How to Calculate ANY Fraction Easily!

Summary

This video from the Tech Math Channel provides a comprehensive guide to solving fraction problems, covering addition, subtraction, multiplication, and division. The presenter walks through various types of fraction questions, including those with common and different denominators, mixed numbers, and improper fractions. Each method is explained with simple examples and step-by-step instructions to make solving fractions easier. The video also includes tips for simplifying fractions and handling more complex operations like division with fractions. Overall, it’s a helpful resource for mastering fractions, whether you're a beginner or looking to refresh your skills.

Takeaways

• 😀 The video covers the easiest ways to solve questions involving fractions, including addition, subtraction, multiplication, and division.
• ➕ When adding fractions with the same denominator, keep the denominator and add the numerators together.
• 🔄 For fractions with different denominators, find a common denominator by multiplying the denominators, then adjust the numerators before adding.
• 💯 To solve mixed number fractions, convert them to improper fractions first before performing the operations.
• ➖ Subtracting fractions follows the same process as addition: find a common denominator, then subtract the numerators.
• 💡 Multiplying fractions is straightforward: multiply the numerators and denominators together. Simplify the result if possible.
• 📏 When multiplying fractions by whole numbers, convert the whole number into a fraction by putting it over 1, then proceed with multiplication.
• 🚫 Division of fractions is the opposite of multiplication: flip the second fraction and multiply the numerators and denominators.
• 🔢 For mixed numbers in division, convert them into improper fractions before following the same division process.
• 👍 The video encourages viewers to interact by commenting, liking, and potentially supporting the Tech Math channel via Patreon.

Q & A

What is the process for adding fractions with the same denominator?

To add fractions with the same denominator, keep the denominator the same and simply add the numerators together. For example, 1/5 + 2/5 = 3/5.

How do you add fractions with different denominators?

To add fractions with different denominators, first find a common denominator by multiplying the denominators together. Then, adjust the numerators accordingly, perform the addition, and simplify the result if needed.

How do you convert mixed numbers into improper fractions?

To convert mixed numbers to improper fractions, multiply the whole number by the denominator, then add the numerator. Place this result over the original denominator.

What steps are involved in adding mixed numbers with different denominators?

First, convert the mixed numbers into improper fractions. Then, find a common denominator, adjust the numerators accordingly, and add the fractions. Finally, simplify the result or convert it back into a mixed number if needed.

How is subtraction of fractions similar to addition?

Subtraction follows the same steps as addition. If the denominators are the same, subtract the numerators and keep the denominator unchanged. If the denominators differ, find a common denominator and adjust the numerators before subtracting.

What is the process for subtracting fractions with different denominators?

To subtract fractions with different denominators, first find a common denominator by multiplying the denominators together. Then adjust the numerators accordingly, perform the subtraction, and simplify the result if necessary.

How do you subtract mixed numbers?

To subtract mixed numbers, first convert them to improper fractions. Then, find a common denominator and adjust the numerators accordingly. Subtract the fractions and simplify the result or convert it back into a mixed number.

What is the easiest way to multiply fractions?

To multiply fractions, multiply the numerators together and the denominators together. Then simplify the resulting fraction if necessary.

How do you multiply a fraction by a whole number?

To multiply a fraction by a whole number, convert the whole number to a fraction by placing it over 1. Then multiply the numerators and the denominators as usual.

How is dividing fractions related to multiplying them?

Dividing fractions is the opposite of multiplying. To divide, flip the second fraction (take its reciprocal) and multiply it by the first fraction.

Outlines

00:00

🔢 Introduction to Solving Fractions Easily

The video introduces a method for solving various types of fraction-related questions, including addition, subtraction, multiplication, and division. The host explains that the video will cover several examples, starting with addition. They begin with a scenario where fractions have the same denominator, showing how to add the numerators while keeping the denominator constant. Then, they proceed to cases where denominators differ, using multiplication to find a common denominator and explaining the steps to add fractions with unlike denominators.

05:01

➖ Simplifying Fraction Subtraction

The speaker transitions to subtraction and demonstrates how similar the process is to addition. In the first example, where both fractions have the same denominator, the numerators are subtracted while keeping the denominator unchanged. For fractions with different denominators, cross-multiplication is used to find a common denominator, and the numerators are subtracted. The speaker also tackles mixed number fractions, converting them into improper fractions before subtraction and then simplifying the result, breaking down each step clearly.

10:01

✖️ Multiplying Fractions

Next, the video covers multiplying fractions, which is described as the easiest operation. The host shares a childhood memory to explain why multiplying fractions results in a smaller number. They walk through examples, multiplying both the numerators and denominators, and simplifying the final result when possible. An example involving a whole number is also shown, where the whole number is converted into a fraction for easier calculation. The method is consistently reinforced through examples and simplification tips.

