What is the product 5 2 3 4

Lesson 4: Multiplying and Dividing Fractions

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Multiplying fractions

A fraction is a part of a whole. In the last lesson, you learned how to add and subtract fractions. But that’s not the only kind of math you can do with fractions. There are times when it will be useful to multiply fractions too.

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

  • What is the product 5 2 3 4

    Let's set up a multiplication example with fractions. Suppose you drink 2/4 of a pot of coffee every morning.

  • What is the product 5 2 3 4

    But your doctor just told you that you need to cut down your coffee drinking by half.

  • What is the product 5 2 3 4

    Now you need to figure out how much 1/2 of 2/4 of a pot of coffee is.

  • What is the product 5 2 3 4

    This may not look like a multiplication problem. But when you see the word of with fractions, it means you need to multiply.

  • What is the product 5 2 3 4

    To set up the example, we'll just replace the word of with a multiplication sign.

  • What is the product 5 2 3 4

    Now our example is ready to be solved.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    So when we multiply 1/2 times 2/4...

  • What is the product 5 2 3 4

    So when we multiply 1/2 times 2/4...our answer will be smaller than 2/4.

  • What is the product 5 2 3 4

    Here's another example. Let's say you have 3/5 of a cup of chocolate filling.

  • What is the product 5 2 3 4

    You want to put an equal amount of filling in each of these 4 cupcakes.

  • What is the product 5 2 3 4

    You could say that you want to put 1/4 of 3/5 of a cup of filling in each cupcake.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    And now our fractions are ready to be multiplied.

  • What is the product 5 2 3 4

Try This!

Try setting up the multiplication problem below. Don't worry about solving it yet!

A recipe calls for 2/3 of a cup of milk. You want to cut the recipe in half.

What is the product 5 2 3 4

Note: Although our example says the correct answer is 2/3 x 1/2, remember, with multiplying order does not matter. 1/2 x 2/3 would also be correct.

Solving multiplication problems with fractions

Now that we know how to set up multiplication problems with fractions, let's practice solving a few. If you feel comfortable multiplying whole numbers, you're ready to multiply fractions.

Click through slideshow to learn how to multiply two fractions.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Just like we did earlier, we'll replace the word of with a multiplication sign. Now we're ready to multiply.

  • What is the product 5 2 3 4

    First, we'll multiply the numerators: 1 and 7.

  • What is the product 5 2 3 4

    1 times 7 equals 7, so we'll write 7 to the right of the numerators.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Now we know 1/2 times 7/10 equals 7/20.

  • What is the product 5 2 3 4

    We could also say 1/2 of 7/10 is 7/20.

  • What is the product 5 2 3 4

    Let's try another example: 3/5 times 2/3.

  • What is the product 5 2 3 4

    First, we'll multiply our numerators. 3 times 2 equals 6.

  • What is the product 5 2 3 4

    Next, we'll multiply our denominators. 5 times 3 equals 15.

  • What is the product 5 2 3 4

    So 3/5 times 2/3 equals 6/15.

  • What is the product 5 2 3 4

Try This!

Try solving the multiplication problems below.

What is the product 5 2 3 4

What is the product 5 2 3 4

What is the product 5 2 3 4

Multiplying a fraction and a whole number

Multiplying a fraction and a whole number is similar to multiplying two fractions. There's just one extra step: Before you can multiply, you'll need to turn the whole number into a fraction. This slideshow will show you how to do it.

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

  • What is the product 5 2 3 4

    Let's multiply 2 times 1/3. Remember, this is just another way of asking, "What's 1/3 of 2?"

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    We can't multiply a whole number and a fraction, so we're going to have to write 2 as a fraction.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Now we're ready to multiply!

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    1 times 3 equals 3. We'll line the 3 up with the denominators.

  • What is the product 5 2 3 4

    So 2/1 times 1/3 equals 2/3. We could also say 1/3 of 2 is 2/3.

