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Multiplication

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visibility 53update 25 days agobookmarkshare

🎯 In this topic you will

Estimate the size of a calculation result before performing the exact calculation.
Multiply whole numbers up to 10,000 by one-digit and two-digit whole numbers.

🧠 Key Words

product

Show Definitions

product: The result obtained when two or more numbers are multiplied together.

📬 Selling Stamps

I magine you sell stamps. Each sheet has 10 columns and 16 rows, and you have 12 sheets of stamps. To find how many stamps you have altogether, you need to multiply the numbers of columns, rows, and sheets together.

📘 Worked example

Find the product of $1347 \times 8$.

Estimate:
$1000 \times 8 = 8000$
$1500 \times 8 = 12000$

The answer should be between $8000$ and $12000$.

Answer:

$1347 \times 8$
$= (1000 \times 8) + (300 \times 8) + (40 \times 8) + (7 \times 8)$
$= 8000 + 2400 + 320 + 56$
$= 10776$

Step-by-step multiplication:

$7 \times 8 = 56$ → Write $6$ and carry $5$ tens.

$40 \times 8 = 320$ → Add the carried $50$ to get $370$. Write $7$ tens and carry $3$ hundreds.

$300 \times 8 = 2400$ → Add the carried $300$ to get $2700$. Write $7$ hundreds and carry $2$ thousands.

$1000 \times 8 = 8000$ → Add the carried $2000$ to get $10000$.

So the final result is $10776$, which matches the estimate range.

❓ EXERCISES

1. Lexi estimates the answer to $1499 \times 59$ to be $900\,000$. Has she made a good estimate? Explain your answer.

👀 Show answer

No. A reasonable estimate would round $1499 \approx 1500$ and $59 \approx 60$. $1500 \times 60 = 90\,000$, not $900\,000$. Lexi’s estimate is ten times too large.

2. Calculate.

a. $4224 \times 7$

b. $6174 \times 6$

c. $3748 \times 8$

Check your answers with your partner.

👀 Show answer

a. $4224 \times 7 = 29\,568$ b. $6174 \times 6 = 37\,044$ c. $3748 \times 8 = 29\,984$

3. Find the product of $1234$ and $7$.

👀 Show answer

$1234 \times 7 = 8638$

4. Pierre calculates $2013 \times 7$. His answer is not correct. Identify the error, then write the correct answer.

👀 Show answer

Correct calculation: $2013 \times 7 = 14\,091$. Pierre made an error in carrying during the multiplication.

5. Which of these multiplications have the answer $24\,000$?

$60 \times 4000$

$400 \times 60$

$80 \times 3000$

$8000 \times 3$

$20 \times 1200$

👀 Show answer

$60 \times 4000 = 240\,000$ (not correct) $400 \times 60 = 24\,000$ ✔ $80 \times 3000 = 240\,000$ (not correct) $8000 \times 3 = 24\,000$ ✔ $20 \times 1200 = 24\,000$ ✔

6. Kiki’s heart beats about $79$ times each minute. How many times does her heart beat in a day?

👀 Show answer

There are $60$ minutes in an hour and $24$ hours in a day. Total minutes per day: $60 \times 24 = 1440$. Heartbeats: $79 \times 1440 = 113\,760$ beats per day.

7. Calculate.

a. $5489 \times 30$

b. $3279 \times 50$

c. $7621 \times 70$

👀 Show answer

a. $5489 \times 30 = 164\,670$ b. $3279 \times 50 = 163\,950$ c. $7621 \times 70 = 533\,470$

8. Calculate.

a. $1356 \times 19$

b. $1571 \times 43$

c. $7625 \times 57$

Check your answers with your partner.

👀 Show answer

a. $1356 \times 19 = 25\,764$ b. $1571 \times 43 = 67\,553$ c. $7625 \times 57 = 434\,625$

9. Each display cabinet has $7$ shelves and each shelf holds $18$ figures. Joe has a collection of $25$ cabinets and each cabinet is full. How many figures are in Joe’s collection? Show your working.

👀 Show answer

Figures per cabinet: $7 \times 18 = 126$ Total figures: $126 \times 25 = 3150$. Joe has $3150$ figures.

10. Copy and complete this calculation by working out the three missing digits.

👀 Show answer

The completed multiplication gives $15\,2334$ as shown in the working. The missing digits are determined from the intermediate products $7254$ and $145080$.

🧠 Think like a Mathematician

Question: Two consecutive numbers multiply together to make $650$. What are the two numbers?

Tip

$20 \times 20 = 400$
$30 \times 30 = 900$

Independent Challenge: Make up some more puzzles like this and solve them on your own.

Follow-up Questions:

1. Which two consecutive whole numbers is $650$ between when you compare nearby square numbers?

2. What are the two consecutive numbers?

3. Write one more puzzle like this and give its answer.

👀 show answer

1: Since $20 \times 20 = 400$ and $30 \times 30 = 900$, the answer must be between $20$ and $30$. More closely, $25 \times 26 = 650$.
2: The two consecutive numbers are $25$ and $26$.
3: Example: Two consecutive numbers multiply together to make $132$. The numbers are $11$ and $12$, because $11 \times 12 = 132$.

📘 What we've learned

We learned how to estimate the size of a multiplication before calculating the exact answer.
We practiced multiplying whole numbers up to $10\,000$ by one-digit and two-digit numbers.
We used place value to break numbers apart when multiplying, for example $1347 = 1000 + 300 + 40 + 7$.
We checked answers by comparing them with an estimate to see if the result is reasonable.
We applied multiplication to real situations such as counting collections, repeated groups, and time calculations.

Multiplication

🎯 In this topic you will

🧠 Key Words

📬 Selling Stamps

❓ EXERCISES

🧠 Think like a Mathematician

Tip

📘 What we've learned

Related Past Papers

Related Tutorials

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