14 7/8 Divided By 2

Lesson 4: Multiplying and Dividing Fractions

/en/fractions/adding-and-subtracting-fractions/content/

Multiplying fractions

A fraction is a function of a whole. In the last lesson, you learned how to add and subtract fractions. But that'south not the simply kind of math you tin practice with fractions. There are times when it will exist useful to multiply fractions besides.

Click through the slideshow to learn how to write a multiplication trouble with fractions.

• 

  Allow's ready a multiplication example with fractions. Suppose yous drink 2/4 of a pot of coffee every forenoon.

• 

  But your doctor only told you lot that you need to cutting down your java drinking past one-half.

• 

  At present you demand to figure out how much ane/2 of 2/4 of a pot of coffee is.

• 

  This may not wait like a multiplication problem. Just when you see the word of with fractions, it means you lot demand to multiply.

• 

  To ready the example, nosotros'll just supervene upon the word of with a multiplication sign.

• 

  Now our example is set up to be solved.

• 

  Unlike regular multiplication, which gives you a larger number...

• 

  Unlike regular multiplication, which gives you a larger number...multiplying fractions will ordinarily give you lot a smaller number.

• 

  So when we multiply one/two times ii/iv...

• 

  Then when we multiply 1/2 times 2/4...our respond volition be smaller than two/4.

• 

  Here's some other example. Let's say you have 3/five of a loving cup of chocolate filling.

• 

  You want to put an equal amount of filling in each of these iv cupcakes.

• 

  You could say that y'all want to put 1/4 of 3/five of a cup of filling in each cupcake.

• 

  Just like we did before, nosotros'll change the word of into a multiplication sign.

• 

  And now our fractions are gear up to be multiplied.

• 

Try This!

Try setting up the multiplication problem below. Don't worry nearly solving it even so!

A recipe calls for ii/iii of a cup of milk. You desire to cut the recipe in half.

Note: Although our case says the correct answer is 2/three x ane/2, recall, with multiplying guild does not matter. i/2 x ii/3 would also exist correct.

Solving multiplication problems with fractions

Now that we know how to fix multiplication problems with fractions, let'southward practice solving a few. If you lot experience comfortable multiplying whole numbers, you lot're ready to multiply fractions.

Click through slideshow to larn how to multiply two fractions.

• 

  Let's multiply to detect 1/2 of 7/10.

• 

  But like we did before, we'll supercede the give-and-take of with a multiplication sign. Now we're ready to multiply.

• 

  Showtime, we'll multiply the numerators: ane and 7.

• 

  1 times 7 equals 7, and then nosotros'll write 7 to the right of the numerators.

• 

  When we added fractions, the denominators stayed the same. Simply when we multiply, the denominators get multiplied too.

• 

  two times 10 equals 20, so we'll write 20 to the right of the denominators.

• 

  Now we know 1/2 times vii/10 equals vii/20.

• 

  Nosotros could as well say 1/two of seven/10 is 7/xx.

• 

  Let's try another example: iii/five times 2/3.

• 

  Commencement, nosotros'll multiply our numerators. 3 times two equals 6.

• 

  Side by side, we'll multiply our denominators. 5 times iii equals 15.

• 

  So 3/v times 2/3 equals half dozen/15.

• 

Effort This!

Effort solving the multiplication problems beneath.

Multiplying a fraction and a whole number

Multiplying a fraction and a whole number is like to multiplying two fractions. There's but one extra footstep: Before you tin multiply, you'll demand to turn the whole number into a fraction. This slideshow volition testify y'all how to do it.

Click through the slideshow to learn how to multiply a fraction and a whole number.

• 

  Let'southward multiply 2 times 1/3. Remember, this is just another way of request, "What'due south 1/3 of 2?"

• 

  Before we start, we need to make sure these numbers are ready to be multiplied.

• 

  We can't multiply a whole number and a fraction, so we're going to take to write ii as a fraction.

• 

  As you learned in Introduction to Fractions, we can also write 2 as 2/1.That's because 2 can exist divided past 1 twice.

• 

  At present nosotros're ready to multiply!

• 

  First, we'll multiply the numerators: 2 and 1.

• 

  2 times 1 equals 2. We'll line the 2 up with the numerators.

• 

  Next, we'll multiply the denominators: 1 and 3.

• 

  1 times iii equals iii. Nosotros'll line the iii up with the denominators.

• 

  And then 2/1 times one/3 equals 2/three. We could also say ane/iii of 2 is ii/three.

• 

  Let's try some other example: 4 times 1/five.

• 

  We'll take to write 4 as a fraction before we start.

• 

  We'll rewrite iv as four/1. At present we're set to multiply.

• 

  Commencement, nosotros'll multiply the numerators: 4 and 1.

