$4 \frac{1}{8}-2 \frac{5}{8}$
Answer (2)
Convert the mixed fractions to improper fractions: 4 8 1 = 8 33 and 2 8 5 = 8 21 .
Subtract the improper fractions: 8 33 − 8 21 = 8 12 .
Simplify the fraction: 8 12 = 2 3 .
Convert the improper fraction back to a mixed fraction: 2 3 = 1 2 1 . The final answer is 1 2 1 .
Explanation
Understanding the problem We are asked to evaluate the expression 4 8 1 − 2 8 5 . This involves subtracting two mixed fractions.
Converting to improper fractions First, we convert the mixed fractions to improper fractions. We have
4 8 1 = 8 4 × 8 + 1 = 8 32 + 1 = 8 33
and
2 8 5 = 8 2 × 8 + 5 = 8 16 + 5 = 8 21
Subtracting the fractions Now we subtract the two improper fractions:
8 33 − 8 21 = 8 33 − 21 = 8 12
Simplifying the fraction We simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
8 12 = 8 ÷ 4 12 ÷ 4 = 2 3
Converting back to a mixed fraction Finally, we convert the improper fraction 2 3 back to a mixed fraction:
2 3 = 1 2 1
Final Answer Therefore, 4 8 1 − 2 8 5 = 8 33 − 8 21 = 8 12 = 2 3 = 1 2 1 .
Examples
Understanding fractions is crucial in everyday situations, such as cooking, where you might need to adjust recipe quantities. For instance, if a recipe calls for 2 2 1 cups of flour, but you only want to make half the recipe, you need to calculate half of 2 2 1 . Converting this to an improper fraction gives 2 5 , and halving it results in 4 5 , which is 1 4 1 cups. This skill ensures your culinary creations turn out perfectly!
To solve 4 8 1 − 2 8 5 , convert the mixed numbers to improper fractions, perform the subtraction, simplify the result, and convert back to a mixed number. The final answer is 1 2 1 .
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