Math

Question Find the value of nn that satisfies the equation n×34=316n \times \frac{3}{4} = \frac{3}{16}.

Studdy Solution

STEP 1

Assumptions
1. We have the equation n×34=316n \times \frac{3}{4} = \frac{3}{16}.
2. We need to find the value of nn that makes the equation true.

STEP 2

To find the value of nn, we need to isolate nn on one side of the equation. We can do this by dividing both sides of the equation by 34\frac{3}{4}.
n=31634n = \frac{\frac{3}{16}}{\frac{3}{4}}

STEP 3

To divide by a fraction, we multiply by its reciprocal. The reciprocal of 34\frac{3}{4} is 43\frac{4}{3}.
n=316×43n = \frac{3}{16} \times \frac{4}{3}

STEP 4

Now, we multiply the numerators and the denominators separately.
n=3×416×3n = \frac{3 \times 4}{16 \times 3}

STEP 5

Simplify the multiplication.
n=1248n = \frac{12}{48}

STEP 6

Now, we reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12.
n=12÷1248÷12n = \frac{12 \div 12}{48 \div 12}

STEP 7

Simplify the fraction to find the value of nn.
n=14n = \frac{1}{4}
The value of nn that makes the equation n×34=316n \times \frac{3}{4} = \frac{3}{16} true is 14\frac{1}{4}.

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