• 

  4 times 1 equals iv, then the numerator of our answer is iv.

• 

  Next, we'll multiply the denominators: 1 and 5.

• 

  i times 5 equals 5, and so 5 is the denominator of our answer.

• 

  And so 4/i times 1/5 equals 4/five.

• 

Try This!

Try solving the multiplication issues beneath.

Dividing fractions

Over the final few pages, you lot've learned how to multiply fractions. Yous might have guessed that you can divide fractions likewise. You split up fractions to meet how many parts of something are in something else. For example, if you wanted to know how many fourths of an inch are in four inches, you could divide 4 by i/four.

Let'due south endeavor another instance. Imagine a recipe calls for 3 cups of flour, but your measuring loving cup just holds i/iii, or 1-third, of a cup. How many thirds of a cup should yous add?

We'll need to find out how many thirds of a cup are in iii cups. In other words, we'll need to dissever three past one-third.

We'd write the problem like this:

3 ÷ 1/iii

Try This!

Try setting upward these segmentation bug with fractions. Don't worry about solving them nevertheless!

A recipe calls for 3/4 of a cup of water. You only have a 1/8 measuring cup.

Solving division issues with fractions

Now that we know how to write segmentation problems, let'due south practice by solving a few. Dividing fractions is a lot similar multiplying. It just requires 1 extra step. If you tin can multiply fractions, you lot tin split up them too!

Click through the slideshow to learn how to divide a whole number by a fraction.

• 

  Let's divide 3 by i/three. Remember, this is just another way to ask, "How many thirds are in iii?"

• 

  In our lesson on sectionalisation, you learned how to write the division sign like this (/).

• 

  When dividing fractions, information technology will aid to apply the other symbol for division ( ÷ ) so we don't mistake it for a fraction.

• 

  Just like multiplication, we'll start by looking for whatsoever whole numbers in our problem. There'southward one: 3.

• 

  Call back, three is the same thing every bit 3/i.

• 

  Before nosotros can divide, we demand to make 1 more change.

• 

  We'll switch the numerator and the denominator of the fraction we're dividing by: 1/three in this example.

• 

  So 1/3 becomes 3/1.

• 

  This is chosen finding the reciprocal, or multiplicative inverse, of the fraction.

• 

  Since we're switching our original fraction, we'll as well switch the segmentation sign ( ÷ ) to a multiplication sign ( 10 ).

• 

  That's because multiplication is the inverse of division.

• 

  Now we tin care for this like a regular multiplication problem.

• 

  First, we'll multiply the numerators: 3 and 3.

• 

  3 times 3 equals 9, and then nosotros'll write that next to the numerators.

• 

  Next, nosotros'll multiply the denominators: i and one.

• 

  one times ane equals one, and then we'll write 1 adjacent to the denominator.
  

• 

  As y'all tin see, iii/ane x 1/3 = nine/1.

• 

  Recall, whatsoever fraction over 1 can besides be expressed as a whole number. So 9/1 = 9.

• 

  iii ÷ 1/3 = 9. In other words, there are nine thirds in 3.

• 

  Let'south try another example: 5 divided by 4/7 .

• 

  Every bit always, we'll rewrite any whole numbers, so five becomes 5/1.

• 

  Next, we'll observe the reciprocal of 4/seven. That's the fraction we're dividing by.

• 

  To do that, we'll switch the numerator and denominator, and then iv/7 becomes 7/4.

• 

  Then nosotros'll change the division sign ( ÷ ) to a multiplication sign ( x ).

• 

  At present we can multiply equally we ordinarily would. Commencement, we'll multiply the numerators: 5 and vii.

• 

  5 times 7 equals 35, and then we'll write that adjacent to the numerators.

• 

  Next, we'll multiply the denominators: 1 and four.

• 

  1 times iv equals iv, so we'll write that side by side to the denominators.
  

• 

  So 5/1 x iv/7 = 35/4 .
  

• 

  As yous learned before, we could convert our improper fraction into a mixed number to make our answer easier to read.

• 

  35/4 = eight 3/4. So 5 ÷ 4/7 = viii 3/four.
  

• 

Try This!

Try solving these partitioning problems. Don't worry most reducing the respond for now.

Dividing two fractions

We but learned how to separate a whole number past a fraction. You tin can utilise the same method to divide two fractions.

Click through the slideshow to acquire how to split with two fractions.

• 

  Allow'south try a problem with two fractions: 2/3 ÷ three/4. Here, we want to know how many 3/iv are in 2/3.
  

• 

  First, we'll find the reciprocal of the fraction nosotros're dividing past: iii/4.

• 

  To do that, we'll switch the numerator and denominator. Then 3/4 becomes 4/three.

• 

  Next, we'll change the partitioning sign ( ÷ ) to a multiplication sign ( x ).

