Math Problem Statement

A dressmaker bought 1/2 meter each of red, blue and white cloth to make a costume. How many total meters of cloth did the dressmaker use if she removed an eighth of each cloth to make it?

Solution

To find out how many total meters of cloth the dressmaker used, we need to perform the following steps:

  1. Determine the amount of cloth removed from each color:
    Each cloth is 1/2 meter. The dressmaker removed 1/8 of each piece.

    Cloth removed per color=18×12=116 meters\text{Cloth removed per color} = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16} \text{ meters}

  2. Calculate the remaining cloth for each color:
    The remaining cloth for each color is the original amount minus the amount removed.

    Remaining cloth per color=12116=816116=716 meters\text{Remaining cloth per color} = \frac{1}{2} - \frac{1}{16} = \frac{8}{16} - \frac{1}{16} = \frac{7}{16} \text{ meters}

  3. Calculate the total amount of remaining cloth:
    Since there are three colors (red, blue, and white), the total amount of cloth used is:

    Total cloth used=3×716=2116 meters\text{Total cloth used} = 3 \times \frac{7}{16} = \frac{21}{16} \text{ meters}

  4. Convert the fraction to a decimal or mixed number (optional):

    2116 meters=1516 meters=1.3125 meters\frac{21}{16} \text{ meters} = 1 \frac{5}{16} \text{ meters} = 1.3125 \text{ meters}

So, the dressmaker used a total of 1.3125 meters of cloth.

Would you like more details or have any questions?


Here are 5 related questions you might find useful:

  1. What if the dressmaker had started with 3/4 meter of each color?
  2. How much cloth would be left after making the costume?
  3. How many costumes can the dressmaker make if each costume requires 1.3125 meters of cloth?
  4. What fraction of the total cloth was removed during the process?
  5. If the dressmaker used 2/3 of the total cloth, how much was left?

Tip: When working with fractions, it's helpful to find a common denominator when adding or subtracting them.

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Math Problem Analysis

Mathematical Concepts

Fractions
Subtraction
Multiplication

Formulas

Cloth removed per color = (1/8) * (1/2) = 1/16 meters
Remaining cloth per color = (1/2) - (1/16) = 7/16 meters
Total cloth used = 3 * (7/16) = 21/16 meters

Theorems

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Suitable Grade Level

Grades 4-6