Write an equation for the situation: A fraction f multiplied by 4 equals 1/2. Please provide the equation.
The Correct Answer and Explanation is:
For this problem, the situation can be translated into the equation:
[
4 \times f = \frac{1}{2}
]
To solve for ( f ), we need to isolate ( f ) on one side of the equation. We can do this by dividing both sides by 4. This step effectively “undoes” the multiplication by 4.
[
f = \frac{1}{2} \div 4
]
When dividing a fraction, we multiply by the reciprocal of the divisor. Therefore, dividing by 4 is the same as multiplying by ( \frac{1}{4} ):
[
f = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}
]
So, the correct answer is:
[
f = \frac{1}{8}
]
Explanation
The given problem describes a relationship where a fraction ( f ) multiplied by 4 results in ( \frac{1}{2} ). To translate this scenario into an equation, we use the phrase “multiplied by 4,” which tells us to place ( f ) in a multiplication expression with 4, resulting in ( 4 \times f ). This multiplication equals ( \frac{1}{2} ), so the equation becomes ( 4 \times f = \frac{1}{2} ).
Next, to solve for ( f ), we need to isolate it by removing the multiplication by 4. To “undo” multiplication, we use division. Dividing both sides by 4 is equivalent to multiplying ( \frac{1}{2} ) by the reciprocal of 4, which is ( \frac{1}{4} ). Therefore, ( \frac{1}{2} \div 4 ) becomes ( \frac{1}{2} \times \frac{1}{4} ).
To multiply fractions, we multiply the numerators and the denominators:
[
\frac{1 \times 1}{2 \times 4} = \frac{1}{8}
]
This gives us ( f = \frac{1}{8} ), meaning the fraction ( f ) that, when multiplied by 4, results in ( \frac{1}{2} ) is indeed ( \frac{1}{8} ).