Fraction Unit! :)

By: Shan Shan

Adding fractions!

Steps when adding fractions:

Step 1: Make sure the denominators (the bottom numbers of the fractions) are the same amount.

Step 2: Add the numerators (the top numbers of the fractions) and put the results over the denominator.

Step 3: Reduce the fraction if needed.


In this example we are using pizzas, it shows that 1/4 of the pizza plus another 1/4 of the pizza sums up to 2/4 of one whole pizza. To reduce the fraction, you would divide the numerator and the denominator by the same number. In this case, this example show that the numerator and denominator are being divided by 2 to create 1/2.


Word problem: You give 1/3 of a pan of brownies to Brooke, and 1/6 of the pan of brownies to Jessica. How much of the pan of brownies did you give away?

Adding mixed numbers

Subtracting Fractions!

Steps when subtracting fractions:

Step 1: Make sure the bottom denominators are the same.

Step 2: Subtract the numerators and add the number onto the top of the denominator.

Step 3: Reduce the fraction if needed.


Subtracting fractions is similar to when adding fractions but different in a very different on the other hand. When adding and subtracting, you always 1. Need to find the lowest common multiple (LCM) 2. Reduce the fractions as equivalent fraction with the lowest common multiple as the denominator. In this example we are using pie charts. This example shows that if you subtract 3/4 by 2/4 you would get 1/4 of the pie left. In this case, you wouldn't be able to reduce the fraction because the numerator can not be divided by another number than 1.


"If adding or subtracting is your aim,
The bottom numbers must be the same!

"Change the bottom using multiply or divide,
But the same to the top must be applied,

"And don't forget to simplify,
Before its time to say good bye"



Word problem: Three candidates were running for student council . One of them got 1/2 of the votes. Another got 2/5 of the votes. What fraction did the third candidate get?

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Mulitplying Fractions!

Steps when multiplying fractions:

Step 1: Multiply the numerators together.

Step 2: Multiply the denominators as well.

Step 3: Reduce the fraction if needed.


Multiplying fractions is the best in my opinion. When multiplying fractions, all you do is, multiply the numerators and denominators to get a may seem a larger fraction. If you are multiplying the fraction by a whole number, simply just multiply the fraction by how many whole numbers there are. Another way to solve the answer is to turn the whole number into a fraction. For example, if you had 8 x 4/5, you can put 8 as the numerator so then you can multiply the numerators and denominators. It then would be 8/1 x 4/5 which gives you then answer of 32/5. You can not reduce this fraction because the denominator can not divide by numbers that aren't 5 and 1.


♫ "Multiplying fractions: no big problem,

Top times top over bottom times bottom.
"And don't forget to simplify,
Before it's time to say goodbye" ♫


Word problem: Tim and his business partner invested $71,000 in a property. Tim invested $51,000, and his partner, $20,000. They had to sell the property at a loss for $48,000. If each one receives the same fraction that they invested, how much will each one receive?

Dividing fractions!

Steps when dividing:

Step 1: Turn the second fraction upside down. Now that fraction is called a reciprocal.

Step 2: Multiply the first fraction by the reciprocal.

Step 3: Reduce the fraction if needed.


When dividing, you don't actually divide in this case. When you flip the second fractions numerator and denominator, you multiply them instead. The fraction may be small and big depending on how large the denominator is when not flipped.


♫ "Dividing fractions, as easy as pie,
Flip the second fraction, then multiply.
And don't forget to simplify,
Before it's time to say goodbye"


Example:

In this case, that makes the problem:

1/2 x 4/1 = ?

We begin by multiplying the numerators:

1 x 4 = 4

And then we multiply the denominators:

2 x 1 = 2

The answer has a numerator of 4 and a denominator of 2. In other words:

1 x 4/2 x 1 =4/2

This fraction can be reduced to the lowest term:

4 ÷ 2/2 ÷ 2 =2/1 = 2


Word problem: Mrs. Tyrer has 1/2 of a liter of apple juice which fills 1/3 of her glass. How many glasses of will 1 liter of apple fill?

