Equivalent fraction for 5/3
The Correct Answer and Explanation is:
An equivalent fraction for ( \frac{5}{3} ) can be generated by multiplying both the numerator (5) and the denominator (3) by the same number. In this case, let’s choose 2 as the multiplier.
So, multiply both the numerator and denominator of ( \frac{5}{3} ) by 2:
[
\frac{5}{3} \times \frac{2}{2} = \frac{10}{6}
]
Thus, ( \frac{10}{6} ) is an equivalent fraction to ( \frac{5}{3} ).
Explanation:
A fraction represents the division of two numbers, with the numerator (the number above the fraction line) indicating how many parts we have, and the denominator (the number below the fraction line) indicating how many equal parts the whole is divided into.
Equivalent fractions are fractions that represent the same value or proportion, even though they may look different. To create equivalent fractions, we multiply or divide both the numerator and the denominator of a fraction by the same nonzero number. This does not change the value of the fraction because the operation preserves the ratio between the numerator and denominator.
In the case of ( \frac{5}{3} ), if we multiply both the numerator and the denominator by a number such as 2, we get:
[
\frac{5}{3} \times \frac{2}{2} = \frac{10}{6}
]
Here, ( \frac{10}{6} ) represents the same quantity as ( \frac{5}{3} ), but the fraction looks different. Both ( \frac{5}{3} ) and ( \frac{10}{6} ) are improper fractions because their numerators are greater than their denominators.
Alternatively, we can simplify a fraction to obtain an equivalent fraction. For example, ( \frac{10}{6} ) can be simplified by dividing both the numerator and the denominator by 2, resulting in ( \frac{5}{3} ). This demonstrates that ( \frac{5}{3} ) and ( \frac{10}{6} ) are equivalent fractions.
In conclusion, equivalent fractions like ( \frac{5}{3} ) and ( \frac{10}{6} ) have the same value but different numerators and denominators. They provide different ways of expressing the same ratio.