$9 \frac{3}{4}-2 \frac{2}{8}$
Answer (1)
Convert the mixed numbers to improper fractions: 9 r a c 3 4 = r a c 39 4 and 2 r a c 2 8 = r a c 18 8 .
Simplify the fraction: r a c 18 8 = r a c 9 4 .
Subtract the fractions: r a c 39 4 − r a c 9 4 = r a c 30 4 .
Simplify the result and convert to a mixed number or decimal: r a c 30 4 = r a c 15 2 = 7 r a c 1 2 = 7.5 . The final answer is 7.5 .
Explanation
Understanding the Problem We are asked to evaluate the expression 9 r a c 3 4 − 2 r a c 2 8 . This involves subtracting two mixed numbers. To do this, we can convert the mixed numbers to improper fractions, find a common denominator, and then subtract the fractions.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions:
9 r a c 3 4 = r a c 9 × 4 + 3 4 = r a c 36 + 3 4 = r a c 39 4
2 r a c 2 8 = r a c 2 × 8 + 2 8 = r a c 16 + 2 8 = r a c 18 8
Simplifying the Fraction Simplify the second fraction:
r a c 18 8 = r a c 9 4
Subtracting the Fractions Now, subtract the two fractions:
r a c 39 4 − r a c 9 4 = r a c 39 − 9 4 = r a c 30 4
Simplifying the Result Simplify the result:
r a c 30 4 = r a c 15 2
Converting Back to a Mixed Number Convert the improper fraction back to a mixed number:
r a c 15 2 = 7 r a c 1 2
Expressing as a Decimal Alternatively, we can express the answer as a decimal:
7 r a c 1 2 = 7.5
Final Answer Therefore, 9 r a c 3 4 − 2 r a c 2 8 = 7 r a c 1 2 = 7.5 .
Examples
Understanding fractions and mixed numbers is crucial in everyday situations, such as cooking and baking. For instance, if a recipe calls for 9 r a c 3 4 cups of flour and you only want to make a smaller batch that requires reducing the ingredients by 2 r a c 2 8 cups, you need to calculate the difference to determine the new amount of flour needed. This problem demonstrates how subtracting mixed numbers can help you adjust recipes accurately, ensuring your culinary creations turn out perfectly.
