How to Multiply and Divide Fractions #10
Summary
TLDRThis educational video script explains the process of multiplying and dividing fractions. It simplifies the multiplication of fractions by demonstrating how to multiply numerators and denominators separately, followed by simplification if possible. The script also covers multiplying fractions by mixed numbers, emphasizing the conversion of mixed numbers to improper fractions for easier calculation. Dividing fractions is addressed by flipping the second fraction and converting division to multiplication. Examples are provided to illustrate each concept, ensuring a clear understanding of fraction operations.
Takeaways
- π’ Multiplying fractions involves multiplying the numerators together to get the new numerator and the denominators together to get the new denominator.
- π After multiplying, it's important to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
- π When multiplying fractions, if both fractions are less than one, the result is a fraction that represents a smaller portion of the whole.
- π To divide fractions, you flip the second fraction (divisor) upside down and change the division to multiplication.
- π An example given is multiplying one-half by one-third, which results in one-sixth, illustrating taking a portion of a portion.
- π When dealing with mixed numbers, it's easier to first convert them to improper fractions before multiplying or dividing.
- π Converting a mixed number to an improper fraction involves multiplying the whole number by the denominator and then adding the original numerator.
- β The video provides a step-by-step guide on how to multiply and divide fractions, including converting mixed numbers and simplifying results.
- π Simplification of fractions is a necessary step to express the answer in its simplest form, which may involve dividing by common factors.
- π The script concludes with a summary that reinforces the methods taught for multiplying and dividing fractions, ensuring understanding.
Q & A
What is the basic method for multiplying fractions?
-To multiply fractions, you multiply the numerators together to get the new numerator and the denominators together to get the new denominator.
How do you simplify a fraction after multiplying?
-After multiplying, you simplify the fraction by dividing the numerator and the denominator by their greatest common divisor.
What is the result when multiplying 7/15 by 3/4?
-Multiplying 7/15 by 3/4 results in 21/60, which simplifies to 7/20 after dividing both the numerator and denominator by 3.
Can you multiply fractions without simplifying?
-Yes, you can multiply fractions without simplifying, but it is common practice to simplify the result for clarity and to reduce the fraction to its simplest form.
What is the result of multiplying 4/7 by 9/5?
-Multiplying 4/7 by 9/5 results in 36/35, which is already in its simplest form and cannot be simplified further.
How do you multiply a fraction by a mixed number?
-To multiply a fraction by a mixed number, it's easier to first convert the mixed number to an improper fraction before multiplying.
What is the improper fraction form of two and three-quarters?
-Two and three-quarters is converted to an improper fraction by multiplying the whole number (2) by the denominator (4) and adding the numerator (3), resulting in 11/4.
What happens when you multiply fractions that are less than one?
-Multiplying fractions that are less than one results in a smaller number, as you are taking a portion of something that is already a fraction of the whole.
How do you divide fractions?
-To divide fractions, you flip the second fraction upside down (invert it) and change the division to multiplication, then multiply the fractions as usual.
What is the result of dividing 3/4 by 5/9?
-Dividing 3/4 by 5/9 results in 27/20, which cannot be simplified further.
How do you convert an improper fraction to a mixed number?
-To convert an improper fraction to a mixed number, divide the numerator by the denominator, use the quotient as the whole number, and the remainder as the new numerator with the same denominator.
Outlines
π Multiplying Fractions
This paragraph explains the process of multiplying fractions. The method involves multiplying both the numerators and denominators of the fractions separately. For instance, multiplying 7/15 by 3/4 results in a new fraction by multiplying 7*3 (numerator) and 15*4 (denominator), yielding 21/60. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 3, resulting in 7/20. The paragraph also covers multiplying fractions by mixed numbers, where it's advised to convert the mixed number to an improper fraction first. An example given is multiplying four-fifths by two and three-quarters, which after converting the mixed number to an improper fraction, results in 44/20, simplifying to 11/5. The concept that multiplying fractions less than one results in an even smaller number is also highlighted.
π Dividing Fractions
The second paragraph focuses on dividing fractions, which is done by flipping the second fraction and changing the division to multiplication. An example given is dividing three-quarters by five-ninths, which after flipping becomes three-quarters times nine-fifths, resulting in 27/20, which cannot be simplified further. Another example involves dividing two-thirds by four-fifths, which after flipping and multiplying results in 10/12, simplifying to 5/6. The paragraph also addresses dividing by a mixed number, requiring the mixed number to be converted to an improper fraction first. An example is dividing three and a half by two-fifths, which after conversion and multiplication results in 35/4, which cannot be simplified and is then converted back to the mixed number form of eight and three over four. The paragraph concludes by summarizing the methods for multiplying and dividing fractions.
Mindmap
Keywords
π‘Multiplying fractions
π‘Numerator
π‘Denominator
π‘Simplifying fractions
π‘Common factor
π‘Mixed number
π‘Improper fraction
π‘Dividing fractions
π‘Reciprocal
π‘Simplified form
π‘Mixed number form
Highlights
Multiplying fractions involves multiplying the numerators and denominators separately.
