How many fractions are equivalent to 4/5
The Correct Answer and Explanation is:
There are infinitely many fractions equivalent to ( \frac{4}{5} ). The reason for this is that any fraction can be made equivalent to another by multiplying both the numerator and the denominator by the same non-zero integer. This is known as multiplying by a “common factor” or using “equivalent fractions.”
Explanation:
A fraction consists of two parts: the numerator (the number on top) and the denominator (the number on the bottom). In the fraction ( \frac{4}{5} ), 4 is the numerator, and 5 is the denominator. To create an equivalent fraction, you can multiply both the numerator and the denominator by any non-zero integer (called the scaling factor).
For example:
- Multiply both the numerator and denominator by 2:
[
\frac{4 \times 2}{5 \times 2} = \frac{8}{10}
]
So, ( \frac{8}{10} ) is equivalent to ( \frac{4}{5} ). - Multiply both the numerator and denominator by 3:
[
\frac{4 \times 3}{5 \times 3} = \frac{12}{15}
]
So, ( \frac{12}{15} ) is equivalent to ( \frac{4}{5} ). - Multiply both the numerator and denominator by 5:
[
\frac{4 \times 5}{5 \times 5} = \frac{20}{25}
]
So, ( \frac{20}{25} ) is equivalent to ( \frac{4}{5} ).
This process can be repeated with any integer. The key point is that the value of the fraction remains the same as long as the scaling factor is applied to both parts of the fraction. The reason for this is that multiplying both the numerator and denominator by the same number does not change the ratio between them.
Thus, there are an infinite number of fractions that are equivalent to ( \frac{4}{5} ), because you can always multiply the numerator and denominator by any non-zero integer to get a new equivalent fraction. The concept is based on the fact that the ratio between the numerator and denominator remains constant across all equivalent fractions.