1.75 as a fraction

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16-01-2025

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Understanding how to convert decimals to fractions is a fundamental skill in math. This guide will walk you through the process of expressing 1.75 as a fraction, explaining the steps clearly and concisely. We'll also explore some practical applications and related concepts.

Understanding Decimals and Fractions

Before diving into the conversion, let's refresh our understanding of decimals and fractions. Decimals represent parts of a whole using a base-ten system (tenths, hundredths, thousandths, etc.). Fractions, on the other hand, represent parts of a whole using a numerator (top number) and a denominator (bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.

Converting 1.75 to a Fraction: Step-by-Step

Here's how to convert the decimal 1.75 into its fractional equivalent:

1. Identify the place value: The last digit in 1.75 is in the hundredths place. This means our denominator will be 100.

2. Write the decimal as a fraction: Write 1.75 as a fraction with 100 as the denominator: 175/100.

3. Simplify the fraction: This fraction can be simplified by finding the greatest common divisor (GCD) of 175 and 100. The GCD of 175 and 100 is 25.

4. Divide both the numerator and the denominator by the GCD: Divide both 175 and 100 by 25: 175 ÷ 25 = 7 and 100 ÷ 25 = 4.

5. Result: The simplified fraction is 7/4.

Therefore, 1.75 expressed as a fraction is 7/4.

Understanding the Result: Mixed Numbers

Notice that 7/4 is an improper fraction (the numerator is larger than the denominator). This can also be expressed as a mixed number, which combines a whole number and a proper fraction. To convert 7/4 to a mixed number:

1. Divide the numerator by the denominator: 7 ÷ 4 = 1 with a remainder of 3.

2. Write the mixed number: The whole number is 1, and the remainder (3) becomes the numerator of the fraction, with the denominator remaining 4.

Therefore, 7/4 is equivalent to 1 ¾.

Practical Applications

Converting decimals to fractions is useful in various contexts:

• Baking and Cooking: Recipes often use fractional measurements.
• Construction and Engineering: Precise measurements are crucial.
• Finance: Calculating percentages and proportions.
• Science: Many scientific calculations involve fractions.

Conclusion

Converting 1.75 to a fraction is a straightforward process involving understanding place value, creating a fraction, and simplifying. The final answer, both as an improper fraction (7/4) and a mixed number (1 ¾), demonstrates the flexibility of representing numerical values. Understanding this conversion is vital for various mathematical applications and everyday tasks. Remember to always simplify your fractions to their lowest terms for the clearest representation.