You can write $\frac{60}{75}$ as a decimal by simplifying the fraction first and then converting it to a decimal. Here's the step-by-step process:

Step 1: Simplify the fraction

To simplify $\frac{60}{75}$, find the greatest common divisor (GCD) of 60 and 75.

• Prime factorization of 60: $60 = 2^2 \times 3 \times 5$
• Prime factorization of 75: $75 = 3 \times 5^2$

The common factors are 3 and 5. So, the GCD of 60 and 75 is $15$.

Now, divide both the numerator and the denominator by their GCD (15):

$\frac{60}{75} = \frac{60 \div 15}{75 \div 15} = \frac{4}{5}$

Step 2: Convert $\frac{4}{5}$ to a decimal

Now, convert $\frac{4}{5}$ into a decimal. We know that:

$\frac{4}{5} = 0.8$

So, $\frac{60}{75}$ as a decimal is 0.8.

Explanation:

Instead of using long division, we simplified the fraction and used basic fraction-to-decimal conversion for a simpler denominator. Since $\frac{4}{5}$ is a well-known fraction that equals 0.8, we can easily write the decimal.

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Would you like further details or have any questions? Here are five related questions to explore:

1. How do you simplify other fractions like $\frac{48}{64}$?
2. Can you convert $\frac{7}{8}$ to a decimal?
3. What is the decimal representation of $\frac{3}{4}$?
4. How can you convert a repeating decimal to a fraction?
5. Why is it useful to simplify fractions before converting them to decimals?

Tip: Simplifying a fraction before converting it to a decimal can make the conversion process much easier!