For 7/15 multiplied by 3/4, multiply 7*3 for the numerator and 15*4 for the denominator.
The result of 7/15 * 3/4 is 21/60, which can be simplified by dividing by a common factor of 3 to get 7/20.
Multiplying 4/7 by 9/5 results in 36/35, which cannot be simplified further.
To multiply a fraction by a mixed number, convert the mixed number to an improper fraction first.
Converting two and three-quarters to an improper fraction involves multiplying the whole number by the denominator and adding it to the numerator.
Multiplying four-fifths by the improper fraction eleven-fourths results in 44/20, which simplifies to 11/5.
When multiplying fractions less than one, the result is a smaller number, as seen with one-half times one-third equals one-sixth.
To divide fractions, flip the second fraction and change the division to multiplication.
Dividing three-quarters by five-ninths is done by multiplying three-quarters by nine-fifths.
The result of dividing three-quarters by five-ninths is 27/20, which cannot be simplified.
When dividing two-thirds by four-fifths, flip four-fifths to five-fourths and change the division to multiplication.
The result of dividing two-thirds by four-fifths is 5/6 after simplification.
For dividing a mixed number by a fraction, convert the mixed number to an improper fraction first.
Converting three and a half to an improper fraction involves multiplying the whole number by the denominator and adding it to the numerator.
Dividing seven and two-fifths by two-fifths results in 35/4, which is then converted to the mixed number eight and three-fourths.
The process of dividing fractions and converting mixed numbers to improper fractions is essential for solving fraction division problems.
Transcripts
in this video we're going to look at how
you multiply and divide fractions
now multiplying fractions is actually
fairly easy
because all you have to do is multiply
both the numerators and denominators
together separately
so for 7 over 15
times 3 over 4
you would first multiply your numerators
so 7 times 3 to give you 21 as your new
numerator
and then do the same thing for your
denominators
so 15 times 4 to give you 60 as your new
denominator
which means that the answer is 21 over
60.
now this answer is entirely correct
already
but in an exam you'll normally have to
simplify your answer
which we can do by dividing the top and
bottom of our fraction
by the common factor of three
which will simplify it to seven over
twenty
for this next question we have to
multiply four over seven
by nine over five
so we multiply 4 by 9 to get 36
and then 7 by 5 to get 35
so we end up with 36 over 35 as our
answer
and this time there's no need to do
anything else because that can't be
simplified
in this one we're being asked to
multiply four-fifths
by two and three-quarters
which is a mixed number
now you can directly multiply fractions
by mixed numbers
but it's a lot easier if you take the
mixed number and convert it to an
improper fraction
first so to do that we multiply the two
by the four to get eight
and then add that eight to the numerator
of three
to get a new numerator of eleven
so we get an improper fraction of eleven
over four
then we can just multiply four fifths by
eleven over four like in our other
examples
so four times eleven is forty 44
and 5 times 4 is 20
which gives us 44 over 20
and then we can simplify that by
dividing top and bottom by 4 to get 11
over 5.
one other thing to point out about
multiplying fractions
is that when we multiply together
fractions that are less than one
like one-half times one-third
we actually get an even smaller number
because we're taking a small portion
of something that was already small
for example if we start with half a
pizza
then by multiplying it by one third
we're effectively selecting one third of
that half pizza
so now we only have one sixth of the
whole pizza
in order to divide fractions we actually
use a trick
first of all you want to write out the
fraction
for example three-quarters divided by
five-ninths
then you flip the second fraction upside
down
so change the five over nine
to nine over five
and then we can rewrite the question
with a multiply instead of a divide
which means that we'll have three
quarters times nine fifths
so all we've done is flip the second
fraction upside down
and change the divide to a multiply
then we can just multiply the fractions
together as usual
so here we're to do 3 times 9 to give us
27
and 4 times 5 to give us 20.
so we have 27 over 20
and the last step we need to check if it
can be simplified
which it can't so the answer stays as 27
over 20.
let's try a couple more
in this one we're dividing two thirds by
four-fifths
so we flip the four-fifths upside down
to make it five over four
and then change the divide to a multiply
so that we can multiply them like normal
two times five is ten
and three times four is twelve
so we have ten over twelve
which we can simplify by dividing top
and bottom by two
to get five over six
in this question we're dividing three
and a half
by two-fifths
the fact that we need the answer in the
form of a mixed number doesn't change
how we do the question at all
it just means that we're gonna have to
convert it into mixed number form at the
end
the first step though is to convert this
three and a half
which is a mixed number
into an improper fraction to make things
easier for ourselves
so we do three times two which is six
and then add that to the numerator
so because six plus one is seven
we end up with seven over two
and our question now reads seven over
two
divided by two over five
then like always we flip the two over
five upside down to get five over 2
and change the divide to a multiply
so we're going to have to do 7 times 5
which is 35
and 2 times 2 which is 4.
to get 35 over 4
and we can't simplify this at all
the last step is to convert this to a
mixed number like they ask for in the
question
so we divide 35 by four to get eight
remainder three
which means that our mixed number would
be eight
and three over four
anyways that's everything for
multiplying and dividing fractions
so hope you found it useful
and we'll see you again soon
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