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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.
The diagram shows pies representing equivalent fractions. The fractions have the same value. However, they are unlike fractions because the pies are divided into different numbers of pieces.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 | 3â‹…5 |
12 | 22â‹…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 | 22â‹…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 | 22â‹…7=28 |
7 | 7 | |
28 | 22â‹…7 |
ba​=b⋅28a⋅28​
aâ‹…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⋠|