7.EE.A.2 Worksheets - Common Core Math - Free Printable

I'll work through each problem step by step to find the equivalent expressions.

Problem 1:
The Martin family has 4 dogs. Each dog eats c cups of food per week. Total food = 4 × c = 4c

Looking at the options:
- c + c + c + c = 4c ✓ (adding c four times)
- c · 4 = 4c ✓ (multiplication)
- 4c ✓ (already simplified)

Answer: c + c + c + c, c · 4, and 4c

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Problem 2:
Tanya completed 5 swim meets last month. At each meet, she swam 6 laps of backstroke and f laps of freestyle. So at each meet: 6 + f laps. For 5 meets: 5(6 + f)

Using distributive property: 5(6 + f) = 5·6 + 5·f = 30 + 5f

Looking at the options:
- 6 · 5f = 30f ✗ (this multiplies all together)
- 6(5 + f) = 30 + 6f (wrong distribution)
- 30 + 5f ✓ (correct after distributing)
- 5(6 + f) ✓ (original expression)

Answer: 30 + 5f and 5(6 + f)

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Problem 3:
There are p people at a pizza party. Each person plans to buy 3/4 of a pizza. Total pizzas = p × (3/4) = (3/4)p or 3p/4

Looking at the options:
- 4p ✗ (wrong)
- (3/4)p ✓ (same as 3/4 times p)
- (3p)/4 ✓ (same thing written differently)
- p ÷ (4/3) = p × (3/4) = (3/4)p ✓ (dividing by 4/3 is same as multiplying by 3/4)

Answer: (3/4)p, (3p)/4, and p ÷ (4/3)

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Problem 4:
Museum offers discount: pay only 40% of admission price d. So you pay 0.40d or (40/100)d = (2/5)d

Also, 40% = 0.4, so 0.4d

Looking at the options:
- d - 0.4d = 0.6d (this is what you SAVE, not what you pay)
- 6d ✗ (way too much)
- 1.4d (this would be more than original)
- 0.6d ✗ (this is the discount amount, not what you pay)

Wait, let me reconsider. If you pay 40%, that's 0.4d. But none of these show 0.4d directly...

Actually, looking more carefully: d - 0.4d means you subtract the 40% discount from the full price, leaving 60%. That's wrong.

Hmm, but 0.6d appears twice in the options. Let me check if I'm reading correctly...

Oh wait! If the discount is "pay only 40%", then you pay 0.4d. But maybe I need to look at this differently.

Actually, I think there might be an error in my understanding. Let me re-read: "a discount where you pay only 40% of the admission price"

So if d is the admission price, you pay 0.4d or (40/100)d = (2/5)d

None of the given options equal 0.4d exactly... unless...

Wait, could "0.6d" appear because they're asking for the discount amount? No, it asks for "the amount of money Sean will spend."

Let me check: d - 0.4d = 0.6d. This equals 60% of d, which would mean you're paying 60%, not 40%.

Unless... OH! Maybe I misread. Let me check if it says you get a 40% DISCOUNT (meaning you pay 60%) vs paying only 40%.

Re-reading: "pay only 40% of the admission price" - this clearly means you pay 40%, not get a 40% discount.

So the answer should be 0.4d, but that's not listed. The closest would be if we interpret it as getting a 40% discount (paying 60%), which would be 0.6d or d - 0.4d.

Given the options provided, I believe the intended interpretation is that you get a 40% discount, meaning you pay 60% = 0.6d.

Answer: d - 0.4d and 0.6d (assuming it means a 40% discount, not paying 40%)

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Problem 5:
Devin listens to audio for 15 minutes every weekday. There are 5 weekdays. Total minutes per week = 5 × 15 = 75 minutes

For w weeks: 75w or 5 × 15 × w = 5(15w) or 15(5w)

Looking at the options:
- 5m + 15 ✗ (doesn't make sense with the variables)
- 10 + 15w ✗ (wrong)
- 5(25 + m) ✗ (wrong numbers)
- 5(m + 15w) - this doesn't match either

Wait, I see 'm' in the options but the problem uses 'w' for weeks. Let me re-read...

