Equivalent Fractions. Grade 3 - Free Printable

The image illustrates a fundamental concept in working with fractions: equivalent fractions.

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🔍 Problem Explanation:

We are given:

$$
\frac{2}{5} = \frac{4}{10}
$$

And arrows show that:
- The numerator (top) is multiplied by 2: $ 2 \times 2 = 4 $
- The denominator (bottom) is also multiplied by 2: $ 5 \times 2 = 10 $

This demonstrates the rule:

> ✔ Whatever you do to the top (numerator), you must do to the bottom (denominator) to keep the fraction equivalent.

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🧠 Why This Works:

A fraction represents a part of a whole. When you multiply both the numerator and the denominator by the same number, you're essentially multiplying the fraction by 1 in the form of $ \frac{2}{2} $, which doesn't change its value.

So:
$$
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
$$

Both $ \frac{2}{5} $ and $ \frac{4}{10} $ represent the same amount — just expressed differently.

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✔ Conclusion:

This is a key principle when simplifying or finding equivalent fractions:
> To create an equivalent fraction, multiply or divide both the numerator and the denominator by the same non-zero number.

In this case:
- $ \frac{2}{5} $ becomes $ \frac{4}{10} $ by multiplying both parts by 2.
- They are equal, even though they look different.

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💡 Tip: You can use this method to:
- Simplify fractions (divide top and bottom)
- Find common denominators (multiply to match)
- Compare fractions

Let me know if you'd like to see how this applies to other problems!