What are equivalent fractions for 4/9?

Understand the Problem

The question is asking for equivalent fractions for the fraction 4/9. This involves multiplying or dividing the numerator and denominator by the same number to find other fractions that represent the same value.

Answer

Equivalent fractions for $\frac{4}{9}$ include $\frac{8}{18}$ and $\frac{12}{27}$, and in general, $\frac{4n}{9n}$ for any whole number $n$.

Steps to Solve

Choose a multiplier
To find equivalent fractions, select a whole number to multiply both the numerator (4) and the denominator (9). Let's use 2 as an example.
Multiply the numerator and denominator
Using the chosen multiplier (2), perform the multiplication: $$ \text{Numerator: } 4 \times 2 = 8 $$ $$ \text{Denominator: } 9 \times 2 = 18 $$ So, one equivalent fraction is $\frac{8}{18}$.
Repeat with a different multiplier
Choose another whole number, say 3, and repeat the multiplication: $$ \text{Numerator: } 4 \times 3 = 12 $$ $$ \text{Denominator: } 9 \times 3 = 27 $$ This gives another equivalent fraction: $\frac{12}{27}$.
General formula
You can generalize this process for any whole number $n$: $$ \frac{4 \times n}{9 \times n} $$ This shows that for any chosen whole number $n$, you can create an equivalent fraction.

The equivalent fractions for $\frac{4}{9}$ can be represented as $\frac{8}{18}$, $\frac{12}{27}$, and generally $\frac{4n}{9n}$ for any whole number $n$.

More Information

Equivalent fractions are different fractions that represent the same value. This method allows for the generation of countless equivalent fractions depending on the multiplier chosen.

Tips

Incorrectly adding or subtracting instead of multiplying: Ensure that both the numerator and denominator are multiplied by the same number to find equivalent fractions.

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