Can you complete the equation? How many fifths are equivalent to [tex] \frac{6}{10} ]?
The Correct Answer and Explanation is :
To find how many fifths are equivalent to (\frac{6}{10}), let’s solve the equation:
- First, simplify (\frac{6}{10}):
[
\frac{6}{10} = \frac{3}{5}
] - We want to express (\frac{3}{5}) in terms of fifths. Fifths are fractions with a denominator of 5, so let’s rewrite (\frac{3}{5}) as:
[
\frac{3}{5} = \frac{3 \times 1}{5} = 3 \times \frac{1}{5}
]
This shows that (\frac{3}{5}) is equivalent to 3 fifths. Thus, the answer is:
[
\frac{6}{10} = 3 \text{ fifths}
]
Explanation
The fraction (\frac{6}{10}) represents a part of a whole, where 10 is the total number of equal parts, and 6 is the number of those parts we’re considering. To convert this to an equivalent fraction in fifths, we need to change its form without changing its value.
Start by simplifying (\frac{6}{10}). Dividing both the numerator and the denominator by their greatest common divisor (2), we get (\frac{6 \div 2}{10 \div 2} = \frac{3}{5}). So, (\frac{6}{10}) is equivalent to (\frac{3}{5}).
Since fifths mean having a denominator of 5, we see that (\frac{3}{5}) represents 3 parts out of 5, or simply “3 fifths.” This equivalency allows us to say that (\frac{6}{10}) and (\frac{3}{5}) are the same amounts, just expressed differently. Converting between fractions like this helps in comparing, adding, or subtracting fractions and is especially useful in many real-life situations, such as measuring ingredients, distances, or portions.
By breaking down the fraction into fifths, we understand that (\frac{6}{10}) can be interpreted directly as “3 of the fifths,” giving us a clear and simplified answer: 3 fifths.