Understanding Fractions: Rules for Addition, Subtraction, Multiplication, and Division

A fraction is a way of expressing a part of a whole. It is composed of two parts: the top number, called the numerator, and the bottom number, called the denominator. The numerator tells us how many equal parts we have, and the denominator tells us how big each part is. For example, in the fraction 3/4, we have three equal parts and each part is one fourth the size of the whole.

10. What are the rules for adding and subtracting fractions with like denominators ?

When adding or subtracting fractions with like denominators, we can add or subtract the numerators and keep the denominator the same. For example, 1/4 + 1/4 = 2/4, and 3/4 - 1/4 = 2/4.

11. What are the rules for multiplying and dividing fractions ?

When multiplying fractions, we multiply the numerators together, then multiply the denominators together. For example, (2/3) x (3/4) = 6/12. When dividing fractions, we invert the second fraction (i.e. change the numerator and denominator), then multiply. For example, (4/5) / (2/3) = 8/15.

12. What is a mixed number ?

A mixed number is a combination of a whole number and a fraction. It is written as a whole number followed by a fraction. For example, 3 1/2 is a mixed number, where 3 is the whole number and 1/2 is the fraction.

13. How do we add and subtract mixed numbers ?

To add or subtract mixed numbers, we first add or subtract the whole numbers, then add or subtract the fractions. For example, 3 1/2 + 2 3/4 = 5 4/4, and 3 1/2 - 1 1/2 = 2 1/2.

14. What is an improper fraction ?

An improper fraction is a fraction that has a numerator that is equal to or greater than the denominator. For example, 5/4 is an improper fraction because 5 is greater than 4.

15. How do we convert an improper fraction to a mixed number ?

To convert an improper fraction to a mixed number, we divide the numerator by the denominator and write the result as a whole number followed by a fraction. For example, 5/4 = 1 1/4.