Multiplying decimals
🎯 In this topic you will
- Estimate results before multiplying numbers with up to two decimal places by a one-digit whole number.
- Estimate results before multiplying numbers with up to two decimal places by a two-digit whole number.
🧠 Key Words
- decimal
- decimal place
- decimal point
- product
Show Definitions
- decimal: A number that includes a decimal point and represents parts of a whole using tenths, hundredths, and smaller place values.
- decimal place: The position of a digit in a decimal number that shows its value, such as tenths, hundredths, or thousandths.
- decimal point: The symbol used to separate the whole number part from the fractional part of a decimal number.
- product: The result obtained when two or more numbers are multiplied together.
🎟️ Calculating the Cost of Tickets
Erik works in a theatre selling tickets. Erik sells 63 tickets, and each ticket costs $45.75. In this section, you will learn how to calculate the total cost of all the tickets Erik sells.
💡 Quick Math Tip
Multiply Quantity by Unit Price: When many identical items are sold at the same price, the total cost can be found by multiplying the number of items by the price of one item. This avoids repeated addition and gives the total quickly.
❓ EXERCISES
1. Calculate.
a. $45.1 \times 5$
b. $38.12 \times 7$
c. $40.09 \times 9$
Check your answers with your partner.
👀 Show answer
a. $45.1 \times 5 = 225.5$
b. $38.12 \times 7 = 266.84$
c. $40.09 \times 9 = 360.81$
2. Find the product of $6$ and $34.56$.
👀 Show answer
$6 \times 34.56 = 207.36$
3. Vincent is thinking of a number.
He says, ‘If I divide my number by $6$ the answer is $17.54$.’
What number is Vincent thinking of?
👀 Show answer
If $x \div 6 = 17.54$, then $x = 17.54 \times 6$
$x = 105.24$
4. Calculate.
a. $74.36 \times 15$
b. $95.36 \times 47$
c. $23.08 \times 83$
Check your answers with your partner.
👀 Show answer
a. $74.36 \times 15 = 1115.4$
b. $95.36 \times 47 = 4481.92$
c. $23.08 \times 83 = 1915.64$
5. Parveen calculates $17.05 \times 15$.
Is her calculation correct? If not, correct any mistakes.
👀 Show answer
The correct calculation is:
$17.05 \times 15 = 255.75$
So Parveen's result $256.25$ is incorrect.
6. Use the digits $5$, $6$ and $7$ to make this calculation correct.
👀 Show answer
$4.7 \times 6.9 = 32.43$ (example approach using the digits)
Students must place $5$, $6$, and $7$ so that the multiplication equals $32.35$.
7. Meals cost $15.25$ at a restaurant.
$12$ people go for a meal.
What is the total cost of the meals?
👀 Show answer
$15.25 \times 12 = 183.00$
Total cost: $183$ dollars.
8. Ravi and Tara buy some stickers.
Ravi buys $36$ stickers at $0.98$ each.
Tara buys $3$ packs of $12$ stickers for $11.50$ a pack.
How much more does Ravi pay than Tara?
👀 Show answer
Ravi: $36 \times 0.98 = 35.28$
Tara: $3 \times 11.50 = 34.50$
Difference: $35.28 - 34.50 = 0.78$
Ravi pays $0.78$ more.
🧠 Think like a Mathematician
You need five cards with the digits $2$, $3$, $4$, $5$ and $6$.
Arrange the cards to make a multiplication calculation in this form:
The first number is a decimal number with one digit after the decimal point. Use each card exactly once.
Task: Investigate different possible calculations.
Which calculation gives an answer closest to $208$?
Show Answers
- One arrangement is $5.2 \times 43 = 223.6$.
- Another is $6.4 \times 32 = 204.8$.
- The result $6.4 \times 32 = 204.8$ is very close to $208$, with a difference of $3.2$.
- Students may find other combinations and compare how close each product is to $208$.