Oh! The problem says "for w weeks" but the options use 'm'. This seems like a typo in the worksheet. Assuming 'm' should be 'w':

Total = 5 weekdays × 15 minutes × w weeks = 75w

Options rewritten with w:
- 5w + 15 ✗
- 10 + 15w ✗
- 5(25 + w) = 125 + 5w ✗
- 5(w + 15w) = 5(16w) = 80w ✗

None of these equal 75w... Let me reconsider.

Actually, maybe 'm' represents something else? Or maybe I should interpret differently?

If we take it literally with 'm' as given:
- Devin listens 15 min/day on weekdays
- For w weeks, that's 5 × 15 × w = 75w minutes

But the options have 'm'... Perhaps 'm' is meant to represent the total minutes? That doesn't fit the structure though.

I think there's likely a typo and 'm' should be 'w'. In that case, none of the options work perfectly, but 5(w + 15) would give 5w + 75, which isn't right either.

Let me try: maybe it's asking for a different interpretation. What if we write it as 5 × 15w = 75w = 5(15w)?

Looking at option 4: 5(m + 15w). If m = 0, this becomes 5(15w) = 75w ✓

But that seems forced. Let me check if any option simplifies to 75w when we substitute appropriately...

Actually, I think the most reasonable answer assuming 'm' is a typo for a number or should be ignored: 5(15w) which would be represented if we had that option. Since we don't, and given the structure, I'll go with the interpretation that makes mathematical sense.

Looking again at option 4: 5(m + 15w). If this is meant to be 5(0 + 15w) or simply the structure allows for it, then 5(15w) = 75w.

But actually, none of these work cleanly. Let me just provide what SHOULD be the answer: 75w or 5(15w) or 15(5w).

Given the constraints, I'll note that there appears to be an error in the problem/options, but the correct mathematical answer is 75w.

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Problem 6:
Current deck: 12 ft long, 4 ft wide. New deck: length increased by x feet, width increased by 4x feet.

New length = 12 + x
New width = 4 + 4x = 4(1 + x)

Area = length × width = (12 + x)(4 + 4x)

Let me expand: (12 + x)(4 + 4x) = 12(4) + 12(4x) + x(4) + x(4x) = 48 + 48x + 4x + 4x² = 48 + 52x + 4x²

Or factor out 4 from the width: (12 + x) · 4(1 + x) = 4(12 + x)(1 + x)

Looking at the options:
- (12 + x)(2 + x) (wrong width)
- (12 + x)(x + 4) = (12 + x)(4 + x) (should be 4 + 4x, not 4 + x)
- 16w + 64 ✗ (wrong variable and doesn't match)
- 16(xw + 4) ✗ (doesn't match)

Wait, let me re-read the problem. "increase both the length and width of the deck by x feet"

OH! I misread. It says increase BOTH by x feet, not the width by 4x feet!

New length = 12 + x
New width = 4 + x

Area = (12 + x)(4 + x)

Expanding: 48 + 12x + 4x + x² = 48 + 16x + x²

Or we can write it as: (12 + x)(x + 4) [commutative property]

Looking at the options again:
- (12 + x)(2 + x) ✗
- (12 + x)(x + 4) ✓ (same as (12 + x)(4 + x))
- 16w + 64 ✗ (wrong variable)
- 16(xw + 4) ✗

Answer: (12 + x)(x + 4)

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Final Answer:

Problem 1: c + c + c + c, c · 4, 4c

Problem 2: 30 + 5f, 5(6 + f)

Problem 3: (3/4)p, (3p)/4, p ÷ (4/3)

Problem 4: d - 0.4d, 0.6d

Problem 5: [Note: There appears to be a typo in the problem - 'm' should likely be 'w'. The correct answer should be 75w or 5(15w), but none of the given options match exactly.]

Problem 6: (12 + x)(x + 4)