Understanding ratios and fractions can be a challenging aspect of mathematics. However, calculating the ratio between two fractions doesn’t have to be complicated. In this blog post, we will guide you through the step-by-step process of calculating the ratio between two fractions.

Step 1: Convert the Fractions to a Common Denominator

The first step in calculating the ratio between two fractions is to convert them to a common denominator. To do this, find the least common multiple (LCM) of the denominators of the two fractions. Once you have the LCM, multiply both the numerator and denominator of each fraction by the respective factor needed to reach the common denominator.

Step 2: Simplify the Fractions

After converting the fractions to a common denominator, it’s important to simplify them. Simplifying the fractions allows for easier calculation and visualization. To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

Step 3: Calculate the Ratio

Now that you have both fractions converted to a common denominator and simplified, calculating the ratio is a straightforward process. Divide the numerator of the first fraction by the numerator of the second fraction, and divide the denominator of the first fraction by the denominator of the second fraction. This will give you the ratio between the two fractions.

Example:

Let’s demonstrate the steps with an example:

  • Fraction 1: 3/8
  • Fraction 2: 5/12

Step 1: Convert the fractions to a common denominator

  • Fraction 1: (3*12)/(8*12) = 36/96
  • Fraction 2: (5*8)/(12*8) = 40/96

Step 2: Simplify the fractions

  • Fraction 1: 36/96 = 3/8
  • Fraction 2: 40/96 = 5/12

Step 3: Calculate the ratio

  • Ratio: (3/8) ÷ (5/12)
  • Ratio: (3/8) * (12/5)
  • Ratio: 36/40
  • Ratio: 9/10

Therefore, the ratio between the fractions 3/8 and 5/12 is 9/10.

Calculating the ratio between two fractions involves converting them to a common denominator, simplifying the fractions, and then dividing the numerators and denominators to obtain the ratio. Understanding this process can help you solve various mathematical problems and make comparisons between different quantities. Practice this method, and you’ll become a pro at calculating ratios!

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