Fractions represent portions of a whole, and different fractions can represent the same value through the concept of equivalent fractions. Equivalent fractions are different fractions that express the same quantity or proportion of a whole.
Identify Fractions that Represent the Same Value
For example, consider the fraction 1/2. There are multiple fractions that represent the same value, including:
- 2/4
- 3/6
- 4/8
Each of these fractions can be simplified to 1/2, and they all denote the same proportion of a whole.
Create Fractions that Represent the Same Value
To create equivalent fractions, you can multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number.
For instance, to find fractions that represent the same value as 1/3, you could:
-
Multiply both the numerator and denominator by 2:
\(1 \times 2 / 3 \times 2 = 2/6\) -
Multiply both by 3:
\(1 \times 3 / 3 \times 3 = 3/9\) -
Divide both by 1 (keeping it the same):
\(1 / 3 = 1/3\)
All these fractions (1/3, 2/6, and 3/9) represent the same value.
In summary, the key to understanding that different fractions can represent the same value lies in the idea of equivalence, where you can create new fractions by scaling (multiplying or dividing) both the numerator and denominator by the same number.
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