Multiplication
🎯 In this topic you will
- Use the associative law to regroup factors in multiplication and make calculations easier.
- Estimate products when multiplying a whole number (up to 1000) by a 1-digit number.
- Multiply a whole number by a 1-digit number accurately.
🧠 Key Words
- associative law
- carry
Show Definitions
- associative law: A multiplication rule that says you can change how numbers are grouped (using brackets) without changing the final product.
- carry: In written addition or multiplication, the step where you move an extra value (like a ten) to the next place value because a digit total is $10$ or more.
🍫 Splitting a Chocolate Bar
Do you enjoy eating chocolate? This bar could be split into $24$ pieces or into $6$ lots of $4$ or $4$ lots of $6$.
🧮 Multiplying and Estimating
In this unit, you will multiply larger numbers by $1$-digit numbers. You should always estimate the size of the answer first to check your answer is about right.
❓ EXERCISES
1. Magda calculates $14 \times 5$ using factors. She spills ink on her work. What number is under the ink blots?
👀 Show answer
Since $14 = 7 \times 2$, the missing number is $2$.
So $14 \times 5 = 7 \times 2 \times 5 = 7 \times 10 = 70$, and both ink blots cover $2$.
2. Amir and Ben work out $4 \times 15$.
Which method do you like best? Explain why.
Discuss your answer with your partner.
Think of other ways to work out $4 \times 15$.
👀 Show answer
Both methods are correct and give $60$.
Amir's method: $4 \times 15 = 4 \times 5 \times 3 = 20 \times 3 = 60$.
Ben's method: $4 \times 15 = 2 \times 2 \times 15 = 2 \times 30 = 60$.
Example preference: Ben's method can feel efficient because doubling $15$ to get $30$ is quick, then doubling again gives $60$.
3. Work out the following. Estimate your answer first.
a. $47 \times 5$
b. $29 \times 4$
c. $89 \times 3$
d. $74 \times 6$
Compare the methods you used with your partner.
Identify the advantages and disadvantages of each method.
👀 Show answer
a. Estimate: $50 \times 5 = 250$. Exact: $47 \times 5 = 235$.
b. Estimate: $30 \times 4 = 120$. Exact: $29 \times 4 = 116$.
c. Estimate: $90 \times 3 = 270$. Exact: $89 \times 3 = 267$.
d. Estimate: $70 \times 6 = 420$ (or $75 \times 6 = 450$). Exact: $74 \times 6 = 444$.
4. Sultan uses the grid method to work out his calculations, but he spills ink on his work.
Copy and complete the calculations.
a. $47 \times 3 =$
b. $93 \times 4 =$
c. $51 \times 5 =$
d. $87 \times 4 =$
👀 Show answer
a. $47 \times 3 = (40 \times 3) + (7 \times 3) = 120 + 21 = 141$. Missing number: $120$.
b. $93 \times 4 = (90 \times 4) + (3 \times 4) = 360 + 12 = 372$. Missing numbers: $90$ and $360$.
c. $51 \times 5 = (50 \times 5) + (1 \times 5) = 250 + 5 = 255$. Missing number: $250$.
d. $87 \times 4 = (80 \times 4) + (7 \times 4) = 320 + 28 = 348$. Missing numbers: $7$ and $320$.
5. Find the product of $56$ and $5$.
👀 Show answer
$56 \times 5 = 280$.
6. Pencils are sold in packs of $5$. Each pack costs $95$ cents. Fatima buys $4$ packs of pencils. How much does she spend?
👀 Show answer
$4 \times 95 = 380$, so she spends $380$ cents (that is $3.80$).
7. Use the digits $2$, $3$ and $5$ once to make the multiplication with the greatest product.
Work out the answer.
Compare your answer with your partner.
The person with the larger answer should explain their method.
👀 Show answer
To make the product as large as possible, use the largest digit as the multiplier and make the largest possible two-digit number with the other two digits.
$32 \times 5 = 160$.
8. Work out the following. Estimate your answer first.
a. $174 \times 4$
b. $129 \times 7$
c. $189 \times 3$
d. $119 \times 8$
Compare the methods you used with your partner.
Identify the advantages and disadvantages of each method.
👀 Show answer
a. Estimate: $170 \times 4 = 680$ (or $175 \times 4 = 700$). Exact: $174 \times 4 = 696$.
b. Estimate: $130 \times 7 = 910$. Exact: $129 \times 7 = 903$.
c. Estimate: $190 \times 3 = 570$. Exact: $189 \times 3 = 567$.
d. Estimate: $120 \times 8 = 960$. Exact: $119 \times 8 = 952$.
🧠 Think like a Mathematician
A 3-digit number is multiplied by 3. There are five different missing digits in the calculation: 1, 2, 6, 7, 8.
Calculation (with blanks):
Clues:
- The sum of the digits of the 3-digit number is 24.
- The digits in the 3-digit number are consecutive numbers, but they are not written in order.
- The answer is between 2000 and 3000.
Follow-up Questions:
👀 show answer
First, the digits are consecutive and sum to 24. So they must be 7, 8, 9 because $7+8+9=24$.
The middle digit shown is 9, so the number is either 897 or 798 (not in order, so 789 is not allowed).
Now multiply by 3 and use the “missing digits are 1, 2, 6, 7, 8” condition:
- 798 × 3 = 2394 (missing digits would include 3 and 4, so it does not match).
- 897 × 3 = 2691 (missing digits are exactly 1, 2, 6, 7, 8, so it matches).
Therefore, the completed calculation is: 897 × 3 = 2691 (and 2691 is between 2000 and 3000).