To create equivalent fractions with different denominators, you need to find a common denominator and then adjust the numerators accordingly. Here's a step-by-step guide:
1. Find a Common Denominator:
The easiest way to find a common denominator is to identify the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators divide into evenly.
- Example: Let's say you want to find equivalent fractions for 2/3 and 1/4.
- The multiples of 3 are: 3, 6, 9, 12, 15...
- The multiples of 4 are: 4, 8, 12, 16...
- The least common multiple (LCM) of 3 and 4 is 12. Therefore, 12 will be our common denominator.
2. Convert the Fractions:
Now you need to convert each fraction into an equivalent fraction with the common denominator. To do this:
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Divide the common denominator by the original denominator.
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Multiply both the numerator and the denominator of the original fraction by the result.
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Example (2/3):
- 12 (common denominator) / 3 (original denominator) = 4
- Multiply the numerator and denominator of 2/3 by 4: (2 4) / (3 4) = 8/12
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Example (1/4):
- 12 (common denominator) / 4 (original denominator) = 3
- Multiply the numerator and denominator of 1/4 by 3: (1 3) / (4 3) = 3/12
3. Result:
You now have equivalent fractions:
- 2/3 is equivalent to 8/12
- 1/4 is equivalent to 3/12
You can now add, subtract, or compare these fractions easily because they have the same denominator.
In summary, the process involves finding a common denominator (usually the LCM) and then multiplying both the numerator and denominator of each fraction by the appropriate factor to achieve that common denominator.
