What is 67.5 as a fraction? Tutorial in mathshowcase.info

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 67.5 to a fraction.

You can try other values to get more familiar with the conversion process.

Often, convert 67 to a fraction or 68 to a fraction, depending on the task.

Understanding the decimal: “67.5”

A decimal number consists of an integer part and a fractional part, separated by a decimal point. The integer part is on the left, and the fractional part is on the right. For example, in 67.5, 67 is the integer part and 5 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 67.5.
- By removing the decimal point, we derive the numerator as 675.
For the denominator:
- Each position after the decimal represents a division by 10.
- Thus, having 1 positions after the decimal equates to 10 or 10¹.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 675 include 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, and 675.
- The factors of 10 comprise 1, 2, 5, and 10.
Greatest Common Divisor (GCD):
- It's the largest number that can evenly divide both the numerator and the denominator.
- In this instance, the GCD for 675 and 10 is 5.

The factors of 675 are:

1 3 5 9 15 25 27 45 75 135 225 675

The factors of 10 are:

1 2 5 10

Conversion formula (equation):

$67.5 = \frac{67.5}{1} = \frac{67.5 × 10}{1 × 10} = \frac{675}{10} = \frac{675÷5}{10÷5} = \frac{135}{2}$

Solution:

67.5 = $\frac{135}{2}$

What is a decimal?

A decimal is a numeral system that includes a point to separate the whole number part from the fractional part. This system makes it easy to work with numbers less than one.

What is a fraction?

A fraction is a mathematical way of showing a part of a whole. It has two parts: the numerator on top and the denominator below, which help express partial values and comparisons.

Step-by-step solution:

Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 67.5 = $\frac{67.5}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 67.5, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10¹ = 10
Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{67.5 × 10}{1 × 10}$ = $\frac{675}{10}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 5. Divide both the numerator and the denominator by this common divisor. $\frac{675 ÷ 5}{10 ÷ 5}$ = $\frac{135}{2}$

Answer in mixed fraction format:

67.5 =

67

1

2

What is 67.5 as a fraction?