Unit 4 - Fractions and Decimals

Vocabulary

Numerator - the top number in a fraction. The number that shows how many equal parts you have.

Denominator - the bottom number of a fraction. This represents the total number of equal pieces.

Improper Fraction - a fraction that has a larger numerator than a denominator.

Mixed Number - a whole number with a fraction.

It is important to remember that fractions cannot be compared unless the wholes are the same size. For example, 1/2 of an extra large pizza is not equal to 1/2 of a small, personal sized pizza, despite the fractions being the same.

Unit Fractions are fractions where the numerator is 1. Each whole can be broken up into unit fractions.

When the wholes are the same everything can be compared. Comparing fractions with like denominators is easy. The pieces are the same size, so whichever numerator is greater is the greater fraction.

If the numerators are the same, think about how the larger the denominator the smaller the piece becomes. You can cut a brownie tray into 16 brownies if you want, but they won't be as big as if you cut it into thirds. If the denominators are different, the larger denominator will end up being the smaller fraction. For example, 2 out of 16 pieces of brownies is a lot less than 2 out of 3.

Adding and Subtracting Fractions

Fractions cannot be added or subtracted unless the denominators are the same. Think about pizza; when you have 1 slice out of 8, then eat another 2 out of 8, you have eaten a total of 3 out of 8, or 3/8 of the pizza. You just add or subtract the numerators and keep the denominators the same. The biggest mistake students make is adding or subtracting the denominators as well.

Mixed Numbers and Improper Fractions

Improper fractions happen when the numerator is larger or equal to the denominator. No one would ever say 8/8ths, they would just say one whole. We also wouldn't leave an improper fraction most of the time. We would change it to a mixed number, which is how many wholes you have and any leftovers writen as a fraction. Here is how to convert between the two.

Adding Mixed Numbers

Subtracting Mixed Numbers

Multiplying Fractions by a Whole Number

When multiplying a fraction by a whole number, relate it to addition. If you have 1/4 three times, then you would add one three times and keep the denominator the same. The easiest way to do this is to multiply the whole number and the numerator and keep the denominator the same.