➗ Dividing Fractions Made Easy

The speaker concludes by explaining division of fractions, which is referred to as the opposite of multiplication. They introduce the concept of flipping the second fraction (finding its reciprocal) and then multiplying. An example is provided to show how to divide fractions, followed by another example with a whole number, where the whole number is turned into a fraction. The process is again simplified step-by-step, ending with a reminder that division of fractions is straightforward if multiplication rules are applied with one extra step.

Keywords

💡Fractions

Fractions are numerical quantities representing parts of a whole, expressed as one number divided by another (e.g., 1/5 or 3/4). In the video, fractions are the main focus, as the host teaches viewers how to perform basic operations such as addition, subtraction, multiplication, and division using fractions.

💡Addition of fractions

This refers to the process of combining two or more fractions. The video explains two scenarios: adding fractions with like denominators and adding fractions with unlike denominators, where a common denominator must be found. For example, the script demonstrates adding 1/5 + 2/5 and 1/4 + 2/3, showing different methods for each case.

💡Common denominator

A common denominator is the shared multiple of the denominators of two or more fractions. In the video, the concept is crucial for adding or subtracting fractions with different denominators. For instance, in the problem 1/4 + 2/3, the denominators 4 and 3 are multiplied to find the common denominator of 12.

💡Improper fractions

Improper fractions are fractions where the numerator (the top number) is greater than or equal to the denominator (the bottom number), such as 14/3. The video shows how to convert mixed numbers (e.g., 1 1/2) into improper fractions before performing operations like addition or subtraction.

💡Mixed numbers

Mixed numbers are numbers that contain both a whole number and a fraction, such as 1 1/2. In the video, the host explains how to convert mixed numbers into improper fractions to simplify operations like addition and subtraction.

💡Multiplication of fractions

This operation involves multiplying the numerators of two fractions and then the denominators to get a product. The video emphasizes that this is one of the easiest operations with fractions. An example given is multiplying 1/2 by 1/2, which results in 1/4.

💡Division of fractions

Dividing fractions involves multiplying the first fraction by the reciprocal (or the flipped version) of the second fraction. The video explains this process in detail, using the example of dividing 3/4 by 1/2 by flipping the second fraction to get 2/1, and then multiplying.

💡Simplifying fractions

Simplifying fractions means reducing them to their lowest terms by dividing both the numerator and the denominator by their greatest common factor. The video repeatedly demonstrates this step, such as when 6/8 is simplified to 3/4 by dividing both the numerator and the denominator by 2.

💡Equivalent fractions

Equivalent fractions are fractions that represent the same value, even though they may look different. In the video, the host explains how fractions like 6/8 and 3/4 are equivalent because they simplify to the same number. This concept is key when simplifying fractions after operations.

💡Numerator and denominator

The numerator is the top number of a fraction, representing how many parts are being considered, while the denominator is the bottom number, indicating the total number of equal parts. The video explains how to handle these two components in different fraction operations, such as adding numerators when denominators are the same.

Highlights

Introduction to the easiest way to solve any fraction question including addition, subtraction, multiplication, and division.

Adding fractions with the same denominator: Keep the denominator and add the numerators.

Adding fractions with different denominators: Multiply denominators to find a common denominator and cross-multiply to keep fractions equivalent.

For mixed numbers, convert them into improper fractions by multiplying the whole number by the denominator, then adding the numerator.

When subtracting fractions with the same denominator: Keep the denominator and subtract the numerators.

Subtracting fractions with different denominators follows a similar approach to addition—find a common denominator and cross-multiply.

For mixed numbers subtraction, convert mixed numbers to improper fractions before solving.

Multiplying fractions: Simply multiply the numerators together and the denominators together.

Multiplying whole numbers by fractions: Convert the whole number to a fraction with 1 as the denominator, then proceed with multiplication.

Dividing fractions: Invert the second fraction and multiply the fractions instead.

To divide a whole number by a fraction, convert the whole number to a fraction, invert the second fraction, and then multiply.

Simplify results when possible by reducing fractions to their simplest form, dividing the numerator and denominator by their greatest common factor.

For mixed numbers division, convert the mixed numbers to improper fractions before inverting the second fraction and multiplying.

Throughout the process of addition, subtraction, multiplication, and division, proper fraction simplification is emphasized to achieve the most accurate result.

A final reminder is given to simplify fractions or convert improper fractions into mixed numbers to avoid issues with math teachers.