What is an equivalent fractions?

Equivalent fractions are fractions that may look different, but are equal to each other. Two equivalent fractions may have a different numerator and a different denominator. A fraction is also equivalent to itself. In this case, the numerator and denominator would be the same. Equivalent fractions can be created by multiplying or dividing both the numerator and denominator by the same number. This number is referred to as a multiplier. We can do this because, if you multiply both the numerator and denominator of a fraction by the same non-zero number, the fraction remains unchanged in value.
Equivalent Fractions
Finding Equivalent Fractions

How do you turn Improper fractions to mixed numbers?

An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In other words, it is top-heavy.

Example: 5/3 (five thirds) and 9/8 (nine eighths) are improper fractions


To turn a improper you always keep the same denominator until you multiply and so on. What you do is, when you have a whole, you multiply the whole number by the denominator. And we are to then add everything onto the numerator. We then may have a fraction where the numerator is larger than the denominator. You'd then want to reduce the fraction to its lowest common multiple.

Mixed numbers to improper fractions

What are proper fractions?

There are proper fractions (1/4) and improper fractions (5/3). A proper fraction is a fraction that has a lower numerator than the denominator. For example, 998/999 is still a proper fraction. Even though the numbers are still large, and their only separated by one, but the numerator is still smaller than the denominator. Proper fractions are more common than improper fractions. Some models you use when showing proper fractions are: fraction tiles, pizzas, pies, ice cubs, rectangles etc.
Proper Fractions

What are mixed fractions?

A mixed fraction is a fraction that is mixed with a proper fraction. Mixed fractions have a whole number at all times. You can convert a mixed number to a improper fraction by finding the number adding the amount of wholes into the numerator. This sounds hard, but it really isn't. For example, the 1 changes to 2/2 because there are 2 halves in a whole. Another example, the 2 becomes 10/5 because there are 5 fifths in a whole. Get it? Once you have done this, then you just add the fraction to it.


Examples of mixed numbers:

  • 1 1/2, 1 1/3 ,2 1/2 ,2 2/5 ,1 4/5


Examples of mixed numbers turning into improper fractions:
  • 3/2, 4/3, 5/2, 12/5, 9/5
Improper Fractions and Mixed Numbers by Shmoop

What are some strategies that we can use when multiplying, subtracting, adding, and diving?

Some popular strategies when adding, subtracting, dividing, and multiplying is using fraction tiles, money model , time model, pie charts, rectangle charts, pizzas, etc. These are the most common and most popular.


Strategy 1:Fraction tiles

Fraction tiles are a visual illustration for the mathematical question. Fraction tiles are used for adding, subtracting, equivalent fractions, multiplying, dividing and ratios.

Strategy 2: Money model

The money model uses money to visualize the illustration.

Strategy 3: Time model

  • 6 minutes= 1/10
  • 5 minutes= 1/12
  • 30 minutes= 1/2
  • 10 minutes= 1/6
  • 20 minutes= 1/3
  • 15 minutes= 1/4
  • 12 minutes= 1/5
  • 60 minutes= 1/1
  • 1 minute= 1/60
  • 2 minutes= 1/30
  • 3 minutes= 1/20


Strategy 4: Pie charts

A pie chart displays data, information, and statistics. The bigger the slice, the more of that particular data was gathered. The main use of a pie chart is to show comparison. When items are presented on a pie chart, you can easily see which item is the most popular and which is the least popular.

Strategy 5: Rectangle charts

A rectangle chart displays data, information, and statistics as well. It is similar to pie charts because rectangle charts are also used to show comparison.

Strategy 6: Pizzas

Pizza charts are the same as pie charts but in a pizza image. It is still a pie shape and but shows the fraction of how much the pizza was taken away or eaten.

Strategy 7: Percentage

Percentage is used order the fractions from least to greatest. It is very common and is the most easiest in my opinion.

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Percentage

Percentage is the most common as well and often used more than other strategies.