Finding Pairs of Equivalent Fractions

Equivalent fractions are fractions that represent the same value despite having different numerators and denominators. Finding pairs of equivalent fractions involves identifying fractions that are equal to each other. Here are the steps to follow when looking for pairs of equivalent fractions:

Step 1: Identify the numerator and denominator of the given fraction.

Step 2: Multiply or divide both the numerator and denominator of the fraction by the same number to get a new fraction that has the same value as the original.

Step 3: Simplify the new fraction to its lowest terms (if possible).

Step 4: Check if the new fraction is equivalent to the original fraction.

Step 5: Repeat steps 2-4 with different numbers until all equivalent fractions have been found.

Example:

Let's find all the pairs of equivalent fractions for the fraction 4/8.

Step 1: The numerator is 4 and the denominator is 8.

Step 2: We can divide both the numerator and denominator by 4 to get 1/2.

4/8 ÷ 4/4 = 1/2

Step 3: The new fraction 1/2 is already in its lowest terms.

Step 4: 1/2 is equivalent to 4/8.

Step 5: We can also multiply both the numerator and denominator by 2 to get 8/16.

4/8 x 2/2 = 8/16

8/16 can be simplified to 1/2, which is equivalent to 4/8.

Therefore, the pairs of equivalent fractions for 4/8 are 1/2 and 8/16.

Conclusion

To find pairs of equivalent fractions, we need to identify the numerator and denominator of the given fraction, multiply or divide them by the same number, simplify the new fraction to its lowest terms, and check if the new fraction is equivalent to the original. By following these steps, we can find all the equivalent fractions for a given fraction.

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