Fractions without a Calculator

Understanding Fractions

Fractions represent a part of a whole. It is comprised of a numerator (the top number) and a denominator (the bottom number). The numerator is the part of the whole and the denominator is the total parts the whole is divided into.
A proper fraction has a numerator smaller than the denominator (for example, 3/4) and represents a value less than 1.
An improper fraction has a numerator larger than the denominator (for example, 7/4) and represents a value more than 1.
A mixed number is a combination of a whole number and a proper fraction (for example, 1 3/4).

To add or subtract fractions, the denominators must be the same, called a common denominator.
If the denominators are already the same, simply add or subtract the numerators and keep the denominator the same.
If the denominators are different, multiply the denominators together to find a common denominator, then adjust the numerators correspondingly.

To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

To divide fractions, flip the divisor (the second fraction) to get its reciprocal, then multiply as you would normally do. This method is known as multiplying by the reciprocal.

A fraction is considered simplified if the numerator and denominator only share 1 as a common factor.
Simplify fractions by dividing the numerator and denominator by their greatest common factor.

Mixing up the numerator and denominator will significantly affect the value of the fraction. Always remember that the numerator is the top number, representing part of the whole, and the denominator is the bottom number, which represents how many parts the whole is divided into.
Forgetting to simplify fractions can make calculations more complex and increase the chance of making errors.
Errors in finding a common denominator can lead to incorrect solutions in addition or subtraction problems with fractions.
In division problems with fractions, forgetting to multiply by the reciprocal (flipping the second fraction and then multiplying) often leads to incorrect answers.