Calculating the ratio between two fractions might seem daunting at first, but with a step-by-step guide, it becomes much easier. Understanding ratios is crucial in many mathematical applications, such as physics, finance, and statistics. In this article, we will walk you through the process of calculating the ratio between two fractions.

Step 1: Understand what a ratio is

A ratio represents the relationship between two numbers and is expressed as a fraction. It shows how many times one number is contained within another. For example, a ratio of 3:5 means that the first number is three times smaller than the second number.

Step 2: Convert fractions to a common denominator

In order to calculate the ratio, you need to have fractions with the same denominator. If the fractions already have a common denominator, you can skip this step. Otherwise, find the least common multiple (LCM) of the two denominators and convert the fractions accordingly.

Step 3: Find the equivalent forms

Next, find the equivalent forms of the fractions by multiplying both the numerator and denominator of each fraction by the same number. This step ensures that the fractions remain in the same ratio while having the same denominator.

  • Example: If you have the fractions 2/5 and 3/8, multiply the first fraction by 8 and the second fraction by 5. This yields 16/40 and 15/40.

Step 4: Simplify the fractions

After finding the equivalent forms, simplify the fractions to their lowest terms. To simplify, divide both the numerator and denominator of each fraction by their greatest common divisor (GCD).

  • Example: For the fractions 16/40 and 15/40, the GCD is 8. Dividing both fractions by 8 gives us 2/5 and 15/8.

Step 5: Calculate the ratio

Finally, the two fractions are in their simplest forms with a common denominator. Now you can calculate the ratio by comparing the numerators.

  • Example: Using the fractions from step 4, the ratio between 2/5 and 15/8 is 2:15.

Now that you know the step-by-step process, calculating the ratio between two fractions becomes much easier. Remember to convert the fractions to a common denominator, find equivalent forms, simplify, and compare the numerators. Understanding ratios is important in many real-life scenarios, so be sure to practice this skill to enhance your mathematical abilities.

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