Algebra 1 Unit 4 Practice Test on the Distributive Property, featuring questions on area calculations, equation properties, and identifying examples of the distributive property.

Here's the solution to Algebra I – Unit 3 Practice Test: Building Blocks of Algebra, with detailed explanations for each question.

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Question 1:

> There are 4648 square yards in an acre. How many square feet are there?

We know:
- 1 yard = 3 feet
- So, 1 square yard = 3 ft × 3 ft = 9 square feet

Therefore:
> 4648 sq yd × 9 sq ft/sq yd = ?

Let’s compute:
4648 × 9
= (4000 × 9) + (600 × 9) + (40 × 9) + (8 × 9)
= 36,000 + 5,400 + 360 + 72
= 41,832 square feet

✔ Answer: (3) 41,832 sq ft

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Question 2:

> If a car is traveling at 38 miles per hour, how far does it go in 3.5 hours?

Use the formula:
Distance = Speed × Time

So:
38 mph × 3.5 h = ?

Compute:
38 × 3.5 = 38 × (3 + 0.5) = (38×3) + (38×0.5) = 114 + 19 = 133 miles

✔ Answer: (4) 133 miles

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Question 3:

> The equation 5 · (3 - 7) = (5 · 3) - (5 · 7) is an example of which property?

This shows distributing multiplication over subtraction:
a(b - c) = ab - ac

That’s the Distributive Property.

✔ Answer: (1) Distributive Property

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Question 4:

> Which of the following equations demonstrates an example of the Commutative Property?

Commutative Property means order doesn’t matter — for addition or multiplication:
a + b = b + a
a × b = b × a

Check each option:

(1) (x + 3) + (x + 7) = x + 3 + x + 7 → This is just removing parentheses (Associative/Grouping), not changing order.

(2) (x + 9) + (x + 7) = (x + 7) + (x + 9) → Here, the two terms being added are swapped. This is Commutative Property of Addition.

(3) (x + 9) + (x + 7) = x + (9 + x) + 7 → Messy grouping, not commutative.

(4) (x + 9) + (x + 7) = x + (7 + 9) + x → Again, regrouping and reordering, but not cleanly commutative.

✔ Answer: (2) — It clearly swaps the order of two addends.

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Question 5:

> Which of the following does NOT demonstrate an application of the Distributive Property?

Recall: Distributive Property = a(b + c) = ab + ac

Check each:

(1) 2(x + 3)(x - 4) = 2x(x - 4) + 3(x - 4)
→ This is distributing the 2 across (x+3), then multiplying by (x-4). Actually, this is applying distributive property twice. ✔️

(2) 2x(x + 3)(x - 4) = 2x²(x - 4) + 6x(x - 4)
→ Here, 2x is distributed over (x+3): 2x·x = 2x², 2x·3 = 6x. Then multiplied by (x-4). Still valid distributive. ✔️

(3) 6x² - 4x + 3x - 2 = 6x² + (-4x + 3x) - 2
→ This is combining like terms, not distributing. You’re just rearranging and simplifying. NOT distributive property. ✔

(4) 6x² + x(8 - 3) - 6x² + 12x + 4
→ This seems messy, but if you look, it may involve distribution inside (like x(8-3)=8x-3x), so likely uses distributive. But even if not, (3) is clearly NOT distributive.

✔ Answer: (3) — It’s combining like terms, not distributing.

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## ✔ Final Answers:

1. (3) 41,832 sq ft
2. (4) 133 miles
3. (1) Distributive Property
4. (2)
5. (3)

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