How to Multiply and Divide Fractions #10

Summary

This 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

• 🔢 Multiplying fractions involves multiplying the numerators together to get the new numerator and the denominators together to get the new denominator.
• 📉 After multiplying, it's important to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
• 📈 When multiplying fractions, if both fractions are less than one, the result is a fraction that represents a smaller portion of the whole.
• 🔄 To divide fractions, you flip the second fraction (divisor) upside down and change the division to multiplication.
• 🍕 An example given is multiplying one-half by one-third, which results in one-sixth, illustrating taking a portion of a portion.
• 📖 When dealing with mixed numbers, it's easier to first convert them to improper fractions before multiplying or dividing.
• 🔄 Converting a mixed number to an improper fraction involves multiplying the whole number by the denominator and then adding the original numerator.
• ✅ The video provides a step-by-step guide on how to multiply and divide fractions, including converting mixed numbers and simplifying results.
• 📉 Simplification of fractions is a necessary step to express the answer in its simplest form, which may involve dividing by common factors.
• 📝 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

00:00

📚 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.

05:02

🔄 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.

Keywords

💡Multiplying fractions

Multiplying fractions refers to the mathematical operation where two fractions are multiplied together. In the video, this is explained as a straightforward process of multiplying the numerators together to form a new numerator and the denominators together to form a new denominator. For instance, multiplying 7/15 by 3/4 results in 21/60. This operation is central to the video's theme of fraction arithmetic, showcasing the foundational steps in fraction multiplication.

💡Numerator

The numerator is the top number in a fraction, representing the number of parts being considered. In the context of the video, when multiplying fractions, the numerators are multiplied together. For example, in the fraction 7/15, '7' is the numerator. The video emphasizes that when multiplying fractions, you multiply the numerators of the two fractions to get the new numerator of the resulting fraction.

💡Denominator

The denominator is the bottom number in a fraction, indicating the total number of equal parts into which the whole is divided. The video explains that when multiplying fractions, the denominators are also multiplied together. In the example of multiplying 7/15 by 3/4, the denominators 15 and 4 are multiplied to get 60, which is the denominator of the resulting fraction.

💡Simplifying fractions

Simplifying fractions involves reducing a fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor. The video demonstrates this by showing how 21/60 can be simplified to 7/20 by dividing both the numerator and the denominator by their common factor of 3. Simplification is an important step in fraction arithmetic to express fractions in their most reduced form.

💡Common factor

A common factor is a number that divides two or more numbers without leaving a remainder. In the video, the concept is used to explain how to simplify fractions by dividing both the numerator and the denominator by their common factor. For example, the fraction 21/60 has a common factor of 3, which is used to simplify it to 7/20.

💡Mixed number

A mixed number is a number that combines a whole number and a proper fraction, such as 2 and 3/4. The video explains that mixed numbers can be converted to improper fractions for easier multiplication with other fractions. For example, the mixed number 2 and 3/4 is converted to the improper fraction 11/4 before being multiplied by 4/5.

💡Improper fraction

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. The video demonstrates the conversion of mixed numbers to improper fractions, such as converting 2 and 3/4 to 11/4, to facilitate multiplication with other fractions. Improper fractions are used in the video to illustrate the multiplication process and simplify the arithmetic involved.

💡Dividing fractions

Dividing fractions is the process of dividing one fraction by another. The video explains that dividing fractions is essentially the same as multiplying the first fraction by the reciprocal of the second fraction. For example, dividing 3/4 by 5/9 involves multiplying 3/4 by the reciprocal of 5/9, which is 9/5, resulting in 27/20.

💡Reciprocal

The reciprocal of a number is what you multiply that number by to get 1. In the context of fractions, the reciprocal is obtained by swapping the numerator and the denominator. The video uses reciprocals to explain how to divide fractions, such as flipping 5/9 to 9/5 to divide 3/4 by 5/9.

💡Simplified form

A simplified form of a fraction is when the fraction is expressed as a ratio of coprime integers, meaning the numerator and the denominator have no common factors other than 1. The video shows the process of checking if a resulting fraction can be simplified further after multiplication or division, such as simplifying 10/12 to 5/6.

💡Mixed number form

A mixed number form is the representation of a fraction as a whole number and a proper fraction. The video includes an example where the improper fraction 35/4 is converted to the mixed number form 8 and 3/4 to meet the requirement of the problem. This step is important when the problem asks for the answer to be in 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