Compute:
a) 3\frac{2}{3} + \frac{1}{4}
The mixed number 3 2/3 is converted to the improper fraction \frac{11}{3}.
Answer (2)
To compute 3 3 2 + 4 1 , first convert the mixed number to an improper fraction: 3 11 . Finding a common denominator of 12, the sum is 12 47 which can be expressed as the mixed number 3 12 11 .
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To solve the given problem of adding fractions, let's break it down step by step. We are asked to add the mixed number 3 3 2 and the fraction 4 1 .
Convert the Mixed Number to an Improper Fraction: - The mixed number 3 3 2 can be converted to an improper fraction. - Multiply the whole number 3 by the denominator 3 and add the numerator 2: 3 × 3 + 2 = 9 + 2 = 11 .
- The improper fraction is 3 11 .
Add the Fractions: - The fractions 3 11 and 4 1 need a common denominator to be added. - The least common denominator (LCD) for 3 and 4 is 12.
Convert Fractions to Have the Same Denominator: - Convert 3 11 to a fraction with a denominator of 12: 3 11 × 4 4 = 12 44 .
- Convert 4 1 to a fraction with a denominator of 12: 4 1 × 3 3 = 12 3 .
Add the Converted Fractions: - Now, add 12 44 and 12 3 : 12 44 + 12 3 = 12 47 .
Convert the Result to a Mixed Number (if necessary): - 12 47 can be converted to a mixed number. - Divide 47 by 12 which gives 3 with a remainder of 11. - The mixed number is 3 12 11 .
Therefore, 3 3 2 + 4 1 = 3 12 11 .
