Math Problem Statement

1. A bottle of eye drops has 0.45 fluid ounces of liquid. How much liquid is in 10^4 bottles of eye drops? 2. Jamal buys 33 bolts that cost $0.38 each. a. Which equation represents the BEST estimate for the total cost of all the bolts? - A. $0.30 × 30 = $9 - B. $0.40 × 30 = $12 - C. $0.50 × 30 = $15 - D. $0.40 × 40 = $16 b. What is the ACTUAL total cost of all the bolts? 3. Which expression shows the area of the shaded part of the grid? - a. 0.04 × 0.07 - b. 0.5 × 0.7 - c. 0.4 × 0.7 - d. 0.3 × 0.6 4. Match the expressions to their products: - 8 × 0.09 = - 0.8 × 0.09 = - 80 × 0.9 = - 8 × 0.9 = 5. Choose all expressions that are equal to 0.7 × 0.41: - 7/10 × 41/100 - 7/10 × 41/10 - 7/100 × 41/10 - 70/100 × 41/10 6. Emily bought seashells from a souvenir shop for $0.75 each. If Emily bought 10 seashells and her friend bought 100 seashells, how much did each spend?

Solution

Let’s solve each question from the uploaded image step by step.


1. A bottle of eye drops has 0.45 fluid ounces of liquid. How much liquid is in 10410^4 bottles of eye drops?

Each bottle has 0.45 fluid ounces. If there are 104=10,00010^4 = 10,000 bottles, the total liquid is:
0.45×10,000=4,500fluid ounces.0.45 \times 10,000 = 4,500 \, \text{fluid ounces}.

Answer: 4,500 fluid ounces


2. Jamal buys 33 bolts that cost $0.38 each.

a. Which equation represents the best estimate for the total cost of all the bolts?

  • 333033 \approx 30, 0.380.400.38 \approx 0.40.
    Thus, the best estimate for the total cost is:
    0.40×30=12.0.40 \times 30 = 12.

Answer: Option B ($0.40 \times 30 = 12$)


b. What is the ACTUAL total cost of all the bolts?

The exact cost is:
33×0.38=12.54.33 \times 0.38 = 12.54.

Answer: $12.54


3. Which expression shows the area of the shaded part of the grid?

The grid shows 4×74 \times 7 small squares shaded. The grid size is 10×1010 \times 10, meaning the area of each small square is 0.1×0.1=0.010.1 \times 0.1 = 0.01. Thus, the shaded area is:
4×7×0.01=0.04×0.07.4 \times 7 \times 0.01 = 0.04 \times 0.07.

Answer: Option A (0.04 × 0.07)


4. Match the expressions to their products

  • 8×0.09=0.728 \times 0.09 = 0.72
  • 0.8×0.09=0.0720.8 \times 0.09 = 0.072
  • 80×0.9=7280 \times 0.9 = 72
  • 8×0.9=7.28 \times 0.9 = 7.2

Answers:

  • 8×0.09=0.728 \times 0.09 = 0.72
  • 0.8×0.09=0.0720.8 \times 0.09 = 0.072
  • 80×0.9=7280 \times 0.9 = 72
  • 8×0.9=7.28 \times 0.9 = 7.2

5. Choose all the expressions equal to 0.7×0.410.7 \times 0.41:

Converting 0.70.7 and 0.410.41 to fractions:
0.7=710,0.41=41100.0.7 = \frac{7}{10}, \quad 0.41 = \frac{41}{100}.
Thus:
0.7×0.41=710×41100=7×4110×100.0.7 \times 0.41 = \frac{7}{10} \times \frac{41}{100} = \frac{7 \times 41}{10 \times 100}.

Valid expressions are:

  • 710×41100\frac{7}{10} \times \frac{41}{100}
  • 7100×4110\frac{7}{100} \times \frac{41}{10}
  • 70100×4110\frac{70}{100} \times \frac{41}{10}.

Answers: Options A, B, C, and E.


6. Emily bought seashells for $0.75 each.

Emily bought 10 seashells, and her friend bought 100. Total cost:

  • Emily: 10×0.75=7.5010 \times 0.75 = 7.50.
  • Friend: 100×0.75=75.00100 \times 0.75 = 75.00.

Total spent: 7.50+75.00=82.507.50 + 75.00 = 82.50.

Answer: $82.50


Questions for further exploration:

  1. How would the answer to Question 1 change if the liquid amount was 0.50.5 fluid ounces per bottle?
  2. What is the cost of 50 bolts at $0.38 each?
  3. What happens to the shaded area calculation if the grid size changes?
  4. What is the sum of the products in Question 4?
  5. How much would Emily and her friend spend if seashells cost $1.00 each instead?

Tip:

To estimate accurately, round numbers based on their magnitude and keep calculations simple!

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Math Problem Analysis

Mathematical Concepts

Multiplication of decimals
Estimation and rounding
Area calculation
Matching expressions to values
Fraction multiplication

Formulas

Area = length × width
Multiplication of fractions: a/b × c/d = (a×c)/(b×d)

Theorems

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Suitable Grade Level

Grades 5-7