Understanding and Solving Fractional Equations: 7/4 of a Number When 2/3 of It Is 10

Introduction to Fractional Equations

Fractional equations are a fundamental part of algebra. They involve fractions as coefficients, and they can be solved using a variety of methods. One common problem involves finding the original number when a fraction of it is given. For instance, if it is known that two-thirds of a number is 10, then we can find the number itself and subsequently solve for other fractions of it.

Solving the Problem: 7/4 of a Number When 2/3 of It Is 10

Step-by-Step Solution

Let's consider the problem at hand: if two-thirds of a number is 10, then find 7/4 of that number.

Let the number be denoted as x. According to the problem, 2/3 of the number is 10. Therefore, we can write the equation: 2/3 * x 10

To solve for x, we can multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:

x 3/2 * 10

This simplifies to:

x 15

Now that we have determined the original number, we can proceed to find 7/4 of it.

Calculating 7/4 of the Number

To find 7/4 of 15, we perform the following calculation:

7/4 * 15 7 * 15 / 4 105 / 4 26.25

This shows that 7/4 of the number 15 is 26.25.

General Solution Methodology

Here is a generalized methodology for solving similar problems:

Let the number be x. Write the given condition as an equation. Solve the equation to find the value of x. Use the obtained value of x to calculate the desired fraction of the number.

Mathematical Problems with Similar Fractions

Let's consider some more problems involving similar fractions:

Problem 1: If 1/3 of a number is 8, then what is 3/4 of that number?

Let the number be y. Given: 1/3 * y 8. Solving for y gives: y 3 * 8 24. Therefore, 3/4 of 24 is: 3/4 * 24 18.

Problem 2: If 4/5 of a number is 20, then what is 2/5 of that number?

Let the number be z. Given: 4/5 * z 20. Solving for z gives: z 5/4 * 20 25. Therefore, 2/5 of 25 is: 2/5 * 25 10.

In conclusion, solving these types of problems involves understanding the basic principles of fractional equations and their solutions. Whether dealing with 2/3, 7/4, or any other fraction, the process remains similar: identifying the given condition, solving for the unknown, and then calculating the desired fraction of the number.