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Add & Subtract Fractions (Unlike Denominators)
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 How to add fractions with UNLIKE denominators.
 How to subtract fractions with UNLIKE denominators.
 This knowledge can help us rollerblade, eat a giant cookie, and even take care of animals!

Discussion Questions
 Before VideoHow do you add [ggfrac]3/5[/ggfrac] + [ggfrac]1/5[/ggfrac]?ANSWER
You add the numerators and the denominator stays the same. [ggfrac]3/5[/ggfrac] + [ggfrac]1/5[/ggfrac] = [ggfrac]4/5[/ggfrac].
You subtract the numerators and the denominator stays the same. [ggfrac]5/8[/ggfrac]  [ggfrac]3/8[/ggfrac] = [ggfrac]2/8[/ggfrac].
Multiply the numerator and denominator of the fraction by the same number.
No, because you have multiplied by 1.
Whole number part and fraction part.
 After VideoWhich part of a fraction tells you the number of equalsized parts that the whole is broken into? ANSWER
The denominator.
The number of equalsized pieces being added or subtracted.
For each fraction, multiply the numerator and denominator by a number so that the denominators of both fractions are equal. One possible multiplier is the denominator of the other fraction.
[ggfrac]1/2[/ggfrac].
No; Rafay subtracted the whole number parts but didn't subtract [ggfrac]1/3[/ggfrac] from 5. He should have regrouped to get 4[ggfrac]3/3[/ggfrac]  3[ggfrac]1/3[/ggfrac] = 1[ggfrac]2/3[/ggfrac].

Vocabulary
 Numerator DEFINE
In a fraction, the number of equal parts being considered.
 Denominator DEFINE
In a fraction, the number of equalsize parts that a whole has been split into.
 Equivalent Fractions DEFINE
Fractions with different numerators and denominators that name the same number.
 Like Denominator DEFINE
The same denominator.
 Unlike Denominator DEFINE
Different denominators.
 Benchmark Number DEFINE
Numbers such as 0, [ggfrac]1/2[/ggfrac], and 1 that can be used to estimate an answer or evaluate the reasonableness of an answer.
 Mixed Number DEFINE
A number that is written using a whole number and a fraction.
 Numerator DEFINE

Reading Material
Download as PDF Download PDF View as Seperate PageWHAT ARE UNLIKE DENOMINATORS?Two fractions have unlike denominators if the numbers in the denominators are not the same. You can use multiplication and division to rewrite fractions to have a common denominator.
To better understand adding and subtracting fractions with unlike denominators…
WHAT ARE UNLIKE DENOMINATORS?. Two fractions have unlike denominators if the numbers in the denominators are not the same. You can use multiplication and division to rewrite fractions to have a common denominator. To better understand adding and subtracting fractions with unlike denominators…LET’S BREAK IT DOWN!
Cookies
Let's say that Marcos and April each have a large cookie. They each ate part of their cookie. Marcos has [ggfrac]1/9[/ggfrac] of his cookie left and April has [ggfrac]2/3[/ggfrac] of hers left. How much cookie do they have left, combined? To answer this question, you need to rewrite the fractions with a common denominator by finding equivalent fractions, and then add. Start with the fraction with the smaller denominator, [ggfrac]2/3[/ggfrac]. We can find an equivalent fraction by multiplying both the numerator and denominator by the same number. Multiply [ggfrac]2/3[/ggfrac] by [ggfrac]3/3[/ggfrac] to find an equivalent fraction with denominator 9. [ggfrac]2/3[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]6/9[/ggfrac].[ggfrac]6/9[/ggfrac] has the same denominator as [ggfrac]1/9[/ggfrac] and is equivalent to [ggfrac]2/3[/ggfrac]. Now we can rewrite the original addition as [ggfrac]1/9[/ggfrac] + [ggfrac]6/9[/ggfrac] = [ggfrac]7/9[/ggfrac]. They have [ggfrac]7/9[/ggfrac] of a cookie left. Try this one yourself. You ate [ggfrac]2/5[/ggfrac] of a pizza and your sister ate [ggfrac]1/10[/ggfrac] of the same pizza. How much of the pizza did you eat in all?
