How to make expressions with fractions

Fractions are an essential part of mathematics, and understanding how to manipulate them is crucial when solving various mathematical problems. Forming expressions with fractions involves combining them using mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will explore the steps in constructing expressions with fractions effectively.

Before diving into creating expressions, let’s first review basic fraction operations. A fraction consists of a numerator and a denominator, separated by a horizontal line. For instance, in the fraction 3/4, 3 is the numerator and 4 is the denominator. Fractions can be added, subtracted, multiplied, and divided just like whole numbers.

To begin constructing expressions with fractions, make sure the fractions have the same denominator. Adding and subtracting fractions can only be done when the denominators are equal. For example, let’s consider the fractions 1/4 and 3/4. Since they have the same denominator, 4, we can add them together by simply adding the numerators: 1/4 + 3/4 = (1+3)/4 = 4/4 = 1. Similarly, subtracting fractions with equal denominators involves subtracting the numerators while keeping the common denominator intact.

However, when the denominators are different, we need to find a common denominator before performing addition or subtraction. To do this, we find the least common multiple (LCM) of the denominators. For example, let’s work with the fractions 1/3 and 2/5. The LCM of 3 and 5 is 15. We need to adjust the fractions so they have the same denominator, which in this case is 15. To achieve this, we multiply the numerator and denominator of 1/3 by 5, resulting in 5/15. We multiply the numerator and denominator of 2/5 by 3, yielding 6/15. Now that both fractions have the same denominator, we can add them: 5/15 + 6/15 = 11/15.

Multiplying fractions is relatively straightforward. To multiply fractions, we simply multiply the numerators together and the denominators together. Consider the fractions 2/3 and 4/5. Their product would be (2*4)/(3*5) = 8/15.

Division of fractions involves multiplying the first fraction by the reciprocal of the second fraction. For example, to divide 1/2 by 3/4, we keep the first fraction as is and multiply it by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3. So, the division becomes (1/2) * (4/3) = (1*4)/(2*3) = 4/6 = 2/3.

Expression construction with fractions often involves combining operations. In such cases, remember to follow the order of operations (PEMDAS/BODMAS). First, perform any necessary operations within parentheses or brackets. Then, evaluate any indices or exponents. Next, perform multiplication and division from left to right. Finally, perform addition and subtraction from left to right.

To illustrate this, let’s create an expression using fractions: (1/2 + 4/5) * 3/4. Following the order of operations, we start by adding 1/2 and 4/5, as they are within parentheses. The sum is 14/10. Then we multiply 14/10 by 3/4, resulting in 42/40, which simplifies to 21/20.

In conclusion, constructing expressions with fractions requires understanding basic fraction operations and applying them correctly. Ensure denominators are the same for addition and subtraction, or find a common denominator. Multiplication involves multiplying numerators and denominators, while division requires the reciprocal of the second fraction. Lastly, remember to follow the order of operations when combining multiple operations within the expression. With practice, you will become more comfortable manipulating expressions with fractions and solving mathematical problems more effectively.