  • What is the product 5 2 3 4

    Let's try another example: 4 times 1/5.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    We'll rewrite 4 as 4/1. Now we're ready to multiply.

  • What is the product 5 2 3 4

    First, we'll multiply the numerators: 4 and 1.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    So 4/1 times 1/5 equals 4/5.

  • What is the product 5 2 3 4

Try This!

Try solving the multiplication problems below.

What is the product 5 2 3 4

What is the product 5 2 3 4

What is the product 5 2 3 4

Dividing fractions

Over the last few pages, you've learned how to multiply fractions. You might have guessed that you can divide fractions too. You divide fractions to see 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 1/4.

Let's try another example. Imagine a recipe calls for 3 cups of flour, but your measuring cup only holds 1/3, or one-third, of a cup. How many thirds of a cup should you add?

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

What is the product 5 2 3 4

We'd write the problem like this:

3 ÷ 1/3

Try This!

Try setting up these division problems with fractions. Don't worry about solving them yet!

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

What is the product 5 2 3 4

Solving division problems with fractions

Now that we know how to write division problems, let's practice by solving a few. Dividing fractions is a lot like multiplying. It just requires one extra step. If you can multiply fractions, you can divide them too!

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

  • What is the product 5 2 3 4

    Let's divide 3 by 1/3. Remember, this is just another way to ask, "How many thirds are in 3?"

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Remember, 3 is the same thing as 3/1.

  • What is the product 5 2 3 4

    Before we can divide, we need to make one more change.

  • What is the product 5 2 3 4

    We'll switch the numerator and the denominator of the fraction we're dividing by: 1/3 in this example.

  • What is the product 5 2 3 4

    So 1/3 becomes 3/1.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Since we're switching our original fraction, we'll also switch the division sign (÷) to a multiplication sign (x).

  • What is the product 5 2 3 4

    That's because multiplication is the inverse of division.

  • What is the product 5 2 3 4

    Now we can treat this like a regular multiplication problem.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    3 times 3 equals 9, so we'll write that next to the numerators.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    1 times 1 equals 1, so we'll write 1 next to the denominator.

  • What is the product 5 2 3 4

    As you can see, 3/1 x 1/3 = 9/1.

  • What is the product 5 2 3 4

    Remember, any fraction over 1 can also be expressed as a whole number. So 9/1 = 9.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    As always, we'll rewrite any whole numbers, so 5 becomes 5/1.

  • What is the product 5 2 3 4

    Next, we'll find the reciprocal of 4/7. That's the fraction we're dividing by.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Now we can multiply as we normally would. First, we'll multiply the numerators: 5 and 7.

  • What is the product 5 2 3 4

    5 times 7 equals 35, so we'll write that next to the numerators.

  • What is the product 5 2 3 4

    Next, we'll multiply the denominators: 1 and 4.

  • What is the product 5 2 3 4

    1 times 4 equals 4, so we'll write that next to the denominators.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    35/4 = 8 3/4. So 5 ÷ 4/7 = 8 3/4.

  • What is the product 5 2 3 4

Try This!

Try solving these division problems. Don't worry about reducing the answer for now.

What is the product 5 2 3 4

What is the product 5 2 3 4

What is the product 5 2 3 4

Dividing two fractions

We just learned how to divide a whole number by a fraction. You can use the same method to divide two fractions.

Click through the slideshow to learn how to divide with two fractions.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    First, we'll find the reciprocal of the fraction we're dividing by: 3/4.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    Now we'll multiply the numerators. 2 x 4 = 8, so we'll write 8 next to the top numbers.

  • What is the product 5 2 3 4

    Next, we'll multiply the denominators. 3 x 3 = 9, so we'll write 9 next to the bottom numbers.

  • What is the product 5 2 3 4

    So 2/3 x 4/3 = 8/9.

  • What is the product 5 2 3 4

    We could also write this as 2/3 ÷ 3/4 = 8/9.

