How to Navigate the Fraction Jungle: A Guide to Adding Fractions with Unlike Denominators

Fractions are everywhere - from dividing a pizza among friends to measuring ingredients in a recipe. But what happens when we need to add fractions with different denominators?

While it might seem a bit tricky at first, with a systematic approach, it becomes a piece of cake. In this post, we’ll break down the steps to successfully add fractions with unlike denominators.

Step-by-step Guide:

1. Understanding the Fraction Structure:

A fraction consists of a numerator (the top number) and a denominator (the bottom number). The denominator indicates the total number of equal parts, while the numerator tells us how many of those parts we’re considering.

2. Identifying Unlike Denominators:

If two fractions have different denominators, they have unlike denominators. For instance, in the fractions \(\frac{2}{3}\) and \(\frac{4}{5}\), the denominators 3 and 5 are different.

3. Finding the Least Common Denominator (LCD):

The LCD is the smallest number that both denominators can divide into. It ensures that we’re working with fractions that describe parts of the same size. For our example, the LCD for 3 and 5 is 15.

4. Adjusting the Fractions to the LCD:

Multiply the numerator and denominator of each fraction by the factor needed to achieve the LCD. For \(\frac{2}{3}\), multiply both the numerator and denominator by 5 to get \(\frac{10}{15}\). For \(\frac{4}{5}\), multiply both by 3 to get \(\frac{12}{15}\).

5. Adding the Fractions:

Now that the fractions have the same denominator, simply add their numerators. Using our example, \(10 + 12 = 22\). So, \(\frac{2}{3} + \frac{4}{5} = \frac{22}{15}\), which can be expressed as \(1 \frac{7}{15}\).

Example 1:

Add \(\frac{1}{4}\) and \(\frac{2}{8}\).

Solution:

The LCD is 8. Adjusting the fractions, \(\frac{1}{4}\) becomes \(\frac{2}{8}\). So, \(\frac{1}{4} + \frac{2}{8} = \frac{4}{8}\), which simplifies to \(\frac{1}{2}\).

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Example 2:

Add \(\frac{3}{6}\) and \(\frac{1}{3}\).

Solution:

The LCD is 6. The fraction \(\frac{3}{6}\) remains the same, while \(\frac{1}{3}\) becomes \(\frac{2}{6}\). So, \(\frac{3}{6} + \frac{1}{3} = \frac{5}{6}\).

Practice Questions:

1. Add \(\frac{1}{5}\) and \(\frac{2}{10}\).

2. Add \(\frac{3}{7}\) and \(\frac{2}{14}\).

3. Add \(\frac{4}{9}\) and \(\frac{2}{3}\).

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Answers:

1. \(\frac{3}{10}\)

2. \(\frac{4}{7}\)

3. \(\frac{10}{9}\) or \(1 \frac{1}{9}\)

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How to Navigate the Fraction Jungle: A Guide to Adding Fractions with Unlike Denominators