- Identify the least common multiple of the denominators 6 and 8, which is 24.
- Convert each fraction: \(\frac{5}{6} = \frac{20}{24}\) and \(\frac{3}{8} = \frac{9}{24}\).
- Sum the fractions to get \(\frac{29}{24}\).
- Convert the result to a decimal and round to the hundredths place, obtaining \(\boxed{1.21}\).
Explanation
- Finding a Common Denominator
To compute the sum of the fractions \(\frac{5}{6} + \frac{3}{8}\), we first need to find a common denominator for the two fractions. The denominators are 6 and 8. The least common multiple (LCM) of 6 and 8 is the smallest positive integer that is divisible by both 6 and 8.
- The prime factorization of 6 is \(2 \times 3\).
- The prime factorization of 8 is \(2^3\).
- The LCM is \(2^3 \times 3 = 8 \times 3 = 24\).
- Converting and Adding Fractions
Now, we convert each fraction to an equivalent fraction with a denominator of 24:
- For \(\frac{5}{6}\), we multiply both the numerator and denominator by 4: \(\frac{5 \times 4}{6 \times 4} = \frac{20}{24}\).
- For \(\frac{3}{8}\), we multiply both the numerator and denominator by 3: \(\frac{3 \times 3}{8 \times 3} = \frac{9}{24}\).
Now, we add the two fractions together: \(\frac{20}{24} + \frac{9}{24} = \frac{29}{24}\).
- Converting to Decimal and Rounding
To express the sum as a decimal, we perform the division \(\frac{29}{24}\):
\(29 \div 24 \approx 1.208333...\)
To round the decimal to the hundredths place, we look at the third decimal digit, which is 8. Since 8 is greater than or equal to 5, we round up the second decimal digit from 0 to 1. Thus, the rounded value is 1.21.
Examples
In cooking, you often need to combine different measurements. If a recipe calls for \(\frac{5}{6}\) of a cup of flour for one batch and you decide to add \(\frac{3}{8}\) of a cup more, you need to calculate the total amount of flour required. Converting these fractions to a single decimal value makes it much easier to measure out the ingredient using standard kitchen tools. In this case, you would need approximately 1.21 cups of flour.