How could you write 60/75 as a decimal without using long division? Show your work and explain your thinking

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!

How could you write 60/75 as a decimal without using long division? Show your work and explain your thinking.

Learn how to convert the fraction 60/75 into a decimal without long division by simplifying the fraction first. The step-by-step process covers the greatest common divisor and fraction-to-decimal conversion. Suitable for students in Grades 6-8.

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