Cookies Let's say that Marcos and April each have a large cookie. They each ate part of their cookie. Marcos has [ggfrac]1/9[/ggfrac] of his cookie left and April has [ggfrac]2/3[/ggfrac] of hers left. How much cookie do they have left, combined? To answer this question, you need to rewrite the fractions with a common denominator by finding equivalent fractions, and then add. Start with the fraction with the smaller denominator, [ggfrac]2/3[/ggfrac]. We can find an equivalent fraction by multiplying both the numerator and denominator by the same number. Multiply [ggfrac]2/3[/ggfrac] by [ggfrac]3/3[/ggfrac] to find an equivalent fraction with denominator 9. [ggfrac]2/3[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]6/9[/ggfrac].[ggfrac]6/9[/ggfrac] has the same denominator as [ggfrac]1/9[/ggfrac] and is equivalent to [ggfrac]2/3[/ggfrac]. Now we can rewrite the original addition as [ggfrac]1/9[/ggfrac] + [ggfrac]6/9[/ggfrac] = [ggfrac]7/9[/ggfrac]. They have [ggfrac]7/9[/ggfrac] of a cookie left. Try this one yourself. You ate [ggfrac]2/5[/ggfrac] of a pizza and your sister ate [ggfrac]1/10[/ggfrac] of the same pizza. How much of the pizza did you eat in all?Algorithm for Finding a Common Denominator
Let's say you want to add [ggfrac]1/3[/ggfrac] + [ggfrac]2/5[/ggfrac]. You know that you need to find a common denominator. Starting with [ggfrac]1/3[/ggfrac], list equivalent fractions: [ggfrac]1/3[/ggfrac] x [ggfrac]2/2[/ggfrac] = [ggfrac]2/6[/ggfrac], [ggfrac]1/3[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]3/9[/ggfrac], [ggfrac]1/3[/ggfrac] x [ggfrac]4/4[/ggfrac] = [ggfrac]4/12[/ggfrac], [ggfrac]1/3[/ggfrac] x [ggfrac]5/5[/ggfrac] = [ggfrac]5/15[/ggfrac], and [ggfrac]1/3[/ggfrac] x [ggfrac]6/6[/ggfrac] = [ggfrac]6/18[/ggfrac]. None of those fractions have a denominator of 5, so you need to find equivalent fractions for [ggfrac]2/5[/ggfrac] as well: [ggfrac]2/5[/ggfrac] x [ggfrac]2/2[/ggfrac] = [ggfrac]4/10[/ggfrac], [ggfrac]2/5[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]6/15[/ggfrac], and [ggfrac]2/5[/ggfrac] x [ggfrac]4/4[/ggfrac] = [ggfrac]8/20[/ggfrac]. Both [ggfrac]1/3[/ggfrac] and [ggfrac]2/5[/ggfrac] have an equivalent fraction with a denominator of 15. Rewrite the original addition as [ggfrac]5/15[/ggfrac] + [ggfrac]6/15[/ggfrac] = [ggfrac]11/15[/ggfrac].
There is a faster way to find a common denominator. If you multiply the numerator and the denominator of each fraction by the denominator of the other fraction, you always get fractions with a common denominator. Here's how this works: Starting with [ggfrac]1/3[/ggfrac], you see that the other fraction, [ggfrac]2/5[/ggfrac], has a denominator of 5 so you multiply the numerator and denominator by 5: [ggfrac]1/3[/ggfrac] x [ggfrac]5/5[/ggfrac] = [ggfrac]5/15[/ggfrac]. Next, you see that [ggfrac]1/3[/ggfrac] has a denominator of 3, so you multiply the numerator and denominator of the other fraction by 3: [ggfrac]2/5[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]6/15[/ggfrac]. Rewrite the original addition as [ggfrac]5/15[/ggfrac] + [ggfrac]6/15[/ggfrac] = [ggfrac]11/15[/ggfrac]. Try this one yourself. Add [ggfrac]1/6[/ggfrac] + [ggfrac]3/4[/ggfrac] by finding a common denominator using the faster way.
