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| 10 Theory slides |
| 9 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.
Dylan is ecstatic to celebrate his birthday party. His mom baked a vanilla-strawberry cake for the party. Dylan cannot control himself and eats one-tenth of the cake before the party even starts. He also eats two-fifteenths of the cake during the party.
Fractions can be classified based on whether they have the same denominator or not.
Two or more fractions that have the same denominator are called like fractions. For example, 83, 85, and 86 are all like fractions whose denominators are 8.
Integers such as 6, 11, and 43 are like fractions because they are considered to have a denominator of 1. Their fraction forms are 16, 111, and 143, respectively.
Fractions with different denominators are called unlike fractions. For example, 82, 32, and 53 are unlike fractions. The denominators of these fractions are 8, 3, and 5, which are different from each other.
Fractions like 31, 62, and 93 are also unlike fractions, even though they all are equivalent to 31. This is because their denominators are different.
Determine whether the given fractions are like fractions or unlike fractions.
The first step in adding and subtracting fractions is to check if they share the same denominator. Here, the methods of performing these operations on fractions and how to convert unlike fractions to like fractions will be discussed with examples.
The numerators of like fractions are added or subtracted when finding the sum or difference of the like fractions, respectively. The denominator remains the same in these situations.
Unlike fractions must first be converted to like fractions when the operation deals with the sum or difference. One way to convert them is to multiply the numerator and denominator of each fraction by the denominator of the other. Then, the given operation can be performed.
Denominator | Prime Factorization |
---|---|
15 | 3⋅5 |
12 | 22⋅3 |
ba=b⋅4a⋅4
Multiply
ba=b⋅5a⋅5
Multiply
Dylan's mother serves a berry pie, a peanut butter pie, and cake at the birthday party. She cuts the berry pie into 10 equal pieces. Dylan takes three berry pie pieces. Dylan's sister smells the sweet aroma of the berry pie and takes two pieces for herself.
Split into factors
Cancel out common factors
Simplify quotient
Denominators | Prime Factorization |
---|---|
2 | 2 |
12 | 22⋅3 |
ba=b⋅6a⋅6
Multiply
Add fractions
Add terms
Perform the indicated operation. Simplify the result if it is possible.
Fractions must have the same denominators when adding and subtracting two or more fractions. What if two fractions with equal denominators are given? In that case, the denominator is kept the same and the sum or difference of the numerators is written into the numerator.
The birthday party is going great. Right now 283 of the guests are dancing, while 71 of the guests are just listening to the music, and the others are playing games.
Subtract the total fraction of the guests who are listening to music and dancing from the whole, or 1.
The given fractions 283 and 71 represent the fraction of the guests who are dancing and listening to music, respectively. The whole or 1 represents all guests at the party.
All Guests | Fraction of the Guests Who Are Dancing | Fraction of the Guests Who Are Listening to Music |
---|---|---|
1 | 283 | 71 |
Denominator | Prime Factorization | LCD |
---|---|---|
1 | 1 | 22⋅7=28 |
7 | 7 | |
28 | 22⋅7 |
ba=b⋅28a⋅28
a⋅1=a
ba=b⋅4a⋅4
Multiply
Add fractions
Add terms
Subtract fractions
Subtract term
Split into factors
Cancel out common factors
Simplify quotient
A guest at the party asks Dylan's mother for the basic recipe of the cake. The recipe she is using calls for 241 cups of flour, 132 cups of sugar, and 21 cup of oil.
acb | ca⋅c+b | Simplify |
---|---|---|
241 | 42⋅4+1 | 49 |
132 | 31⋅3+2 | 35 |
Denominator | Prime Factorization | LCD |
---|---|---|
4 | 22 | 22⋅3=12 |
3 | 3 | |
2 | 2 |
ba=b⋅3a⋅3
ba=b⋅4a⋅4
ba=b⋅6a⋅6
Multiply
Add fractions
Add terms
Write as a sum
Write as a sum of fractions
Calculate quotient
Add terms
Their is a key point in adding and subtracting fractions. Make sure that the denominators of the fractions are the same. Additionally, the following three steps are applied to perform arithmetic operations on mixed numbers. Remember, such operations include addition and subtraction.
