$8 \frac{1}{12}-5 \frac{5}{12}$
Answer (2)
Convert the mixed numbers to improper fractions: 8 12 1 = 12 97 and 5 12 5 = 12 65 .
Subtract the improper fractions: 12 97 − 12 65 = 12 32 .
Simplify the resulting fraction: 12 32 = 3 8 .
Convert the improper fraction back to a mixed number: 3 8 = 2 3 2 . The final answer is 2 3 2 .
Explanation
Understanding the Problem We are asked to subtract two mixed numbers: 8 12 1 and 5 12 5 .
Converting to Improper Fractions First, let's convert the mixed numbers to improper fractions. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. This result becomes the new numerator, and we keep the same denominator.
For 8 12 1 , we have 8 × 12 + 1 = 96 + 1 = 97 . So, 8 12 1 = 12 97 .
For 5 12 5 , we have 5 × 12 + 5 = 60 + 5 = 65 . So, 5 12 5 = 12 65 .
Subtracting the Fractions Now, we subtract the two improper fractions: 12 97 − 12 65 = 12 97 − 65 = 12 32
Simplifying the Fraction Next, we simplify the resulting fraction. Both the numerator and the denominator are divisible by 4: 12 32 = 12 ÷ 4 32 ÷ 4 = 3 8
Converting Back to a Mixed Number Finally, we convert the improper fraction back to a mixed number. To do this, we divide the numerator by the denominator. The quotient becomes the whole number part, the remainder becomes the new numerator, and we keep the same denominator.
Dividing 8 by 3, we get a quotient of 2 and a remainder of 2. So, 3 8 = 2 3 2 .
Final Answer Therefore, 8 12 1 − 5 12 5 = 2 3 2 .
Examples
Understanding how to subtract mixed numbers is useful in everyday situations, such as when you're measuring ingredients for a recipe. For example, if you need 8 12 1 cups of flour and you only have 5 12 5 cups, you can calculate how much more flour you need to borrow from a neighbor. This skill is also helpful in woodworking or sewing when you need to cut materials to specific lengths.
To subtract the mixed numbers 8 12 1 and 5 12 5 , we convert them to improper fractions, subtract them to get 12 32 , simplify it to 3 8 , and convert back to a mixed number, resulting in 2 3 2 .
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