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### Course: Class 6 (Old)>Unit 5

Lesson 6: Adding or subtracting unlike fractions

# Adding fractions with unlike denominators

Learn how to add two fractions with different denominators. It can be challenging to combine fractions when the denominators don't match. It is important to find a common denominator. Finally, the resource shows how to find a common multiple of the two denominators in order to convert the fractions so they can be added together.

## Want to join the conversation?

• How do I find the common denominator for 3/4+3/8??
• First, you'll want to figure out whether or not the larger denominator (3/8) is divisible by the smaller one (3/4). In this case, the 8 is divisible by 4, (8/4 = 2), so you're going to multiply the smaller one (4) by 2, bringing it to 8. Now, you have to remember, whenever you scale fractions, you have to multiply both, so now it's 6/8+3/8 = 9/8 = 1 1/8. In other cases where the larger denominator isn't divisible by the smaller one, find the LCM (least/smallest common multiple), and scale both fractions so the denominators are equal. Hope this helped!
• Can the Rule of Four be used for what he teaches at ? Or is this something different?
• I like airsoft
• At to . Since Sal says that 9/10 and 27/10 are the same number, could you have written only 9/10 or 27/30.
• Good Question! You can do it either ways! But sal is not switching the numbers in this video! You could do both but only can do 27/30 when switching numbers!
• I don't understand what he did in , someone please explain
• the fraction was a improper fraction so he made it a proper fraction by saying 15 goes into 16 1 time and there's a re
remainder of 1
• I do not understand what if it is a whole number times a fraction
• If there is a whole number, you would make the whole number look like this: (this is just an example) 3/1. If the whole number is 3, then you just make the whole number over one. 3/1.
I hope this helped you!!

P.S. Sorry for the three-year-late response!!
• How do you make fractions into decimals.
• To convert fractions into decimals, divide the denominator into 100, then multiply the answer by the numerator, and finally add the decimal point, i guess. For example, 3/5 is equal to 0.6 because 5 going into 100 is 20 which would make the decimal 0.2. The numerator is 3 and 0.2 x 3 = 0.6. I hope this helped!
• what is the best way to multiply fractions
• Say you are multiplying 7/8 times 4/9 it would also be written as 7 times 4 which equals 28 and 8 times 9 equals 72 giving you an answer of 28/72. If you didn't understand you multiply the numerator by the numerator and the denominator by the denominator then combine the two to get your answer.
• 6 13/21
• Yes, it is fraction +, but it might take a bit to solve.
• For improper fractions, for example 32/30, does the denominator always have to be equal? If yes, why?
• When you're adding/subtracting, the denominators have to be equal regardless of whether the fraction is proper or improper. We can easily think of an improper fraction as a mixed number, right? We have a whole number plus a fractional number. For example, if we add two improper fractions that are converted to mixed numbers, it could look like this:
5/3 + 28/5 = ?
1 2/3 + 5 3/5 = ?
(1 + 2/3) + (5 + 3/5) = ?
Then, using the associative property, we can switch around the parenthesis like this:
(1 + 5) + (2/3 + 3/5) = ?
Now you see we have a completely normal unlike denominator problem, and we just add 6 to the answer. As with any unlike denominator adding/subtracting problem, you have to get the fractions to the same denominator. In this case, it would be a denominator of 15.
= 6 + 10/15 + 9/15
= 6 + 19/15
= 6 + 1 + 4/15
= 7 4/15, or 109/15
• Does anyone know why when adding 2 fractions you would multiply each fraction by 1?

I am reading a book and it does not seem clear to me how or why it works or why you would use it at all rather than the easy cross multiplication method. I just don't want to ignore it just in case there are situations where it needs to be used which I find is always the case that there are rules that work for some combination of things and not others.

The book I am reading has stumped me in the addition of fractions. Here is a snippet of it:

1/7 + 3/4

"Here, we can neither convert sevenths to quarters nor quarters to sevenths, so we’re going to learn a method that you can use to add or subtract any fractions. To get identical bottom numbers, we begin by multiplying each number by 1, written as quarters in one case, and as sevenths in the other."

1x 1/7 + 1x3/4 = 4/4 x 1/7 + 7/7 x 3/4

I have no idea how they got the 4/4 and 7/7 try as I might and how the strange-looking order of the terms after the equal sign even if I overlooked how they got those numbers to begin with.

I thought I worked out how they did it but my brain refused to accept what it thought was either a convoluted approach or that I was creating my own incorrect method lol

Can anyone provide a possible clarification of why they would suggest using this method rather than the easy cross multiplication method?
• Some basic info you need to know:

1) The denominator of a fraction tells you the size of each portion. Visualize a pizze that was cut into 8 slice. Each slice is 1/8 of the pizza. If a pizza is cut int 4 slices, then each slice is 1/4 of the pizza and a slice is twice as big as a slice of 1/8

2) To add & subtract fractions we need to work with fractions of the same size. So, we have to force the denominators to have a common value. This is called a "common denominator".

3) Equivalent fractions are created by multiplying both numerator & denominator by the same value. Why? This is based upon the identity property of multiplication: Any number times 1 = the original number. So, by multiplying a fraction by 4/4 = 1, we aren't changing the value of the fraction. We're just converting it to an equivalent value.

Now to your questions - Where did the 4/4 and 7/7 come from?

Since the fractions in the video don't have a common denominator, they need to be converted to have a common denominator. So, we start by find the lowest common multiple(LCM), also called the lowest common denominator (LCD) of the fractions. The LCM for 4 and 7 is 28. There are lessons on finding an LCM at: https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-lcm/v/least-common-multiple-exercise

To convert the fraction 1/7 to have a denominator of 28, you ask yourself the question: what times 7 will create 28? The answer is 4. You do the same thing to determine how to convert 3/4 to have a denominator of 28. What times 4 will create a denominator of 28? The answer is 7. These values 4 and 7 become 4/4 and 7/7 because we have to multiply each fraction by a value = 1 to have an equivalent fraction.

Hope this helps.