How to Calculate ANY Fraction Easily!
Summary
TLDRThis 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
🔢 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.
➖ 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.
✖️ 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.
Mindmap
Keywords
💡Fractions
💡Addition of fractions
💡Common denominator
💡Improper fractions
💡Mixed numbers
💡Multiplication of fractions
💡Division of fractions
💡Simplifying fractions
💡Equivalent fractions
💡Numerator and denominator
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
some help if it was please remember
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and that is all I will see you next time
bye
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