The problem asks us to compare $80\%$ and $\frac{3}{4}$ and determine which sign ($>, <, =$) makes the statement true.

1. Problem Description

The problem asks us to compare $80\%$ and $\frac{3}{4}$ and determine which sign ($>, <, =$) makes the statement true.

2. Solution Steps

First, we convert $80\%$ to a fraction. We know that $80\% = \frac{80}{100}$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20:

$\frac{80}{100} = \frac{80 \div 20}{100 \div 20} = \frac{4}{5}$

Next, we convert the fraction $\frac{3}{4}$ to a decimal by dividing 3 by 4:

$\frac{3}{4} = 0.75$

We convert $80\%$ to a decimal:

$80\% = \frac{80}{100} = 0.80 = 0.8$

Comparing $0.8$ and $0.75$, we see that $0.8 > 0.75$. Alternatively, we can convert both fractions to have a common denominator. $\frac{4}{5}$ can be written as $\frac{4 \cdot 4}{5 \cdot 4} = \frac{16}{20}$. $\frac{3}{4}$ can be written as $\frac{3 \cdot 5}{4 \cdot 5} = \frac{15}{20}$.

Since $\frac{16}{20} > \frac{15}{20}$, we have $\frac{4}{5} > \frac{3}{4}$, thus $80\% > \frac{3}{4}$.

3. Final Answer

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