Transcripts

good day welcome to the tech math

Channel what we're going to be having a

look at in this video is the easiest way

to solve any question involving

fractions be they addition questions

subtraction questions multiplication

questions or division questions and we

are going to go through and have a look

at all of these there going to be a bit

to go through so please bear with us but

these are going to be the easiest way of

solving any questions involving

fractions so we're going to start with

addition questions there's going to be

about three types of questions you'll

get with these the first is where we

have the same denominator questions like

this one here say for instance you are

asking to add 1/5 + 25s now what you're

going to notice straight away is that we

have the same bottom number the same

denominator if this is the case what we

do for our answer is we keep that same

denominator so in this case the

denominator is five for our answer the

denominator will also be five now for

the numerator the top number all we do

is we just go through and add 1 + 2 is

equal to 3

and that's how you add fractions with

like denominators with the same

denominator keep that denominator in

your answer and just add the numerators

add those top numbers together but what

about where we have different

denominators a question like this one

here say we had one qu and to this we

wanted to add 2/3 now the easiest way to

do this is we're going to find a common

denominator between the four and the

three here we have two different

denominators and we're going to find a

common denominator the easiest way to do

that is through a bit of

multiplication first thing we do is

we're going to multiply these

denominators together so 4 * 3 that

gives us the answer of 12 that gives us

the denominator of our answer which is

12 now what we're going to do is

starting at the top left here we're

going to multiply by the bottom right of

these fractions here so 1 * 3 1 * 3 is

equal to 3 what you're going to notice

is we've multiplied the 4 by 3 and the 3

by three so we've kept these fractions

equivalent now what we're going to do is

moving over to the right here we're

going to start with the top right number

here the two and multiply by the bottom

left number here two ulti 4 is equal to

8 once again this just keeps the

fractions equivalent we're adding so

we're just going to go 3 + 8 this gives

us our answer 11/ 12 now that's a second

type of question what about we have a

look at a third type of question and

that's this one here with where we have

mixed numbers something like 1 and 1/2 +

4 and 2/3 how we would go through and

solve this now the way we do this is

fairly simple we're going to just turn

these mixed numbers into improper

fractions that is just where they're

simply fractions but this is going to be

a bigger number than the bottom number

you'll see what I mean so let's do this

way we do this is as follows we're going

to keep the same bottom numbers the same

denominators here so we're going to have

a two and we're going to have a three

all right we're going to be adding still

but what's going to go on the top well

we get this as follows first off we're

going to multiply the whole number by

the denominator we have 1 * 2 which is

equal to 2 and then we add that

numerator so 1 * 2 is 2 + 1 is equal to

3 so we have three halves in 1 and a

half now for 4 and 2/3 we do the same

process 4 * 3 is equal to 12 + 2 is

equal to 14 there you go we have 14 18/3

all together now what we're going to do

is we're simply going to go through and

do the same process we did for this

second fraction set here so let's do

that first off we had 2 * 3 this gives

us the denominator 2 3es a six now what

we do is we're going to multiply 3 by 3

to give us 9 and we have 14 * 2 which

gives us 28 we're adding so let's add

those together 9 + 28 gives us 37 so we

have 376 as our answer answer but don't

ever just leave this answer like this so

your math teacher will be really annoyed

at you they're going to ask you to

simplify this further now how do we

simplify this simple this means 37 / 6

any fraction even if it's this one here

means 3 / 5 11 / 12 and this one means

37 / 6 so let's just do that 37 / 6 well

66 is a 36 so the answer is going to be

six and there is one left over this one

goes over that six at that same

denominator there cool that's how you go

through and you add any fraction

together now you can probably guess how

to subtract because it's a very similar

process so let's have a look so when

we're subtracting fractions the process

is very similar to addition we're going

to start off with a nice easy question

say 7/ 8 - 1/8 you should be able to get

that one straight away what do you think

it is ah you've got it 7 - 1 is 6 and

that bottom number the denominator stays

the same it's 68 we can simplify this a

bit further cuz we look for a number

that goes into both the top and the

bottom two goes into both the top and

the bottom so 6 / 2 is equal to 3 and 8

/ 2 is equal to 4 that's just a

simplified version equivalent version of

6 over8 what about if we have a

different denominator say we have

something like this say we have uh 4

over 5 and from this I want to subtract

1/3 okay I think you can guess how we're

going to do this uh to get the bottom

number we multiply 5 * 3 is equal to 15

now we do that cross multiplication that

the cross uh cross working out 4 * 3 is

equal to 12 1 * 5 is equal to 5 we are

