Calculate the Product: Finding Total Gifts When Wrapping 9 Daily for 23 Days

Q: Why do I multiply instead of add the numbers?

Because Sarah wraps 9 gifts each day for 23 days! You need 9 + 9 + 9... added 23 times, which equals $ 9 \times 23 $. Addition would only give you 9 + 23 = 32.

Q: How can I remember the formula for rate problems?

Use the formula: Total = Rate × Time. Think of it like earning money: if you earn $5 per hour for 8 hours, you get $ 5 \times 8 = 40 $ dollars total!

Q: What if the numbers were bigger and harder to multiply?

Break it down! For $ 9 \times 23 $, you can think: $ 9 \times 20 = 180 $ and $ 9 \times 3 = 27 $, then add: $ 180 + 27 = 207 $.

Q: How do I check if my answer makes sense?

Ask yourself: Does 207 gifts seem reasonable? That's about 9 gifts per day, which matches the problem. Also try: $ 207 ÷ 23 = 9 $ ✓

Q: Can I solve this problem a different way?

Yes! You could add $ 9 + 9 + 9... $ twenty-three times, but multiplication is much faster. Both methods give the same answer: 207 gifts.

Multiplication with Multi-Day Applications

Sarah wraps 9 gifts per day, how many gifts does she wrap in 23 days?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many gifts does Sarah wrap in 23 days?

00:03 Given: number of gifts per day, number of days

00:07 We will use long multiplication to calculate

00:11 We will solve each multiplication separately and then substitute in the long multiplication

00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Sarah wraps 9 gifts per day, how many gifts does she wrap in 23 days?

Step-by-step solution

To determine how many gifts Sarah wraps in 23 days, we need to calculate the total number of gifts by multiplying the number of gifts she wraps each day by the total number of days.

Step 1: Identify the number of gifts Sarah wraps each day. In this case, Sarah wraps $9$ gifts per day.
Step 2: Identify the total number of days which is given as $23$ .
Step 3: Apply the multiplication formula to find the total number of gifts:

$\text{Total Gifts} = (\text{Gifts per day}) \times (\text{Number of days})$

Substitute the numbers into the formula:

$\text{Total Gifts} = 9 \times 23$

Now, calculate the result:

$9 \times 23 = 207$

Therefore, Sarah wraps a total of $207$ gifts over the course of 23 days.

Final Answer

$207$

Key Points to Remember

Essential concepts to master this topic

Rule: Total equals rate per unit times number of units
Technique: Set up $9 \times 23 = 207$ for gifts per day times days
Check: Divide total by days: $207 ÷ 23 = 9$ gifts per day ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying the values
Don't add 9 + 23 = 32 gifts! This only gives you the sum of daily rate and time period, not the total output. Always multiply rate times time to find total quantity produced.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I multiply instead of add the numbers?

Because Sarah wraps 9 gifts each day for 23 days! You need 9 + 9 + 9... added 23 times, which equals $9 \times 23$ . Addition would only give you 9 + 23 = 32.

How can I remember the formula for rate problems?

Use the formula: Total = Rate × Time. Think of it like earning money: if you earn 5 per hour for 8 hours, you get $\( 5 \times 8 = 40$ dollars total!

What if the numbers were bigger and harder to multiply?

Break it down! For $9 \times 23$ , you can think: $9 \times 20 = 180$ and $9 \times 3 = 27$ , then add: $180 + 27 = 207$ .

How do I check if my answer makes sense?

Ask yourself: Does 207 gifts seem reasonable? That's about 9 gifts per day, which matches the problem. Also try: $207 ÷ 23 = 9$ ✓

Can I solve this problem a different way?

Yes! You could add $9 + 9 + 9...$ twenty-three times, but multiplication is much faster. Both methods give the same answer: 207 gifts.

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