller than the other arrangements.