7⅓ + 9⅓ + 12⅓ =
Understand the Problem
The question is asking to calculate the sum of three fractions: 7⅓, 9⅓, and 12⅓. The approach involves first converting each mixed fraction into an improper fraction or directly adding the whole numbers and then the fractions.
Answer
29
Answer for screen readers
The sum of the fractions is (29).
Steps to Solve
- Convert Mixed Numbers to Improper Fractions
Convert each mixed number into an improper fraction.
For (7 \frac{1}{3}): $$ 7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3} $$
For (9 \frac{1}{3}): $$ 9 \frac{1}{3} = \frac{9 \times 3 + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3} $$
For (12 \frac{1}{3}): $$ 12 \frac{1}{3} = \frac{12 \times 3 + 1}{3} = \frac{36 + 1}{3} = \frac{37}{3} $$
- Add the Improper Fractions
Now that we have the improper fractions, we can add them together:
$$ \frac{22}{3} + \frac{28}{3} + \frac{37}{3} $$
Since the denominators are all the same, add the numerators:
$$ \frac{22 + 28 + 37}{3} = \frac{87}{3} $$
- Simplify the Fraction (if necessary)
The improper fraction can be simplified or converted back to a mixed number:
To convert ( \frac{87}{3} ):
- Divide (87) by (3): $$ 87 \div 3 = 29 \text{ remainder } 0 $$
Thus, ( \frac{87}{3} = 29 ).
The sum of the fractions is (29).
More Information
The process of adding mixed numbers involves converting them to improper fractions, which makes it simpler to perform the addition. The end result of (29) shows that when combining these values, the total is a whole number with no remainder.
Tips
- Forgetting to convert all mixed numbers to improper fractions before adding.
- Adding the whole number parts and fractional parts separately without proper consideration of the shared denominator in fractions.
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