Fractional Parts of a Whole: Comparison and Sum What are fractional parts? Imagine dividing a whole into different parts with equal-sized pieces. These p...
What are fractional parts?
Imagine dividing a whole into different parts with equal-sized pieces. These pieces are called fractional parts, and they represent parts of the whole that are not whole numbers. For example, if a cake is divided into 6 equal pieces, each piece would be 1/6 of the whole cake.
How are they compared?
Fractional parts are compared by comparing the denominators (bottom numbers) of the fractions. The fraction with the larger denominator is considered larger. This means that the fractional part of the whole that it represents is larger than the fractional part of the whole that the other fraction represents.
How are they added?
To add fractions with different denominators, we need to find a common denominator. This means finding the smallest multiple of the denominators of the fractions that is greater than or equal to both denominators. Once the common denominator is found, we can add the numerators of the fractions and keep the denominator the same.
Examples:
1/3 + 2/3 = 3/3 = 1
1/4 + 3/4 = 4/4 = 1
1/5 - 2/5 = -1
Comparison and sum in mixed quantitative problems:
In mixed quantitative problems, we are often asked to compare and add fractions with different denominators. To solve these problems, we need to follow these steps:
Convert the fractions to equivalent fractions with equal denominators. This can be done by finding a common denominator and multiplying the numerator and denominator of each fraction by the appropriate factor.
Add the fractions together.
Reduce the resulting fraction to its simplest form.
Key points:
Fractional parts are parts of the whole that are not whole numbers.
Comparing fractions involves comparing their denominators.
Adding fractions with different denominators requires finding a common denominator and adding the numerators.
Fractions can be compared and added in mixed quantitative problems