Denominator | Prime Factorization | LCD |
---|---|---|
10 | 2⋅5 | 2⋅3⋅5=30 |
15 | 3⋅5 |
Rewrite 1 as 3030
Subtract fractions
Subtract term
Determine whether the diagrams represent like fractions or unlike fractions.
Let's compare the denominators of the fractions. 4/14 and 4/24 We see that one fraction has a denominator of 14 and the other has a denominator of 24. The fractions do not have the same denominator. Therefore, we can say that they are unlike fractions.
Let's first determine which fractions the diagrams represent. Each diagram consists of 10 parts. The number of shaded parts is 3 for the diagram on the left and 7 for the other diagram.
The diagram on the left with three shaded parts represents 310. The diagram on the right with seven shaded regions parts 710. Both fractions have the same denominator. Therefore, they are like fractions.
We see that both fractions have a denominator of 12. 7/12 + 5/12 The fractions are like fractions. The sum of the fractions is the sum of the numerators divided by 12.
We can simplify this fraction to 1 because the numerator and denominator are the same. 12/12 = 1
We want to find the difference of two fractions that have the same denominator.
15/16-3/16
We subtract the numerators to find this difference.
The numerator and denominator have a common factor, which is 4. We can simplify the fraction. Let's rewrite the numerator and denominator as a product of its factors. Then we will cancel out the common factors.
The difference of the fractions is 34.
We see that the fractions have different denominators. 11/12 - 5/8 To subtract fractions with different denominators, we need to rewrite the fractions as equivalent fractions with the least common denominator. We need to determine the prime factors of the denominators to find the least common denominator.
Denominators | Prime Factorization |
---|---|
12 | 2^2 * 3 |
8 | 2^3 |
The least common denominator is the product of the highest power of each factor. Least Common Denominator 2^3 * 3 = 24 We can now rewrite the denominators. We will multiply the numerator and the denominator of the first fraction by 2. Then, we will multiply the numerator and the denominator of the second fraction by 3. Once the fractions have the same denominator, we can subtract them.
The difference of the fractions is 724.
We want to find the sum of two fractions that are unlike fractions.
7/8+1/2
To add fractions with different denominators, we need to rewrite the fractions as equivalent fractions with the least common denominator. To do so, let's first determine the prime factors of the denominators.
Denominators | Prime Factorization |
---|---|
8 | 2^3 |
2 | 2 |
The least common denominator is the product of the highest power of each factor. Least Common Denominator 2^3 = 8 We see that the first fraction already has this as its denominator. We need to rewrite the second fraction. To do so, we will multiply the numerator and the denominator of it by 4. Once the fractions have the same denominator, we can add them.
The sum of the fractions is an improper fraction, 118. We can write it as a mixed number.
We want to evaluate the sum of the mixed numbers. - 4 34 + ( - 3 14 ) We will start by rewriting the mixed numbers as improper fractions.
- a bc | - (a* c+b/c ) | Simplify |
---|---|---|
- 4 34 | - (4* 4+3/4 ) | - 19/4 |
- 3 14 | - (3* 4+1/4 ) | - 13/4 |
The mixed numbers are converted into improper fractions. - 4 34 + ( - 3 14 ) ⇕ - 19/4 + (- 13/4 ) Fractions should have the same denominator when we add or subtract them. In this case, the fractions have the same denominators. That means the sum of the fractions is the sum of the numerators divided by 4.
The sum of the mixed number is - 8.
We want to find the given difference.
3 15 - 5 13
Again, we will start by rewriting the mixed numbers as improper fractions.
a bc | a* c+b/c | Simplify |
---|---|---|
3 15 | 3* 5+1/5 | 16/5 |
5 13 | 5* 3+1/3 | 16/3 |
The mixed numbers are converted into improper fractions. 3 15 - 5 13 ⇕ 16/5 - 16/3 Fractions should have the same denominator when they go through addition or subtraction. In this expression, the fractions have different denominators. We multiply the numerator and denominator of each fraction by the denominator of the other to make them like fractions. Let's do it.
We will rewrite the numerator as 30 plus 2 with the aim of writing the fraction as a mixed number.
We see that the expression contains two like fractions, - 38 and 118. Let's write these fractions next to each other. We will use the Commutative Property of Addition to do this. Also, we can change the order of the fractions in the parentheses by the same property.
Next, we can group the last two fractions by the Associative Property of Addition.
We can now add the like fractions.
The value of the expression is 1 211.