Math Problem Statement
How could you write 60/75 as a decimal without using long division? Show your work and explain your thinking
Solution
You can write 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 , find the greatest common divisor (GCD) of 60 and 75.
- Prime factorization of 60:
- Prime factorization of 75:
The common factors are 3 and 5. So, the GCD of 60 and 75 is .
Now, divide both the numerator and the denominator by their GCD (15):
Step 2: Convert to a decimal
Now, convert into a decimal. We know that:
So, 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 is a well-known fraction that equals 0.8, we can easily write the decimal.
Would you like further details or have any questions? Here are five related questions to explore:
- How do you simplify other fractions like ?
- Can you convert to a decimal?
- What is the decimal representation of ?
- How can you convert a repeating decimal to a fraction?
- 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!
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Math Problem Analysis
Mathematical Concepts
Fractions
Decimal Conversion
Simplification
Greatest Common Divisor (GCD)
Formulas
Simplification: GCD of numerator and denominator
Fraction to Decimal Conversion
Theorems
None explicitly, but uses the concept of simplifying fractions
Suitable Grade Level
Grades 6-8