Question

Solve the equation.
four ninths y minus one fourth
equalsone third
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Part 1
yequals
  
enter your response here
​(Type an integer or a simplified​ fraction.)

Answer 1

To solve the equation

\[
\frac{4}{9}y - \frac{1}{4} = \frac{1}{3},
\]

we start by isolating \( y \).

1. First, add \(\frac{1}{4}\) to both sides:

\[
\frac{4}{9}y = \frac{1}{3} + \frac{1}{4}.
\]

2. To add the fractions on the right side, we need a common denominator. The least common multiple of 3 and 4 is 12. Convert both fractions:

\[
\frac{1}{3} = \frac{4}{12} \quad \text{and} \quad \frac{1}{4} = \frac{3}{12}.
\]

So now we have:

\[
\frac{4}{9}y = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}.
\]

3. Next, multiply both sides by \(\frac{9}{4}\) to solve for \( y \):

\[
y = \frac{7}{12} \times \frac{9}{4}.
\]

4. Multiplying the fractions:

\[
y = \frac{7 \times 9}{12 \times 4} = \frac{63}{48}.
\]

5. Now, simplify \(\frac{63}{48}\). Both numbers can be divided by 3:

\[
\frac{63 \div 3}{48 \div 3} = \frac{21}{16}.
\]

Thus, the solution to the equation is

\[
y = \frac{21}{16}.
\]

So, you can enter \(\frac{21}{16}\) as your response.