Fractions are an essential part of mathematics, and they are an essential aspect of everyday life. Whether it is baking a cake or dividing pizzas, are everywhere. But when it comes to making expressions with fractions, it can be challenging for some students. However, with the right guidance and understanding, anyone can master expressions with fractions. Before we proceed, it is essential to understand what fractions are. Fractions are numerical representations of a part of a whole or a set, and they are written in the form of a numerator and a denominator separated by a fraction bar. The numerator represents the part of the set or the whole, while the denominator shows the total number of equal parts or the whole. For instance, the fraction 3/4 represents the part three out of four equal parts. Making expressions with fractions requires a basic knowledge of mathematics and the ability to apply some fundamental rules. These rules are as follows: 1) Simplify fractions - Simplify each fraction in the equation before proceeding further. A fraction is simplified if the numerator and the denominator do not have any common factors other than 1. 2) Find the common denominator - To add or subtract fractions, you need to find the common denominator. The common denominator is the least common multiple of the denominators of the given fractions. 3) Add or subtract fractions - Once you have found the common denominator, add or subtract the numerators. 4) Multiply fractions - To multiply fractions, multiply the numerators and denominators. 5) Divide fractions - To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Now, let us take a look at some examples of making expressions with fractions. Example 1: Adding and Subtracting Fractions Suppose you need to add the fractions 1/3 and 2/5. Step 1: Find the common denominator. The common denominator is 15, which is the least common multiple of 3 and 5. Step 2: Add the fractions. 1/3 x 5/5 = 5/15 2/5 x 3/3 = 6/15 5/15 + 6/15 = 11/15 Therefore, 1/3 + 2/5 = 11/15. To subtract the fractions, follow the same steps but subtract the numerators instead of adding them. Example 2: Multiplying Fractions Suppose you need to multiply the fractions 2/3 and 5/6. Step 1: Multiply the numerators. 2 x 5 = 10 Step 2: Multiply the denominators. 3 x 6 = 18 Therefore, 2/3 x 5/6 = 10/18, which can be simplified to 5/9. Example 3: Dividing Fractions Suppose you need to divide the fractions 3/4 by 2/5. Step 1: Multiply the first fraction by the reciprocal of the second fraction. 3/4 x 5/2 = 15/8 Therefore, 3/4 divided by 2/5 = 15/8. In summary, making expressions with fractions requires a basic understanding of mathematics and the ability to apply some fundamental rules. Whether you are adding, subtracting, multiplying, or dividing fractions, following these rules will help you tackle any expression with fractions. With practice, you will become more confident and proficient in dealing with fractions, paving the way for success in mathematics.
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