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| 11 Theory slides |
| 8 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
In order to state what part of the pizza each person will eat, a certain type of numbers should be used.
In the definition of rational numbers, the word fraction
showed up but was not explained in detail. To clarify any doubts, its definition will now be presented.
Fractions are a specific type of ratio that compares a part to a whole. Fractions are rational numbers written in the form ba, where the numerator a is the part and the denominator b is the whole.
a over b.Fractions where a is less than b are called proper fractions. Fractions where a is greater than or equal to b are called improper fractions.
Split into factors
Cross out common factors
Cancel out common factors
Consider a bar that is split into different parts. Find the fraction that describes the relationship between the shaded parts and the bar as a whole. Any shaded parts on the right-hand side indicate that the fraction is an improper fraction. Do not simplify the fractions.
When a fraction has a large numerator and denominator, it can be hard to estimate its value. Simplifying such a fraction and finding an equivalent fraction with a smaller numerator and denominator can be helpful.
After having a lot of fun with her friends on Saturday, Jordan woke up rested and energized the next day and decided to do her math homework. When she finished, she texted her answers to her friend Emily and asked if she got the same results.
Find the greatest common factor (GCF) of the numerator and denominator of a fraction, then use it simplify the fraction.
Notice that Emily's fractions are written in their simplest form, but Jordan's fractions are not simplified. Therefore, to find the equivalent fractions, each of Jordan's fractions will be analyzed and simplified, one at a time.
Consider the given fraction. Can it be simplified? If yes, write the given fraction in its simplest form. If the fraction is already simplified, write it as it is.
On top of the topics mentioned in this lesson, there are many other real-life applications of fractions. Here are some of them.
Write the fraction corresponding to the given diagram. Do not simplify the fraction.
Let's start by recalling the definition of a fraction. l part→ whole→ a/b l←numerator ←denominator We can see that a fraction is a ratio that compares a part to a whole. Now, let's analyze the given diagram and try to identify the part and the whole.
There are 6 bars in total on the left-hand side of the diagram, which is the whole. Only 5 of the bars are colored, which represents the part. We can substitute these numbers into the ratio to write the desired fraction. 5/6 Therefore, 56 is the fraction that corresponds to the given diagram.
Let's now examine the second given diagram in a similar fashion.
This time there are also colored bars on the right-hand side of the diagram. Since the lines are dashed and there is no rectangle, these bars are additional, so to speak. The rectangle on the left-hand side, consisting of 5 colored bars, represents the whole. If we add the 3 extra colored bars from the right side, we get a part of 8. 8/5 This is an improper fraction. This result makes sense because there are more colored bars than just the ones in the rectangle representing the whole.
Let's now analyze the final diagram.
First, we need to count how many bars there are in the rectangle. We can see that there are 9 bars in the rectangle. This is the number of the whole. Also, there are 3 colored bars, so 3 is the part. Now we have enough information to write the fraction. 3/9
Tearrik's parents bought 14 tangerines. Tearrik ate 3 of them. What fraction describes the amount of tangerines that Tearrik ate?
Let's start by recalling the definition of a fraction. l part→ whole→ a/b l←numerator ←denominator To write a fraction representing the situation, we need to identify the part and the whole. We know that Tearrik's parents bought 14 tangerines, so this is the whole. Of these, Tearrik ate 3 tangerines, which represents the part. Let's substitute these values into the fraction. 3/14 Therefore, 314 describes the part of the tangerines that Tearrik ate.
Simplify the given fractions.
Let's start by analyzing the first given fraction. 10/24 We can simplify it by dividing both the numerator and denominator by their greatest common factor (GCF). To find the GCF, we first need to split the numbers into their prime factors. 10 & = 2* 5 24 & = 2* 2* 2* 3 We can see that 10 and 24 share only one common factor, 2. This is their GCF. GCF(10,24)=2 Let's divide the numerator and denominator of the fraction by 2 to simplify it.
The simplified fraction is 512.
We will begin by considering the second given fraction. 15/40 To simplify it, we need to divide both the numerator and denominator by their GCF. First, we need to split the numbers into their prime factors. 15 & =3* 5 40 & =2* 2* 2* 5 We can see that 15 and 40 share only one common factor, 5. This is their GCF. GCF(15,40)=5 Let's divide the numerator and denominator of the fraction by 5 to simplify it.
The simplified fraction is 38.
Let's analyze the last given fraction. 36/28 We will simplify it by dividing both the numerator and denominator by their GCF. First, we will split the numbers into their prime factors. 36 & = 2* 2* 3* 3 28 & = 2* 2* 7 We see that 36 and 28 share two common factors, 2 and 2. The product of these factors is the GCF of 36 and 28. GCF(36,28)=2* 2=4 Let's divide the numerator and denominator of the fraction by 4 to simplify it.
The simplified fraction is 97.
To find the equivalent fraction pairs, let's analyze each fraction in the left column one at a time.
The first fraction is 1612. To find an equivalent fraction, let's simplify 1612 by dividing the numerator and denominator by their greatest common factor (GCF). First, let's split 16 and 12 into their prime factors. 16&= 2* 2* 2* 2 12&= 2* 2* 3 The GCF of two numbers is the product of their common factors. Since 16 and 12 share two common factors, their GCF is 2* 2=4. GCF(16,12)=4 Next, we will divide the numerator and denominator by the GCF.
Therefore, the equivalent fraction is 43.
We can find an equivalent fraction of the second fraction 1976 by simplifying it. First, let's split the numerator of 19 and the denominator of 76 into their prime factors. 19&= 19* 1 76&= 19* 4 Since 19 and 76 share only one common factor, their GCF is 19. GCF(19,76)=19 Now, let's divide the numerator and denominator by the GCF.
Therefore, the equivalent fraction is 14.
The third fraction is 3577. Let's simplify it! First, we can split the numerator of 35 and the denominator of 77 into their prime factors. 35&=5* 7 77&= 7* 11 Since 35 and 77 share only one common factor, their GCF is 7. GCF(35,77)=7 Now, let's divide the numerator and denominator by the GCF.
Therefore, the equivalent fraction is 511.
The fourth and final fraction is 8448. We can find an equivalent fraction by simplifying it. Let's start by splitting the numerator and denominator into prime factors. 84&= 2* 2* 3* 7 48&= 2* 2* 2* 2* 3 We can see that 84 and 48 share three common factors. We can find the GCF of the numbers by multiplying these factors. GCF(84,48)=2* 2* 3=12 Now, let's divide the numerator and denominator by 12.
Therefore, the equivalent fraction is 74.