$2 \frac{7}{11}-\frac{7}{8}$
Answer (1)
Convert the mixed number to an improper fraction: 2 r a c 7 11 = r a c 29 11 .
Find a common denominator: The least common multiple of 11 and 8 is 88.
Convert to equivalent fractions: r a c 29 11 = r a c 232 88 and r a c 7 8 = r a c 77 88 .
Subtract the fractions: r a c 232 88 − r a c 77 88 = \f r a c 155 88 .
Explanation
Understanding the Problem We are asked to evaluate the expression 2 r a c 7 11 − r a c 7 8 . This involves mixed numbers and fractions, so we need to convert the mixed number to an improper fraction before performing the subtraction.
Converting to Improper Fraction First, convert the mixed number 2 r a c 7 11 to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (11) and add the numerator (7). This gives us 2 im es 11 + 7 = 22 + 7 = 29 . So, 2 r a c 7 11 = r a c 29 11 .
Finding a Common Denominator Now we rewrite the expression with the improper fraction: r a c 29 11 − r a c 7 8 . To subtract these fractions, we need to find a common denominator. The least common multiple of 11 and 8 is 11 im es 8 = 88 .
Creating Equivalent Fractions Next, we convert both fractions to equivalent fractions with the common denominator of 88. To convert r a c 29 11 to an equivalent fraction with a denominator of 88, we multiply both the numerator and the denominator by 8: r a c 29 im es 8 11 im es 8 = r a c 232 88 . To convert r a c 7 8 to an equivalent fraction with a denominator of 88, we multiply both the numerator and the denominator by 11: r a c 7 im es 11 8 im es 11 = r a c 77 88 .
Subtracting the Fractions Now we can subtract the two fractions: r a c 232 88 − r a c 77 88 = r a c 232 − 77 88 = r a c 155 88 .
Final Answer The resulting fraction is r a c 155 88 . We can leave it as an improper fraction, or convert it to a mixed number. To convert it to a mixed number, we divide 155 by 88. The quotient is 1 and the remainder is 155 − 88 = 67 . So, r a c 155 88 = 1 r a c 67 88 . The problem asks for the result of the subtraction, so the final answer is \f r a c 155 88 .
Examples
Understanding fraction arithmetic is essential in various real-life situations, such as cooking, where you might need to adjust ingredient quantities. For instance, if a recipe calls for 2 r a c 7 11 cups of flour, but you only want to make 8 7 of the recipe, you'd need to calculate 2 r a c 7 11 − 8 7 to determine how much flour to reduce. This calculation ensures that your adjustments maintain the recipe's intended balance and flavor.
