Exercise: Fractions & Decimals

Questions for: Conversion and Calculation

A tailor needs a total of 4 1/2 meters of fabric for a custom order. They currently have one piece measuring 2.75 meters and another piece measuring 7/8 meters. How much more fabric, in meters, does the tailor need to acquire to complete the order?
A: 0.875 m
B: 1.75 m
C: 1.05 m
D: 0.85 m
Answer: A
1. Convert all measurements to a consistent format, in this case, decimals. 2. Total fabric needed = 4 1/2 meters = 4.5 meters. 3. First piece on hand = 2.75 meters. 4. Second piece on hand = 7/8 meters = 0.875 meters. 5. Calculate the total fabric the tailor currently possesses: 2.75 + 0.875 = 3.625 meters. 6. Calculate the remaining fabric needed: 4.5 - 3.625 = 0.875 meters. Why others are wrong: B — This result (1.75 m) is obtained if only the 2.75 m piece is subtracted from the total needed, neglecting the 7/8 m piece (4.5 - 2.75 = 1.75). C — This result (1.05 m) is obtained if 7/8 is incorrectly converted or approximated as 0.7 (2.75 + 0.7 = 3.45; 4.5 - 3.45 = 1.05). D — This result (0.85 m) is obtained if 7/8 is incorrectly converted or approximated as 0.9 (2.75 + 0.9 = 3.65; 4.5 - 3.65 = 0.85).
A bakery uses 1/3 cup of flour for a small batch of cookies. To fulfill a special order, the baker needs to prepare 2.5 times this quantity. How much flour, expressed as a simplified fraction, will the baker need for the special order?
A: 5/6 cup
B: 2/3 cup
C: 1 1/6 cups
D: 1 2/3 cups
Answer: A
1. Identify the base quantity: 1/3 cup of flour. 2. Identify the multiplier: 2.5 times the quantity. 3. Convert the decimal multiplier to a fraction: 2.5 = 25/10 = 5/2. 4. Multiply the base quantity by the fractional multiplier: (1/3) * (5/2). 5. Perform the multiplication: (1 * 5) / (3 * 2) = 5/6. 6. The amount of flour needed is 5/6 cup. Why others are wrong: B — This results from multiplying 1/3 by 2 instead of 2.5, (1/3)*2 = 2/3. C — This results from an incorrect conversion of 2.5 to 7/2, leading to (1/3)*(7/2) = 7/6 = 1 1/6. D — This results from incorrectly multiplying 1/3 by 5, perhaps misinterpreting 2.5, (1/3)*5 = 5/3 = 1 2/3.
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