Percent Word Problems as Decimal Expressions Worksheet Download - Free Printable

Let's solve each of these percent word problems step by step, converting percentages into decimal expressions and determining the correct mathematical expression for each situation.

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1) A mall kiosk needed to buy 40 cell phone cases at z dollars a piece. Because they were buying so many they got 18% off the price. Which expression shows how much money they saved?

- Original total cost: $ 40z $
- Discount: 18% off → $ 0.18 \times 40z $
- Money saved = $ 0.18 \times 40z $

✔ Answer: A. 0.18 × 40z

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2) A box of cereal advertised having 49% more marshmallows. The original cereal had y cups of marshmallow. Which expression shows the how many cups of marshmallows the new cereal has?

- Original amount: $ y $
- 49% more means: $ y + 0.49y = 1.49y $
- So, new amount = $ y \times 1.49 $

✔ Answer: A. y + 1.49
Wait — this is not quite right. Let’s check:

Actually, A is y + 1.49, which would be adding 1.49 cups (not 49%), so that’s wrong.

Correct expression: $ y + 0.49y = y(1 + 0.49) = 1.49y $

But none of the options say $ 1.49y $? Let's look again:

- A. y + 1.49 → no
- B. y × 0.49 → only the increase, not total
- C. y + (0.49 × y) → yes! This is $ y + 0.49y $
- D. y + 0.49 → no

✔ Answer: C. y + (0.49 × y)

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3) Billy drew a square with each side being exactly 8 centimeters long. If he wanted to make the square 13% larger which expression can he use to find the new sides length?

- Original side: 8 cm
- Increase by 13% → multiply by $ 1 + 0.13 = 1.13 $
- New side = $ 8 \times 1.13 $

✔ Answer: B. 8 × 1.13

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4) A cell phone company dropped the prices on their phones by 10%. Which expression shows the new price of the phones (p)?

- Original price: $ p $
- 10% decrease → subtract $ 0.10p $
- New price = $ p - 0.1p $

✔ Answer: D. p - 0.1p

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5) A store raised the price on watermelons 14%. The original price for each was X dollars. Which expression shows the new price of the watermelons?

- Original: $ X $
- Increase by 14% → $ X + 0.14X = 1.14X $

So, new price = $ X \times 1.14 $

✔ Answer: D. X + 1.14 ✘ Wait — that's not correct.

Wait: Option D is $ X + 1.14 $ → adds 1.14 dollars, not 14%.

But option C is: $ X + (0.14 × X) $ → that's $ X + 0.14X = 1.14X $

✔ Answer: C. X + (0.14 × X)

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6) Joe was earning $8 an hour before his raise. After his 5% raise he was making $8.4 an hour. Which expression shows how his new hourly rate was calculated?

- Original: $ 8 $
- 5% raise → $ 8 + 0.05 \times 8 = 8 \times (1 + 0.05) = 8 \times 1.05 $

✔ Answer: D. 8 × 1.05

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7) Over the summer gas prices dropped 2%. Which expression shows the new price of a gallon of gas? (the old price is represented by g)

- Old price: $ g $
- Decrease by 2% → $ g - 0.02g = g(1 - 0.02) = 0.98g $
- So, new price = $ g - 0.02g $

Look at options:

- A. g - 0.02 → subtracts $0.02, not 2%
- B. g - 1.02 → negative
- C. g - 0.02g → ✔ Yes!
- D. g × 0.02 → only 2% of price

✔ Answer: C. g - 0.02g

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8) A company was having a sale for 11% off the price of computer monitors. Which expression shows how much money you would save if you bought monitors for z dollars a piece?

- Price per monitor: $ z $
- Save 11% → $ 0.11 \times z $
- Total savings: $ 0.11z $

But wait — it says “you bought monitors” — but number isn't specified.

Wait: It says “for z dollars a piece” — so one monitor costs $ z $.

Then savings = $ 0.11z $

But the options have $ 20z $. That suggests maybe 20 monitors?

But the problem says: “if you bought monitors for z dollars a piece” — ambiguous.

But option A: $ 20z - 0.11 $ → doesn’t make sense

B: $ 0.11 × 20z $ → implies 20 monitors at $ z $ each → total savings = $ 0.11 × 20z $

C: $ 20z + 0.11 $ → no

D: $ 20z + 1.11 $ → no

So likely, it's implying 20 monitors, each costing $ z $, total cost $ 20z $, then 11% off → savings = $ 0.11 × 20z $

So B. 0.11 × 20z

✔ Answer: B. 0.11 × 20z

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9) A house was on sell for $22,871. If you wanted to offer 13% less than the asking price (p), which expression shows how much you should offer?

- Asking price: $ p $
- Offer 13% less → $ p - 0.13p = 0.87p $
- So, offer = $ p - 0.13p $

Options:

- A. p - 1.13 → no
- B. p - 0.13 → subtracts $0.13, not 13%
- C. p × 0.13 → only 13%, not the offer
- D. p - 0.13p → ✔ Yes!

✔ Answer: D. p - 0.13p

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10) The regular price of a computer was 484 dollars, but over the weekend it'll be on sale for 10 percent off. Which expression shows the difference in price from normal (n) to sale?

- Regular price: $ n $
- Sale price: $ n - 0.10n = 0.90n $
- Difference = $ n - 0.90n = 0.10n $

But the question asks: difference in price from normal to sale → that's the discount amount: $ 0.10n $

Now look at options:

- A. n - 10 → subtracts $10
- B. n × 0.1 → $ 0.1n $ → yes, same as 10% of n
- C. n - 0.1 → subtracts $0.10
- D. n - 1.1 → no

So, B. n × 0.1 represents the amount saved (10% of n)

✔ Answer: B. n × 0.1

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✔ Final Answers:

1. A. 0.18 × 40z
2. C. y + (0.49 × y)
3. B. 8 × 1.13
4. D. p - 0.1p
5. C. X + (0.14 × X)
6. D. 8 × 1.05
7. C. g - 0.02g
8. B. 0.11 × 20z
9. D. p - 0.13p
10. B. n × 0.1

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📝 Summary Explanation:

Each problem involves converting a percentage change into a decimal expression:
- Increase: Add the percent as a decimal times original value.
- Decrease: Subtract the percent as a decimal times original value.
- Savings: Multiply original price by percent discount (as decimal).
- Always ensure units and context match (e.g., total vs. per item).

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