Unit 3: Fractions
Fractions allow us to perform calculations with numbers that are not whole. For example, imagine you baked a pie. If your family eats half the pie for dessert one day, you could use fractions to determine that half a pie remains. If you eat another slice, you could use fractions yet again to see how much is left. We use fractions every day to calculate sale prices, measurements, money, and many other situations. In this unit, we explore how to add, subtract, multiply, divide, and reduce fractions.
Completing this unit should take you approximately 11 hours.
3.1: Identifying Parts of Fractions
Before we can perform calculations with fractions, we need to be able to identify the parts of a number written as a fraction.
3.2 Equivalent Fractions
Equivalent fractions are fractions written differently but with the same value. Imagine a pizza cut into four slices.
Each slice is 1/4 of the pizza. If you eat half the pizza, you are eating 1/2 the pizza. You can also say that you ate two slices, or 2/4 of the pizza. The fractions 1/2 and 2/4 are equivalent fractions because they have the same value.
3.3: Proper and Improper Fractions
We can write fractions as proper fractions, where the numerator is less than the denominator. We can also write fractions as improper fractions, where the numerator is greater than the denominator. You should be able to identify these different types of fractions.
3.4: Mixed Numbers and Improper Fractions
Mixed numbers are a different way to write improper fractions. In a mixed number, we write the whole number with the remainder as a fraction. For example, the improper fraction 3/2 would be written as 1 ½. This means that 3/2 is 1 + ½.
3.5: Converting Between Improper Fractions and Mixed Numbers
We often need to convert between fractional numbers written as improper fractions and mixed numbers.
3.6: Fractions in Lowest Terms
Before we can complete calculations involving fractions, we must be able to manipulate fractions to to change their denominators. As you will see, it is often easiest to have fractions with the same denominator when performing calculations like addition or multiplication.
One way we can manipulate fractions is by writing them in their lowest terms. A fraction in lowest terms has the lowest possible denominator. We can write the fraction 4/8 in lowest terms as ½.
3.7: Finding Common Denominators
To be able to perform calculations with fractions, we must first write fractions with the same denominator. This is called finding the common denominator. To do this, you will need to know how to write fractions in their lowest terms and find common multiples, both of which which we learned earlier.
3.8: Adding and Subtracting Fractions with Like Denominators
When we add or subtract fractions, we have to consider two different cases: when the fractions have the same denominator, and when the fractions have different denominators. First, we are going to focus on adding and subtracting fractions with the same denominator.
3.9: Adding and Subtracting Fractions with Unlike Denominators
When we have fractions with different denominators, we need to take an extra step before we can add or subtract them. First, we must find the common denominator and rewrite the fractions using that common denominator.
3.10: Adding and Subtracting Mixed Numbers
There are two different ways to add and subtract mixed numbers. One way is to treat the whole numbers and fractions separately. The other approach is to convert mixed numbers into improper fractions and then use the addition and subtraction methods learned in the last two sections.
3.11: Applications of Adding and Subtracting Fractions
Adding and subtracting fractions and mixed numbers comes up in a variety of real-world applications: for example, cooking, and making change from money.
3.12: Multiplying Fractions and Mixed Numbers
We now are ready to learn how to multiply fractions and mixed numbers.
3.13: Dividing Fractions and Mixed Numbers
The last important skill we need for fractions and mixed numbers is knowing how to divide them. Dividing fractions and mixed numbers follows similar rules to multiplying.
3.14: Applications of Multiplying and Dividing Fractions
Multiplying and dividing fractions appear in a variety of real-world applications.