Adding Subtracting Fractionswith Unlike Denominators Strategy ... - Free Printable

Problem:

The task involves adding fractions with unlike denominators. The example provided is:

$$
\frac{1}{2} + \frac{2}{5}
$$

We are asked to solve this step by step, following the guidelines given in the image.

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Solution:

#### Step 1: Find a common denominator by finding the Least Common Multiple (LCM)

To add or subtract fractions with different denominators, we need a common denominator. The denominators here are 2 and 5.

- Multiples of 2: $ 2, 4, 6, 8, 10, 12, 14, \ldots $
- Multiples of 5: $ 5, 10, 15, 20, 25, \ldots $

The smallest multiple that both denominators share is the Least Common Multiple (LCM). In this case, the LCM of 2 and 5 is 10. Therefore, the common denominator will be 10.

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#### Step 2: Make your equivalent fractions

Now, we convert each fraction to an equivalent fraction with the common denominator of 10.

1. For $\frac{1}{2}$:
- To get a denominator of 10, we multiply both the numerator and the denominator by 5:
$$
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
$$

2. For $\frac{2}{5}$:
- To get a denominator of 10, we multiply both the numerator and the denominator by 2:
$$
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
$$

So, the equivalent fractions are:
$$
\frac{1}{2} = \frac{5}{10} \quad \text{and} \quad \frac{2}{5} = \frac{4}{10}
$$

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#### Step 3: Add the equivalent fractions

Now that both fractions have the same denominator, we can add them directly by adding their numerators:

$$
\frac{5}{10} + \frac{4}{10} = \frac{5 + 4}{10} = \frac{9}{10}
$$

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#### Step 4: Check if the answer is in lowest terms

The fraction $\frac{9}{10}$ is already in its simplest form because 9 and 10 have no common factors other than 1. Therefore, no further reduction is needed.

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Final Answer:

$$
\boxed{\frac{9}{10}}
$$