What two equivalent fractions equal 5/4
The Correct answer and Explanation is :
The correct answer is: ( \frac{10}{8} ) and ( \frac{15}{12} )
To find two equivalent fractions for ( \frac{5}{4} ), we can multiply the numerator and the denominator by the same non-zero integer. Equivalent fractions are fractions that represent the same value or proportion, even though they may have different numerators and denominators.
Step 1: Understanding Equivalent Fractions
An equivalent fraction can be obtained by multiplying or dividing both the numerator and the denominator by the same number. For example, if you have the fraction ( \frac{a}{b} ), multiplying both ( a ) and ( b ) by an integer ( k ) will give you ( \frac{ak}{bk} ), which is equivalent to ( \frac{a}{b} ).
Step 2: Finding Equivalent Fractions for ( \frac{5}{4} )
- First Equivalent Fraction:
- Let’s multiply the numerator and denominator of ( \frac{5}{4} ) by ( 2 ):
[
\frac{5 \times 2}{4 \times 2} = \frac{10}{8}
] - So, ( \frac{10}{8} ) is one equivalent fraction.
- Second Equivalent Fraction:
- Now, let’s multiply both the numerator and denominator of ( \frac{5}{4} ) by ( 3 ):
[
\frac{5 \times 3}{4 \times 3} = \frac{15}{12}
] - Thus, ( \frac{15}{12} ) is another equivalent fraction.
Summary of Equivalent Fractions
The two equivalent fractions for ( \frac{5}{4} ) that we found are ( \frac{10}{8} ) and ( \frac{15}{12} ). Both fractions simplify back to ( \frac{5}{4} ), confirming they are indeed equivalent. This method can be applied to find an infinite number of equivalent fractions simply by choosing different integers to multiply the numerator and denominator.
In conclusion, understanding how to generate equivalent fractions is essential in mathematics, as it allows us to work with different representations of the same value, which can be useful in various mathematical contexts, such as adding or comparing fractions.