• 

  Now nosotros'll multiply the numerators. ii ten 4 = viii, so nosotros'll write 8 next to the top numbers.

• 

  Next, we'll multiply the denominators. iii ten iii = nine, so we'll write nine next to the bottom numbers.
  

• 

  And so ii/three x 4/iii = viii/9.
  

• 

  We could too write this as ii/3 ÷ iii/4 = viii/9.
  

• 

  Allow's try another example: iv/seven divided by 2/ix.

• 

  There are no whole numbers, and so we'll find the reciprocal of the fraction we're dividing by. That's ii/ix.

• 

  To practise that, we'll switch the numerator and denominator. And then 2/9 becomes 9/2.

• 

  Now nosotros'll change the segmentation sign ( ÷ ) to a multiplication sign ( x ) and multiply as normal.

• 

  Kickoff, we'll multiply the numerators. 4 x ix = 36.

• 

  Next, we'll multiply the denominators. 7 x 2 = xiv.

• 

  So 4/7 ten 9/ii = 36/14. But similar earlier, you could convert this improper fraction into a mixed number.

• 

  And so 4/7 ÷ 2/9 = 2 eight/14.

• 

Effort This!

Attempt solving these sectionalisation problems. Don't worry almost reducing the answer for now.

Multiplying and dividing mixed numbers

How would yous solve a problem like this?

As yous learned in the previous lesson, whenever you're solving a problem with a mixed number you'll need to catechumen it into an improper fraction first. Then you tin can multiply or divide as usual.

Using canceling to simplify issues

Sometimes y'all might accept to solve problems like this:

Both of these fractions include large numbers. Y'all could multiply these fractions the same style as whatsoever other fractions. However, big numbers like this tin be hard to sympathize. Can y'all picture 21/50, or twenty-one fiftieths, in your head?

21/50 x 25/14 = 525/700

Fifty-fifty the respond looks complicated. Information technology's 525/700, or five hundred twenty-five seven-hundredths. What a mouthful!

If y'all don't like working with large numbers, you tin can simplify a problem similar this by using a method called canceling. When yous abolish the fractions in a problem, y'all're reducing them both at the same fourth dimension.

Canceling may seem complicated at showtime, only we'll show yous how to do information technology step by step. Let's take another look at the instance we only saw.

Step ane

Starting time, wait at the numerator of the start fraction and the denominator of the second. We want to run across if they can be divided past the same number.

In our example, it looks like both 21 and 14 can be divided by 7.

Step 2

Side by side, we'll separate 21 and 14 past vii. First, we'll divide our top number on the left: 21.

21 ÷ seven = 3

Then we'll divide the bottom number on the right: 14.

14 ÷ vii = 2

We'll write the answers to each problem adjacent to the numbers we divided. Since 21 ÷ seven equals iii, we'll write 3 where the 21 was. 14 ÷ 7 equals 2, so nosotros'll write 2 where the 14 was. Nosotros can cantankerous out, or cancel, the numbers we started with.

Our trouble looks a lot simpler at present, doesn't it?

Stride 3

Allow's expect at the other numbers in the fraction. This time we'll look at the denominator of the get-go fraction and the numerator of the second. Can they be divided past the same number?

Notice they can both be divided by 25! Y'all might have too noticed they can both exist divided by five. Nosotros could utilize v too, but by and large when you lot are canceling, you desire to look for the biggest number both numbers can be divided by. This fashion you won't take to reduce the fraction again at the end.

Step 4

Adjacent, we'll cancel just like we did in step 2.
Nosotros'll divide our bottom number on the left: fifty.

50 ÷ 25 = ii

Then we'll divide the acme number on the right: 25.

25 ÷ 25 = 1

Nosotros'll write the answers to each problem next to the numbers nosotros divided.

Step v

Now that nosotros've canceled the original fractions, we can multiply our new fractions like we normally would. As always, multiply the numerators first:

3 x 1 = 3

Then multiply the denominators:

2 ten 2 = 4

Then three/2 x ane/2 = 3/4, or iii-fourths.

Footstep 6

Finally, let's double check our work. 525/700 would accept been our answer if nosotros had solved the problem without canceling. If we carve up both 525 and 700 by 175, nosotros can meet that 525/700 is equal to 3/4.

Nosotros could also say that we're reducing 525/700 to 3/4. Call up, canceling is simply another mode of reducing fractions before solving a problem. You'll become the aforementioned answer, no affair when you reduce them.

/en/fractions/converting-percentages-decimals-and-fractions/content/

14 7/8 Divided By 2,

Source: https://edu.gcfglobal.org/en/fractions/multiplying-and-dividing-fractions/1/

Posted by: padulaablumersy.blogspot.com

Share this post