Algorithm for Finding a Common Denominator Let's say you want to add [ggfrac]1/3[/ggfrac] + [ggfrac]2/5[/ggfrac]. You know that you need to find a common denominator. Starting with [ggfrac]1/3[/ggfrac], list equivalent fractions: [ggfrac]1/3[/ggfrac] x [ggfrac]2/2[/ggfrac] = [ggfrac]2/6[/ggfrac], [ggfrac]1/3[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]3/9[/ggfrac], [ggfrac]1/3[/ggfrac] x [ggfrac]4/4[/ggfrac] = [ggfrac]4/12[/ggfrac], [ggfrac]1/3[/ggfrac] x [ggfrac]5/5[/ggfrac] = [ggfrac]5/15[/ggfrac], and [ggfrac]1/3[/ggfrac] x [ggfrac]6/6[/ggfrac] = [ggfrac]6/18[/ggfrac]. None of those fractions have a denominator of 5, so you need to find equivalent fractions for [ggfrac]2/5[/ggfrac] as well: [ggfrac]2/5[/ggfrac] x [ggfrac]2/2[/ggfrac] = [ggfrac]4/10[/ggfrac], [ggfrac]2/5[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]6/15[/ggfrac], and [ggfrac]2/5[/ggfrac] x [ggfrac]4/4[/ggfrac] = [ggfrac]8/20[/ggfrac]. Both [ggfrac]1/3[/ggfrac] and [ggfrac]2/5[/ggfrac] have an equivalent fraction with a denominator of 15. Rewrite the original addition as [ggfrac]5/15[/ggfrac] + [ggfrac]6/15[/ggfrac] = [ggfrac]11/15[/ggfrac]. There is a faster way to find a common denominator. If you multiply the numerator and the denominator of each fraction by the denominator of the other fraction, you always get fractions with a common denominator. Here's how this works: Starting with [ggfrac]1/3[/ggfrac], you see that the other fraction, [ggfrac]2/5[/ggfrac], has a denominator of 5 so you multiply the numerator and denominator by 5: [ggfrac]1/3[/ggfrac] x [ggfrac]5/5[/ggfrac] = [ggfrac]5/15[/ggfrac]. Next, you see that [ggfrac]1/3[/ggfrac] has a denominator of 3, so you multiply the numerator and denominator of the other fraction by 3: [ggfrac]2/5[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]6/15[/ggfrac]. Rewrite the original addition as [ggfrac]5/15[/ggfrac] + [ggfrac]6/15[/ggfrac] = [ggfrac]11/15[/ggfrac]. Try this one yourself. Add [ggfrac]1/6[/ggfrac] + [ggfrac]3/4[/ggfrac] by finding a common denominator using the faster way.Guinea Pig Weights
Let's say that you have two tiny guinea pigs. One weighs [ggfrac]4/5[/ggfrac] of a pound and the other weighs [ggfrac]2/3[/ggfrac] of a pound. You want to figure out how much more one guinea pig weighs than the other. You can find this difference using the equation [ggfrac]4/5[/ggfrac]  [ggfrac]2/3[/ggfrac] = ?. First, find the equivalent fractions that have a common denominator. The second fraction has a denominator of 3, so multiply the numerator and denominator of the first fraction by 3. [ggfrac]4/5[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]12/15[/ggfrac]. Next, multiply [ggfrac]2/3[/ggfrac] x [ggfrac]5/5[/ggfrac] since 5 is the denominator of [ggfrac]4/5[/ggfrac]. [ggfrac]2/3[/ggfrac] x [ggfrac]5/5[/ggfrac] = [ggfrac]10/15[/ggfrac]. Rewrite the original subtraction [ggfrac]4/5[/ggfrac]  [ggfrac]2/3[/ggfrac] as [ggfrac]12/15[/ggfrac]  [ggfrac]10/15[/ggfrac] = [ggfrac]2/15[/ggfrac]. One guinea pig weighs [ggfrac]2/15[/ggfrac] of a pound more than the other guinea pig. Try this one yourself. My bag of candy weighs [ggfrac]3/4[/ggfrac] of a pound and my friend's bag of candy weighs [ggfrac]2/3[/ggfrac] of a pound. How much more does my bag of candy weigh?
Guinea Pig Weights Let's say that you have two tiny guinea pigs. One weighs [ggfrac]4/5[/ggfrac] of a pound and the other weighs [ggfrac]2/3[/ggfrac] of a pound. You want to figure out how much more one guinea pig weighs than the other. You can find this difference using the equation [ggfrac]4/5[/ggfrac]  [ggfrac]2/3[/ggfrac] = ?. First, find the equivalent fractions that have a common denominator. The second fraction has a denominator of 3, so multiply the numerator and denominator of the first fraction by 3. [ggfrac]4/5[/ggfrac] x [ggfrac]3/3[/ggfrac] = [ggfrac]12/15[/ggfrac]. Next, multiply [ggfrac]2/3[/ggfrac] x [ggf