Verified Answer :

  • Identify the least common multiple of the denominators 10 and 4, which is 20.
  • Convert each fraction to an equivalent fraction with a denominator of 20: \(\frac{3}{10} = \frac{6}{20}\) and \(\frac{1}{4} = \frac{5}{20}\).
  • Add the numerators while maintaining the common denominator: \(\frac{6}{20} + \frac{5}{20} = \frac{11}{20}\).
  • Conclude that the result is \(\boxed{\frac{11}{20}}\).

Explanation

  1. Finding the Common Denominator

To add the fractions \(\frac{3}{10}\) and \(\frac{1}{4}\), we must ensure they have a common denominator. The denominators are 10 and 4. The least common multiple (LCM) of 10 and 4 is the smallest number that is a multiple of both. Listing the multiples:

  • Multiples of 10: 10, 20, 30, 40, ...
  • Multiples of 4: 4, 8, 12, 16, 20, 24, ...

The least common multiple is 20.

  1. Converting Fractions to Equivalent Fractions

We convert both fractions to have 20 as their denominator:

  • For \(\frac{3}{10}\), multiply the numerator and denominator by 2: \(\frac{3 \times 2}{10 \times 2} = \frac{6}{20}\).
  • For \(\frac{1}{4}\), multiply the numerator and denominator by 5: \(\frac{1 \times 5}{4 \times 5} = \frac{5}{20}\).
  1. Adding the Fractions and Simplifying

Now that the fractions have the same denominator, we add them by summing their numerators:
\[\frac{6}{20} + \frac{5}{20} = \frac{6 + 5}{20} = \frac{11}{20}.\]
Since 11 is a prime number and not a factor of 20, the fraction \(\frac{11}{20}\) is already in its simplest form.

Examples

Adding fractions is a fundamental skill used in everyday situations like cooking, where you might need to add fractional portions of ingredients. For example, if a recipe calls for \(\frac{3}{10}\) of a cup of sugar for a base mixture and you decide to add an extra \(\frac{1}{4}\) cup of sugar for sweetness, you calculate the total amount of sugar needed as \(\frac{3}{10} + \frac{1}{4} = \frac{11}{20}\) of a cup. This skill helps ensure your measurements are accurate and your proportions are correct.

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