Which of the fractions is equivalent to 2/5
The Correct Answer and Explanation is:
The fraction equivalent to 25\frac{2}{5}52 can be found by multiplying both the numerator (2) and the denominator (5) by the same number, a process known as “scaling” or “multiplying by a factor.” When two fractions have the same ratio between the numerator and denominator, they are considered equivalent.
Let’s explore a few possibilities:
- Multiplying by 2:
If we multiply both the numerator and denominator of 25\frac{2}{5}52 by 2: 25×22=410\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}52×22=104 Thus, 410\frac{4}{10}104 is equivalent to 25\frac{2}{5}52. - Multiplying by 3:
Similarly, multiplying both parts of 25\frac{2}{5}52 by 3: 25×33=615\frac{2}{5} \times \frac{3}{3} = \frac{6}{15}52×33=156 So, 615\frac{6}{15}156 is another equivalent fraction. - Multiplying by 4:
We can also scale by 4: 25×44=820\frac{2}{5} \times \frac{4}{4} = \frac{8}{20}52×44=208 In this case, 820\frac{8}{20}208 is equivalent to 25\frac{2}{5}52.
Why Does This Work?
Fractions represent division. For example, 25\frac{2}{5}52 represents 2 divided by 5, or 0.4. To find an equivalent fraction, we need to scale the original fraction in such a way that the result still represents the same value. The key point here is that when you multiply the numerator and the denominator of a fraction by the same number (whether it’s 2, 3, 4, or any other nonzero number), you are not changing the value of the fraction. You are simply expressing it in a different form.
In summary, fractions like 410\frac{4}{10}104, 615\frac{6}{15}156, and 820\frac{8}{20}208 are all equivalent to 25\frac{2}{5}52 because they maintain the same value (0.4), even though they look different in their numerators and denominators.
