Multiplying & Dividing Integers Word Problems Task Card Set - Great for 7th Grade! 24 Cards!

It looks like you've uploaded an image of a "Multiplying & Dividing Integers Word Problems Task Card Set" designed for 7th-grade students. This set includes 24 task cards, each containing a real-world word problem that requires students to apply multiplication and division of integers.

While I can't see the full content of all 24 cards, I can help solve and explain a few sample problems from the visible cards in the image. Let’s go through some of them step by step.

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🔹 Problem 1 (Card #21):

> Over the last 40 weeks, Mr. Louie has lost $2400 playing the lottery. What is his average loss per week?

#### Step-by-step Solution:
We are given:
- Total loss = $2400 (negative because it's a loss → -$2400)
- Time period = 40 weeks

To find the average loss per week, divide total loss by number of weeks:

$$
\text{Average loss per week} = \frac{-2400}{40} = -60
$$

✔ Answer: Mr. Louie lost an average of $60 per week.

> ✔ *This involves dividing integers: negative ÷ positive = negative.*

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🔹 Problem 2 (Card #22):

> Meyrick and his Aunt Angie like to pick blackberries. Together they have picked 8 ¾ pounds of blackberries. They want to divide them evenly between themselves and 7 family members. How many pounds should they put in each person’s container?

#### Step-by-step Solution:
Total people = Meyrick + Aunt Angie + 7 family members = 9 people

Total blackberries = $ 8\frac{3}{4} = \frac{35}{4} $ pounds

Now divide:
$$
\frac{35}{4} \div 9 = \frac{35}{4} \times \frac{1}{9} = \frac{35}{36}
$$

✔ Answer: Each person gets $ \frac{35}{36} $ pounds ≈ 0.972 pounds.

> ✔ *This involves dividing a mixed number (positive integer) by a whole number — still an integer operation conceptually.*

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🔹 Problem 3 (Card #23):

> The amount of salt in the Bath County's storage unit to use on icy roads decreased by 12 ¼ feet over a 4 ¼ week time period. What is the rate that the salt has been decreasing per week?

#### Step-by-step Solution:
Decrease in salt = $ 12\frac{1}{4} = \frac{49}{4} $ feet
Time = $ 4\frac{1}{4} = \frac{17}{4} $ weeks

Rate = change in quantity ÷ time
$$
\text{Rate} = \frac{-49/4}{17/4} = -\frac{49}{4} \times \frac{4}{17} = -\frac{49}{17} \approx -2.88 \text{ feet per week}
$$

✔ Answer: The salt decreased at a rate of –2.88 feet per week (or $-\frac{49}{17}$ ft/week).

> ✔ *Negative result indicates decrease; this is division of rational numbers involving integers.*

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🔹 Problem 4 (Card #24):

> The cafeteria purchased French bread pizza for lunch next week. If they would have purchased the pizza last week while it was on sale, it would only have cost $2.00 per pizza. Now, 7 days later, the price is $3.78 per pizza. What integer represents the average increase in the price of the pizza per day?

#### Step-by-step Solution:
Price increase = $3.78 – $2.00 = $1.78
Number of days = 7

Average daily increase:
$$
\frac{1.78}{7} \approx 0.254 \text{ dollars per day}
$$

But the question asks for an integer representing the average increase.

Since $0.254 is closer to 0 than to 1, and we're rounding to the nearest integer, the answer is:

✔ Answer: 0 (since the increase per day is less than $0.50)

> ⚠️ Note: This might be a trick question or one where students must round appropriately. However, if the teacher wants the exact value as an integer, they may expect rounding down or truncating, which would also give 0.

> ✔ *This involves interpreting decimal results and converting to integers when appropriate.*

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🔹 Problem 5 (Card #10):

> After being exposed to an electromagnetic shrinking machine, your height decreased by 120 cm over 10 seconds. Your height decreased by the same amount each second. How much did your height change each second?

#### Step-by-step Solution:
Total decrease = –120 cm
Time = 10 seconds

$$
\text{Change per second} = \frac{-120}{10} = -12 \text{ cm per second}
$$

✔ Answer: Height changed by –12 cm per second.

> ✔ *Simple division of integers with sign interpretation.*

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🔹 Problem 6 (Top-left card):

> You loaned $5 to 20 people each. You recorded each loan by writing –$5 in your bank book. What is the total amount of money you lost from the loan?

#### Step-by-step Solution:
Each loan = –$5
Number of people = 20

Total = $ 20 \times (-5) = -100 $

✔ Answer: You lost $100 (represented as –$100).

> ✔ *Multiplication of a positive and negative integer.*

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## 🧠 Key Concepts Covered:
These problems reinforce:
- Sign rules:
- Negative × Positive = Negative
- Negative ÷ Positive = Negative
- Positive ÷ Positive = Positive
- Real-world applications: money, temperature, elevation, rates, etc.
- Converting word problems into mathematical expressions
- Working with fractions and decimals as integers (rational numbers)

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## ✔ Teaching Tips:
- Use these cards for math centers, small group work, or review games.
- Encourage students to write the expression first, then compute.
- Emphasize interpreting signs: negative means "loss", "decrease", "below zero", etc.

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Let me know if you'd like:
- A printable version of solutions
- Answer key for all 24 cards
- A worksheet format
- Or help creating similar problems!

I'm happy to assist further!