Question

Solve for bb. Express your answer as a proper or improper fraction in simplest terms.
one quarter, b, minus, one half, equals, start fraction, 2, divided by, 5, end fraction
4
1
​
b−
2
1
​
=
5
2
​

Answer 1

To solve for \( b \) given the equation

\[
\frac{1}{4}b - \frac{1}{2} = \frac{2}{5},
\]

we can follow these steps:

1. **Isolate \( \frac{1}{4}b \)**:

Start by adding \( \frac{1}{2} \) to both sides:

\[
\frac{1}{4}b = \frac{2}{5} + \frac{1}{2}.
\]

2. **Find a common denominator for the right-hand side**:

The denominators are 5 and 2, and the least common multiple (LCM) of 5 and 2 is 10. We convert each fraction:

\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10},
\]
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}.
\]

Now we can add both fractions:

\[
\frac{1}{4}b = \frac{4}{10} + \frac{5}{10} = \frac{9}{10}.
\]

3. **Solve for \( b \)**:

Next, multiply both sides by 4 to solve for \( b \):

\[
b = 4 \cdot \frac{9}{10}.
\]

This simplifies to:

\[
b = \frac{36}{10}.
\]

4. **Simplify the fraction**:

Now simplify \( \frac{36}{10} \) by dividing both the numerator and denominator by their greatest common divisor, which is 2:

\[
b = \frac{36 \div 2}{10 \div 2} = \frac{18}{5}.
\]

Thus, the solution for \( b \) is

\[
\boxed{\frac{18}{5}}.
\]