What is 1.25 as a fraction

Understanding 1.25 as a Fraction

To convert 1.25 into a fraction, follow these steps:

1. Write down the decimal divided by 1:

   $$\frac{1.25}{1}$$

2. Multiply both the numerator and the denominator by 100 (since 1.25 has two digits after the decimal point, we use 100):

   $$\frac{1.25 \times 100}{1 \times 100} = \frac{125}{100}$$

3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

   The GCD of 125 and 100 is 25:

   $$\frac{125 \div 25}{100 \div 25} = \frac{5}{4}$$

So, 1.25 as a fraction is:

This fraction, $\frac{5}{4}$, is also known as an improper fraction because the numerator is greater than the denominator.

Understanding the Concept of Converting Decimal to Fraction

The process of converting a decimal to a fraction involves several steps to ensure the conversion is accurate and straightforward. Here's a detailed guide to help you understand this process.

Step 1: Identify the Decimal

First, look at the decimal you need to convert. For example, let's consider the decimal 0.75.

Step 2: Place the Decimal over 1

Next, write the decimal number over 1. This creates a fraction:

Step 3: Eliminate the Decimal Point

To eliminate the decimal point, multiply both the numerator and the denominator by a power of 10 that converts the decimal to a whole number. For 0.75, multiply by 100:

Step 4: Simplify the Fraction

Now, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number. The GCD of 75 and 100 is 25:

So, 0.75 converts to the fraction $\frac{3}{4}$.

Step 5: Verify the Conversion

Finally, check your work by converting the fraction back into a decimal. Divide the numerator by the denominator:

Example

Let's do another example with the decimal 0.125.

1. Place the decimal over 1:

   $$\frac{0.125}{1}$$

2. Eliminate the decimal by multiplying by 1000 (since there are 3 decimal places):

   $$\frac{0.125 \times 1000}{1 \times 1000} = \frac{125}{1000}$$

3. Simplify the fraction by finding the GCD of 125 and 1000, which is 125:

   $$\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$$

So, 0.125 converts to the fraction $\frac{1}{8}$.

Summary

By following these steps, any decimal can be successfully converted into a fraction. The key points include identifying the decimal, eliminating the decimal point by multiplying, and simplifying the fraction. Practice will help you become more proficient at converting decimals to fractions.

Simplifying Fractions

Simplifying fractions is a fundamental concept in mathematics that involves reducing a fraction to its simplest form. A fraction is simplified when both its numerator (top number) and denominator (bottom number) are divided by their greatest common divisor (GCD).

Steps to Simplify a Fraction

1. Identify the GCD: Find the greatest common divisor of the numerator and the denominator.
2. Divide Both Terms: Divide both the numerator and the denominator by the GCD.

Let's take a fraction $\frac{18}{24}$ as an example.

1. Determine the GCD: The factors of 18 are: 1, 2, 3, 6, 9, 18 The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

   The greatest common divisor (GCD) is 6.

2. Divide the Numerator and Denominator by the GCD:

   $$\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$$

So, $\frac{18}{24}$ simplifies to $\frac{3}{4}$.

Practical Application

Fractions in simplest form are easier to work with in mathematical operations like addition, subtraction, multiplication, and division. They also provide a more understandable way to compare different fractions.

Example of Simplifying:

If you have the fraction $\frac{32}{48}$, follow the steps:

1. Find the GCD of 32 and 48:

   $$\text{Factors of 32}: 1, 2, 4, 8, 16, 32 \\ \text{Factors of 48}: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \\ \text{GCD} = 16$$

2. Divide by the GCD:

   $$\frac{32 \div 16}{48 \div 16} = \frac{2}{3}$$

Hence, $\frac{32}{48}$ simplifies to $\frac{2}{3}$.

Conclusion

Understanding how to simplify fractions is essential for solving more complex mathematical problems effectively. By identifying the greatest common divisor and dividing the numerator and denominator, any fraction can be reduced to its simplest form, making calculations easier and results more intuitive.