subtracting 12 subtract 5 our answer is

7 really simple right okay what about a

mixed number here so say we have

something like uh let's go three and 1/3

and from this I wish to subtract uh

let's go 2 and A4 and see how this goes

so with this the first thing we're going

to do is turn these mixed numbers into

improper fractions the same way as

before this is going to be number over

three and this is going to be a number

over four and we are going to be

subtracting so let's do that uh 3 * 3 is

9 + 1 is 10 2 * 4 is 8 + 1 is 9 now what

we're going to do is that same cross

fraction sort of thing that we did over

here okay so let's do that 3 * 4 is

equal to

12 and now we're going to do this bit of

working out 10 * 4 is equal to 40 3 * 9

is equal to 27 we're subtracting 40 take

away 27 is equal to

13 all right can we leave it like that

you've got it this is an improper

fraction we're going to have to change

it so let's do that that 13 / 12 is

equal to 1 and there's 1 left over

that's 1 over 12 cool now let's have a

look at multiplying fractions all right

so multiplying fractions is nice and

easy I think it's the easiest operation

you can do with fractions I remember as

a kid my brother told me this and it's

always stuck with me and always helped

me when I was trying to remember how to

multiply fractions uh he remember he

told me when I was very little I wasn't

at school yet that a half multi by a

half is equal to 1/4 no that was a

little bit strange you know how did you

multiply by something and get a smaller

number all right novity value aside it

did help me to remember this and it

makes perfect sense because what's 1

half of a half another way of thinking

of this a half of a half well if you

think of that with a pizza for instance

or a pie you cut that in half you have

half a pizza and then half of that is

one4 of a pizza right or that we have

one quarter a half of a half is equal to

a quarter all right so the way that we

do this uh it's not just to remember my

uh little childhood stories just have a

look at this 1 multi by 1 is equal to 1

2 ultip by 2 is equal to 4 top by the

top bottom by the bottom got your answer

happy days so let me give you a harder

question here so say for instance we

wanted to go uh what's 3/4 multiplied by

1/3 okay nice and simple 3 * 1 is equal

to 3 4 * 3 is equal 12 uh now that's our

answer but we can simplify this further

into equivalent fraction it's you know a

bit smaller because there's a three that

goes into both the top and the bottom

divide by 3 divide by 3 we get 1 over 4

our answer is one4 cool now just one

last thing what do we do if we have a

whole number well if we have a mixed

number before we we do the same like we

did before there's nothing major there

but I in particular want to show you

something like this say for instance I

wanted to know what half multili by 7

was now the easiest way to deal with

this is as follows we're going to keep

that half the same and we're multiplying

by this seven which we're going to turn

into a fraction now this is a fraction

is equal to 7 over 1 all right makes

sense because 7 / 1 is equal to 7 all

right this is 7 as a fraction now we can

go through and solve this really easy

right 1 * 7 is 7 2 * 1 is equal to 2 we

can simplify this 7 / 2 is equal to 3 uh

and there's one left over that's three

and a half what's half of seven well of

course it's 3 and 1/2 right all right so

now let's go have a look at division so

now we're going to have a look at

dividing fractions and these are really

easy to do as long as you remember the

division is the opposite of

multiplication now multiplication was

pretty easy so there's just one extra

step we need to do to turn it into the

opposite so so let's do that um first

off let's give a question up here uh we

have something like this one here 3/4

and I want to divide into this one2 I

want to see how many halves are in 3/4

all right so as I said the opposite of

division is multiplication so we're

going to rewrite this out a little bit

3/4 and we're going to be multiplying

we're not going to be multiplying by

half we're going to be multiplying by

the opposite of a half now the opposite

of a half well if you get this whole

fraction here and you flip it on its

head if you flip these around you get

the opposite of 1/2 you have 2 over 1

okay now we just turned it into a nice

easy multiplication so let's do that 3 *

2 is equal to 6 4 * 1 is equal to 4 we

have 6 over 4 which is equal to uh

that's 1 and two left over 2 4 and we

can simplify this further because two

goes into both the top and the bottom

this is equal to 1 and a half simple

right now what do we do if we have a

whole number here well no surprise here

say I wanted to go what is 4 fths and I

want divide that by six okay what would

that equal uh we're just going to do

that same process here we have 4 fths

and this is divided by 6 over1 now we

don't want to be dividing we want to do

a bit of multiplication here so let's

just change this around we have 4 fths

and we're going to multiply by 1/ 6 so

let's do that now what we have is 4 * 1

is equal to 4 and 5 * 6 is equal to 30

and we can simplify this because 2 goes

into both the top and the bottom we have

2 over 15 and there is our answer that's

how you go through and you divide with

fractions anyway that's the four

operations addition subtraction

multiplication and division as they go

with fractions now I hope that was of

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bye