Extending multiplication and division
🎯 In this topic you will
- Estimate and multiply numbers up to 100 using the 2, 3, 4, and 5 times tables.
- Estimate and divide numbers up to 100 by 2, 3, 4, and 5.
- Understand what a remainder means and how to interpret it in real problems.
🧠 Key Words
- approach
- interpret
Show Definitions
- approach: A method or way of starting and solving a problem step by step.
- interpret: To explain what results or information mean, especially in the context of a maths problem.
🔢 Working with Larger Numbers
I n this section, you will extend the numbers that you work with when multiplying and dividing. You will also explore what the remainder after division represents. Sometimes you will need to increase the answer by 1, depending on the problem.
❓ EXERCISES
1. Estimate the product of $23 \times 4$. Record the multiplication calculation in the grid and find the product.
👀 Show answer
Exact calculation: split $23$ into $20$ and $3$.
$20 \times 4 = 80$, $3 \times 4 = 12$.
$80 + 12 = 92$.
Therefore, $23 \times 4 = 92$.
2. Estimate and then find the product for each multiplication.
a. $35 \times 4 =$
b. $58 \times 3 =$
c. $94 \times 2 =$
d. $76 \times 5 =$
👀 Show answer
b. Estimate: $60 \times 3 = 180$. Exact: $58 \times 3 = 174$.
c. Estimate: $100 \times 2 = 200$. Exact: $94 \times 2 = 188$.
d. Estimate: $80 \times 5 = 400$. Exact: $76 \times 5 = 380$.
3. Choose a number from the table. Spin the spinner to find out whether to divide by $2$, $3$, $4$ or $5$. Remember to estimate before you calculate. Do this twice.
👀 Show answer
First try: choose $87$, spinner shows $3$.
Estimate: $90 \div 3 = 30$. Exact: $87 \div 3 = 29$.
Second try: choose $49$, spinner shows $5$.
Estimate: $50 \div 5 = 10$. Exact: $49 \div 5 = 9$ remainder $4$.
The remainder tells you how many are left over after sharing equally.
🧠 Think like a Mathematician
Question: Find a number that is less than $100$ that can be divided by $2$, $3$, $4$ and $5$ with no remainder.
Method:
- Think about what it means for a number to be divisible by several values.
- Find a common multiple of $2$, $3$, $4$, and $5$.
- Check that your number is less than $100$.
Show Answer
- One possible answer is $60$.
- Explanation: $60 \div 2 = 30$, $60 \div 3 = 20$, $60 \div 4 = 15$, and $60 \div 5 = 12$ — all whole numbers.
- So $60$ is divisible by $2$, $3$, $4$, and $5$ with no remainder, and it is less than $100$.
❓ EXERCISES
4. There are $46$ tennis balls. Four tennis balls fit into each tube. How many tubes are needed for $46$ balls?
👀 Show answer
5. There are $36$ marbles in a set. Five children are playing. How many marbles do they get each?
👀 Show answer
6. Ten children can sit on each bench. How many benches are needed to seat $37$ children?
👀 Show answer
7. Make up a problem for these divisions.
a. $31 \div 4 = 7$ r$3$
b. $77 \div 3 = 25$ r$2$
👀 Show answer
b. Example: $77$ stickers are shared between $3$ friends. Each friend gets $25$ stickers and $2$ stickers are left over.