QuestionSolve $\frac{n}{8}=\frac{28}{32}$ for the unknown quantity, $n$ . $n=4$ $n=224$ $n=7$ $n=112$

Studdy Solution

STEP 1

1. The equation $\frac{n}{8} = \frac{28}{32}$ is a proportion, which means two ratios are equal.
2. We can solve for $n$ by using cross-multiplication.
3. The solution will be one of the provided options: $n = 4$ , $n = 224$ , $n = 7$ , $n = 112$ .

STEP 2

1. Simplify the given fraction on the right side of the equation.
2. Use cross-multiplication to solve for $n$ .
3. Verify the solution by substituting it back into the original equation.

STEP 3

Simplify the fraction $\frac{28}{32}$ .
Find the greatest common divisor (GCD) of 28 and 32, which is 4.
Divide both the numerator and the denominator by 4:
$\frac{28}{32} = \frac{28 \div 4}{32 \div 4} = \frac{7}{8}$
Now the equation is $\frac{n}{8} = \frac{7}{8}$ .

STEP 4

Use cross-multiplication to solve for $n$ .
The equation $\frac{n}{8} = \frac{7}{8}$ implies:
$n \times 8 = 7 \times 8$
Simplify:
$n = 7$

STEP 5

Verify the solution by substituting $n = 7$ back into the original equation:
Substitute $n = 7$ into $\frac{n}{8}$ :
$\frac{7}{8} = \frac{28}{32}$
Simplify $\frac{28}{32}$ to $\frac{7}{8}$ as done in Step 1, confirming both sides are equal.
The solution is:
$\boxed{7}$

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