Multiplication
🎯 In this topic you will
- Estimate the size of an answer before calculating it
- Multiply whole numbers by 1-digit and 2-digit whole numbers
🧠 Key Words
- product
Show Definitions
- product: The result of multiplying two or more numbers together.
Multiplication in Real Life
We all learn how to multiply in school and many people use multiplication in their jobs.
Applying Multiplication in the Workplace
Imagine you work in a large warehouse. Your job is to load boxes onto a lorry. You have to work out what the mass of all the boxes will be.
Why Multiplication Is Needed Here
The calculations involve multiplication.
❓ EXERCISES
1. Calculate. Remember to estimate the size of your answer before you calculate it.
a. $400 \times 9$
b. $60 \times 8$
c. $300 \times 7$
d. $90 \times 6$
e. $900 \times 4$
f. $40 \times 8$
👀 Show answer
a. $400 \times 9 = 3600$
b. $60 \times 8 = 480$
c. $300 \times 7 = 2100$
d. $90 \times 6 = 540$
e. $900 \times 4 = 3600$
f. $40 \times 8 = 320$
2. Which calculations give the answer $2400$?
$30 \times 80 \quad 60 \times 40 \quad 30 \times 60 \quad 120 \times 20 \quad 80 \times 20$
👀 Show answer
The calculations that give $2400$ are $30 \times 80$, $60 \times 40$ and $120 \times 20$.
This is because $30 \times 80 = 2400$, $60 \times 40 = 2400$ and $120 \times 20 = 2400$, while $30 \times 60 = 1800$ and $80 \times 20 = 1600$.
3. A hummingbird beats its wings about $75$ times each second.
About how many times does it beat its wings in a minute?
👀 Show answer
There are $60$ seconds in a minute, so the hummingbird beats its wings about $75 \times 60 = 4500$ times in a minute.
4. Find the product of $31$ and $76$.
👀 Show answer
$31 \times 76 = 2356$
5. Sofia is calculating $299 \times 60$.
She estimates that the answer is $180\,000$.
Has she made a good estimate?
Explain your answer.
👀 Show answer
The exact answer is $299 \times 60 = 17\,940$.
A good estimate would be $300 \times 60 = 18\,000$, which is close to $17\,940$.
Sofia’s estimate of $180\,000$ is not good because she added an extra zero, making it ten times too large.
6. A storeroom has boxes stacked in $12$ rows.
Each row contains $96$ boxes.
How many boxes are there altogether?
👀 Show answer
The total number of boxes is $12 \times 96 = 1152$.
7. Arun multiplied $24$ by $12$.
Here is his working.
What error has Arun made? How should he improve his work?
👀 Show answer
Arun treated the $1$ in $12$ as if it were $100$, giving $24 \times 100 = 2400$ instead of $24 \times 10 = 240$.
He should multiply $24 \times 10 = 240$ and $24 \times 2 = 48$, then add them to get $240 + 48 = 288$.
The correct answer is $24 \times 12 = 288$.
8. Calculate $37 \times 25$.
Discuss with your partner the most efficient way of working out the answer.
👀 Show answer
One efficient method is to use $25 = \dfrac{100}{4}$.
Then $37 \times 25 = 37 \times \dfrac{100}{4} = \dfrac{3700}{4} = 925$.
So the answer is $925$.
9. Calculate.
a. $236 \times 48$
b. $179 \times 57$
c. $987 \times 36$
👀 Show answer
a. $236 \times 48 = 11\,328$
b. $179 \times 57 = 10\,203$
c. $987 \times 36 = 35\,532$
🧠 Think like a Mathematician
You need four cards:
3 5 4 6
Arrange the cards as a multiplication calculation.
Investigate different answers. Try to find as many as you can and then find the largest and smallest answers.
You will show you are specialising when you find solutions to the problem.
Follow-up questions:
👀 show answer
- 1: The smallest product is $34 \times 56 = 1904$. We minimise the result by placing the smallest digits in the tens position.
- 2: The largest product is $65 \times 43 = 2795$. We maximise the result by placing the largest digits in the tens position.
- 3: The tens digit has a greater effect than the ones digit. Putting the larger numbers in the tens place increases the value of the whole number and therefore gives a larger product.