Subtract. Reduce to lowest terms.
$10 \frac{1}{4}-9 \frac{5}{6}=$
A. $1 \frac{5}{12}$
B. $1 \frac{7}{12}$
C. $\frac{7}{12}$
D. $\frac{5}{12}$
Answer (2)
Convert the mixed numbers to improper fractions: 10 a rc 1 4 = a rc 41 4 and 9 a rc 5 6 = a rc 59 6 .
Find a common denominator and subtract: \farc 41 4 − \farc 59 6 = \farc 123 12 − \farc 118 12 .
Subtract the numerators: \farc 123 12 − \farc 118 12 = \farc 5 12 .
The result is already in lowest terms: \farc 5 12 .
Explanation
Problem Analysis We are asked to subtract two mixed numbers, 10 a rc 1 4 and 9 a rc 5 6 , and reduce the result to lowest terms.
Convert to Improper Fractions First, convert the mixed numbers to improper fractions. 10 a rc 1 4 = a rc 10 × 4 + 1 4 = a rc 41 4
9 a rc 5 6 = a rc 9 × 6 + 5 6 = a rc 59 6
Find Common Denominator Now, subtract the improper fractions. To do this, we need a common denominator. The least common multiple of 4 and 6 is 12. \farc 41 4 − \farc 59 6 = \farc 41 × 3 4 × 3 − \farc 59 × 2 6 × 2 = \farc 123 12 − \farc 118 12
Subtract Fractions Subtract the numerators: \farc 123 12 − \farc 118 12 = \farc 123 − 118 12 = \farc 5 12
Reduce to Lowest Terms The fraction \farc 5 12 is already in its lowest terms, since the greatest common divisor of 5 and 12 is 1.
Final Answer Therefore, 10 a rc 1 4 − 9 a rc 5 6 = a rc 5 12 .
Examples
Understanding fractions is essential in everyday situations, such as cooking, where you might need to adjust recipe quantities. For instance, if a recipe calls for 2 a rc 1 2 cups of flour, but you only want to make half the recipe, you need to calculate half of 2 a rc 1 2 . This involves multiplying fractions, which is a practical application of the math we just did. Similarly, when splitting a bill among friends after a meal, you often need to divide the total cost by the number of people, which again involves fractions and decimals.
To subtract 10 4 1 and 9 6 5 , we first convert them to improper fractions, find a common denominator, and subtract the fractions. The solution yields 12 5 , which is already in its lowest terms. The correct choice is D. 12 5 .
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