Fraction Problems

Understanding Fractions

A fraction is a way of expressing a number that is less than one, or the division of one quantity by another.
Fractions consist of two parts: a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of parts we have, and the denominator represents how many of these parts make up a whole.

To add or subtract fractions, you must make sure the denominators are the same. If the denominators are different, you need to find a common denominator by finding the least common multiple.
Once the fractions have the same denominator, you can add or subtract the numerators directly. For example, if you are tasked with adding 2/3 and 1/3, the denominators are the same and you would simply add the numerators, resulting in 3/3 = 1.
If you are asked to subtract 2/3 from 5/3, you will subtract the numerators, giving you a result of 3/3 = 1.

To multiply fractions, you simply multiply the numerators together to get the new numerator and the denominators together to get the new denominator. Simplify the result, if needed.
For example, to multiply 3/4 by 2/3, you would multiply the numerators (3 x 2 = 6) and the denominators (4 x 3 = 12), resulting in 6/12, which simplifies to 1/2.
To divide fractions, you actually multiply by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
For instance, to divide 3/4 by 2/3, you would multiply 3/4 by the reciprocal of 2/3 (which is 3/2), resulting in 9/8 or 1 1/8 when written as a mixed number.

Knowing some common fraction to decimal conversions can make working with fractions simpler. For example, 1/2 is 0.5, 1/4 is 0.25, and 3/4 is 0.75.
Converting fractions to decimals involves dividing the numerator by the denominator.

Adding or subtracting fractions with different denominators without adjusting them first is a common mistake.
Understanding the operation in division of fractions and forgetting to multiply by the reciprocal can cause errors.
Failing to simplify your answer where possible may lose marks. Always look to reduce your fractions to their simplest form.
Inaccuracy in converting fractions to decimals can result in wrong answers. Always be careful when making conversions.