$2 \frac{1}{4}-\left(-3 \frac{1}{6}\right)$
Answer (2)
To find the value of the expression 2 4 1 − ( − 3 6 1 ) , we first convert the mixed numbers to improper fractions, rewrite the expression as a sum, find a common denominator, and then add the fractions. This results in an answer of 5 12 5 .
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Convert the mixed numbers to improper fractions: 2 4 1 = 4 9 and − 3 6 1 = − 6 19 .
Rewrite the expression as a sum: 4 9 + 6 19 .
Find a common denominator (12) and convert the fractions: 12 27 + 12 38 .
Add the fractions and convert back to a mixed number: 12 65 = 5 12 5 .
5 12 5
Explanation
Understanding the problem We are asked to evaluate the expression 2 4 1 − ( − 3 6 1 ) . This involves mixed numbers and the subtraction of a negative number, which is the same as addition.
Converting to improper fractions First, let's convert the mixed numbers to improper fractions. We have:
2 4 1 = 4 2 × 4 + 1 = 4 8 + 1 = 4 9 and
3 6 1 = 6 3 × 6 + 1 = 6 18 + 1 = 6 19
Rewriting the expression Now, we can rewrite the original expression as:
4 9 − ( − 6 19 ) = 4 9 + 6 19
Finding a common denominator To add these fractions, we need to find a common denominator. The least common multiple of 4 and 6 is 12. So, we convert both fractions to have a denominator of 12:
4 9 = 4 × 3 9 × 3 = 12 27 and
6 19 = 6 × 2 19 × 2 = 12 38
Adding the fractions Now we can add the fractions:
12 27 + 12 38 = 12 27 + 38 = 12 65
Converting back to a mixed number Finally, we convert the improper fraction 12 65 back to a mixed number. We divide 65 by 12:
65 ÷ 12 = 5 with a remainder of 5 .
So, 12 65 = 5 12 5
Final Answer Therefore, 2 4 1 − ( − 3 6 1 ) = 5 12 5 .
Examples
Understanding how to add and subtract mixed numbers is useful in everyday situations, such as when you're cooking and need to combine different amounts of ingredients. For example, if a recipe calls for 2 4 1 cups of flour and you want to increase the recipe, you might need to add 3 6 1 cups more. Knowing how to perform these calculations accurately ensures your recipe turns out perfectly!
