NF - Operations with Fractions Lesson

Operations with Fractions

Adding and Subtracting Fractions

numerator / denominator We are starting the first of several tasks on fractions. Some of this will be review, but it will help you be successful in later tasks. We are starting with writing fractions in lowest terms. This means that the numerator and the denominator do not have any common factors text annotation indicator . Anytime you have a number over itself like this equation image indicator $LaTeX: \frac{3}{3}$ $\frac{3}{3}$ , it can be reduced to 1 (because this literally means three divided by three). So we can cancel common factors to write a fraction in lowest terms.

Mixed and Improper Numbers

A mixed number is a whole number and a fraction. You will see this frequently in a recipe. You may need equation image indicator $LaTeX: 2\frac{1}{2}$ $2\frac{1}{2}$ cups of flour. This is an example of a mixed number.

An improper fraction text annotation indicator is one where the numerator is greater than the denominator.

Let's use our knowledge of the basics of fractions to perform operations with them.

When you add and subtract fractions with like denominators, you add the numerators and leave the denominators. What happens if we have unlike denominators? To add or subtract these fractions, we need the least common denominator . To find this we find the LCM of the denominators.

For example, if the denominators were 2 and 3, the LCM would be 6.

We would multiply the two fractions by factors of 6 so that each was an equivalent fraction with a denominator of 6.
Then we can add. When we add mixed numbers we add the whole number portion and then add the fractions.
If the fractions are improper fractions, we need to change them to a mixed number and again add the whole numbers. The same goes for subtraction.

Follow through the examples below for additional explanations!

Multiplying Fractions

When we multiply fractions, we multiply the numerators and then the denominators. Then you need to write the answer in lowest terms. You can also reduce the fractions and eliminate common factors text annotation indicator before you multiply. This is a better method when you're using large numbers. For example, when multiplying I can simplify the the fractions to before I multiply.

Multiplying Mixed Numbers

When you multiply mixed numbers, they need to be written as improper fractions. Then follow the process of multiplying and change it back to a mixed number if necessary.

For example: text annotation indicator $LaTeX: 2\frac{1}{2}\times3\frac{2}{2}=\frac{5}{2}\times\frac{11}{3}$ $2\frac{1}{2}\times3\frac{2}{2}=\frac{5}{2}\times\frac{11}{3}$

Notice how I changed the mixed numbers to improper fractions. This will make multiplying the fractions easier! Now let's discuss dividing fractions.

Division of Fractions

Reciprocals

Before we can talk about dividing, we need to define a reciprocal. The reciprocal of a fraction is found by switching the numerator and denominator.

numerator / denominator
denominator / numerator

Dividing Fractions

When you divide fractions, you'll take the reciprocal of the divisor text annotation indicator and change the problem to a multiplication problem.

Here's the general formula:

A/B ÷ C/D = A/B x D/C

Dividing Mixed Numbers

When dividing mixed numbers, the same rules apply. Change the mixed numbers to improper fractions and then follow the rules for division.

Partition of Fair-Sharing Idea of Division

A bag contains 453 jelly beans. If six students share the bag of jelly beans, how many jelly beans will each student get?

image of people and jellybeans

This problem can be modeled using base ten blocks as a guide, then using a table to organize the information:

image of building blocks

A number that is divided by another number.

Student 1	Student 2	Student 3	Student 4	Student 5	Student 6
50	50	50	50	50	50
10	10	10	10	10	10
10	10	10	10	10	10
5	5	5	5	5	5
½	½	½	½	½	½

QUESTION: So how many jellybeans will each student get?

ANSWER: Each student will get $LaTeX: 75\:and\:\frac{1}{2}$ $75\:and\:\frac{1}{2}$ jellybeans.

Measurement or Repeated Subtraction Idea of Division

Jumbo the elephant loves peanuts. His trainer has 625 peanuts. If he gives Jumbo 20 peanuts each day, how many days will the peanuts last?

First add groups of 20.

20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 560, 580, 600, 620 text annotation indicator ... with 5 left over

ANSWER: Think of this as counting by 20 until you get to the number closest to 625. We count by 20 because that is how many peanuts he got a day. We stopped at 620 because the number of peanuts is 625.

Now count the total number of groups....

31 groups of 20 with 5 peanuts left over.

QUESTION: So how many days will the peanuts last?

ANSWER: The trainer has enough peanuts for 31 days with 5 leftover.

Watch the videos below for more examples.

IMAGES CREATED BY GAVS