How to Add 1/2 + 1/2: A Step-by-Step Guide

Mathematics is a subject that is used in our everyday life, and fractions are one of the essential components of this subject. Fractions are the numbers that represent a part of a whole, and they are used in various operations such as addition, subtraction, multiplication, and division. In this blog, we will discuss step by step how to add two fractions with a common denominator, specifically 1/2 + 1/2, and the different methods to solve such problems.

Step by Step Solution:

Adding two fractions with a common denominator is a straightforward process. The first step is to find the common denominator, which is the lowest common multiple of the denominators. In this case, the denominators are both 2, so the common denominator is also 2. Once we have found the common denominator, we can add the numerators and write the sum over the common denominator. Hence, 1/2 + 1/2 = (1+1)/2.

The next step is to simplify the fraction to its lowest terms. We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor (GCF). In this case, the GCF of 2 and 2 is 2, so we divide both 2 and 2 by 2, which gives us 1/1.

Therefore, the final answer is 1/1, which can also be written as just 1. Hence, 1/2 + 1/2 = 1.

Alternative Method:

Another method to add fractions is by using the cross-multiplication method. This method involves multiplying the numerator of one fraction by the denominator of the other fraction and adding the two products. The result is written over the product of the denominators. The formula for this method is as follows:

(a/b) + (c/d) = (ad + bc) / bd

Using this formula, we can add 1/2 and 1/2 as follows:

(1/2) + (1/2) = (1 x 2 + 1 x 2) / 2 x 2 = 4/4

Simplifying the fraction 4/4 by dividing both the numerator and the denominator by their GCF of 4 gives us 1/1 or just 1.

FAQs:

What is a fraction?

A fraction is a number that represents a part of a whole.

What is a denominator?

The denominator is the bottom number in a fraction and represents the total number of equal parts.

What is a numerator?

The numerator is the top number in a fraction and represents the number of parts being considered.

What is a common denominator?

A common denominator is the lowest common multiple of the denominators of two or more fractions.

What is the formula to add two fractions?

The formula to add two fractions with a common denominator is (a/b) + (c/b) = (a + c)/b.

What is the cross-multiplication method to add fractions?

The cross-multiplication method involves multiplying the numerator of one fraction by the denominator of the other fraction and adding the two products. The result is written over the product of the denominators.

How do you simplify a fraction?

To simplify a fraction, divide both the numerator and the denominator by their greatest common factor.

What is the greatest common factor (GCF)?

The greatest common factor is the largest number that divides evenly into two or more numbers.

What is a proper fraction?

A proper fraction is a fraction where the numerator is less than the denominator.