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To solve the problem of adding the fractions and , we start by finding the least common denominator (LCD).
First, we identify the denominators: 2 and 6. The least common multiple of 2 and 6 is 6, which will be our LCD.
Next, we convert each fraction to have the denominator of 6:
Convert to an equivalent fraction with a denominator of 6. Since , multiply the numerator by 3: .
The fraction already has the desired common denominator.
Now that the fractions are and , we can add them:
.
The solution to the problem is , which matches choice 2.
Complete the following exercise:
\( \frac{3}{4}:\frac{5}{6}=\text{?} \)
You can't add fractions by adding across because fractions represent parts of different-sized wholes. means 1 part out of 2, while means 4 parts out of 6. You need the same-sized parts first!
Look for the smallest number that both denominators divide into evenly. For 2 and 6: since 6 ÷ 2 = 3 (no remainder), the LCD is 6. You can also list multiples: 2, 4, 6, 8... and 6, 12, 18...
That's perfectly fine! is correct as an improper fraction. You could convert it to , but both forms are mathematically correct.
It's good practice to check if your answer can be simplified, but is already in lowest terms since 7 and 6 share no common factors other than 1.
Same process! Find the LCD by listing multiples: 8, 16, 24... and 12, 24, 36... The LCD is 24. Convert each fraction to twenty-fourths, then add the numerators.
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