- Find the least common multiple of 6 and 8, which is 24.
- Convert both fractions to an equivalent form with a denominator of 24: \(\frac{20}{24}\) and \(\frac{9}{24}\).
- Sum the fractions to get \(\frac{29}{24}\).
- Perform the division and round to two decimal places, resulting in \(\boxed{1.21}\).
Explanation
- Finding a Common Denominator
To find the sum of \(\frac{5}{6}\) and \(\frac{3}{8}\), we first need to express them with a common denominator. The least common multiple (LCM) of the denominators 6 and 8 is 24.
- Converting \(\frac{5}{6}\) to a denominator of 24: \(\frac{5 \times 4}{6 \times 4} = \frac{20}{24}\).
- Converting \(\frac{3}{8}\) to a denominator of 24: \(\frac{3 \times 3}{8 \times 3} = \frac{9}{24}\).
- Summing the Fractions
Now that both fractions share the same denominator, we can add them directly:
\(\frac{20}{24} + \frac{9}{24} = \frac{20 + 9}{24} = \frac{29}{24}\).
- Converting to a Decimal and Rounding
To convert the fraction \(\frac{29}{24}\) to a decimal, we perform the division:
\(29 \div 24 = 1.208333...\).
Rounding this value to the nearest hundredth, we look at the third decimal digit, which is 8. Since 8 is greater than 5, we round up the second decimal digit, resulting in 1.21. Thus, the sum is approximately 1.21.
Examples
Understanding how to add fractions is essential in various real-life scenarios, such as cooking, where you might need to combine different measurements of ingredients. For example, if a recipe calls for \(\frac{5}{6}\) of a cup of flour and then adds \(\frac{3}{8}\) of a cup more, you need to add these amounts together to know the total, which would be \(\frac{29}{24}\) or approximately \(1.21\) cups. Mastering this simple arithmetic helps in everyday tasks like project planning, construction, and managing finances.