  • What is the product 5 2 3 4

    Let's try another example: 4/7 divided by 2/9.

  • What is the product 5 2 3 4

    There are no whole numbers, so we'll find the reciprocal of the fraction we're dividing by. That's 2/9.

  • What is the product 5 2 3 4

    To do that, we'll switch the numerator and denominator. So 2/9 becomes 9/2.

  • What is the product 5 2 3 4

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

  • What is the product 5 2 3 4

    First, we'll multiply the numerators. 4 x 9 = 36.

  • What is the product 5 2 3 4

    Next, we'll multiply the denominators. 7 x 2 = 14.

  • What is the product 5 2 3 4

    So 4/7 x 9/2 = 36/14. Just like before, you could convert this improper fraction into a mixed number.

  • What is the product 5 2 3 4

    So 4/7 ÷ 2/9 = 2 8/14.

  • What is the product 5 2 3 4

Try This!

Try solving these division problems. Don't worry about reducing the answer for now.

What is the product 5 2 3 4

What is the product 5 2 3 4

What is the product 5 2 3 4

Multiplying and dividing mixed numbers

How would you solve a problem like this?

What is the product 5 2 3 4

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

Using canceling to simplify problems

Sometimes you might have to solve problems like this:

What is the product 5 2 3 4

Both of these fractions include large numbers. You could multiply these fractions the same way as any other fractions. However, large numbers like this can be difficult to understand. Can you picture 21/50, or twenty-one fiftieths,in your head?

21/50 x 25/14 = 525/700

Even the answer looks complicated. It's 525/700, or five hundred twenty-five seven-hundredths. What a mouthful!

If you don't like working with large numbers, you can simplify a problem like this by using a method called canceling. When you cancel the fractions in a problem, you're reducing them both at the same time.

Canceling may seem complicated at first, but we'll show you how to do it step by step. Let's take another look at the example we just saw.

What is the product 5 2 3 4

Step 1

First, look at the numerator of the first fraction and the denominator of the second. We want to see if they can be divided by the same number.

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

What is the product 5 2 3 4

Step 2

Next, we'll divide 21 and 14 by 7. First, we'll divide our top number on the left: 21.

21 ÷ 7 = 3

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

14 ÷ 7 = 2

We'll write the answers to each problem next to the numbers we divided. Since 21 ÷ 7 equals 3, we'll write 3 where the 21 was. 14 ÷ 7 equals 2, so we'll write 2 where the 14 was. We can cross out, or cancel, the numbers we started with.

What is the product 5 2 3 4

Our problem looks a lot simpler now, doesn't it?

What is the product 5 2 3 4

Step 3

Let's look at the other numbers in the fraction. This time we'll look at the denominator of the first fraction and the numerator of the second. Can they be divided by the same number?

What is the product 5 2 3 4

Notice they can both be divided by 25! You might have also noticed they can both be divided by 5. We could use 5 too, but generally when you are canceling, you want to look for the biggest number both numbers can be divided by. This way you won't have to reduce the fraction again at the end.

Step 4

Next, we'll cancel just like we did in step 2.
We'll divide our bottom number on the left: 50.

50 ÷ 25 = 2

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

25 ÷ 25 = 1

We'll write the answers to each problem next to the numbers we divided.

What is the product 5 2 3 4

Step 5

Now that we'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 x 2 = 4

So 3/2 x 1/2 =3/4, or three-fourths.

What is the product 5 2 3 4

Step 6

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

What is the product 5 2 3 4

We could also say that we're reducing 525/700 to 3/4. Remember, canceling is just another way of reducing fractions before solving a problem. You'll get the same answer, no matter when you reduce them.

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How do you find the product?

When looking to find what the product of a number is, you can find each product of a number by multiplying it by another number. For example, 27 is a product of 9 and 3, because 9 x 3 = 27.

What is the product of 2/3 and 4?

Answer. The product of -2,3 and 4 is -24.

What is the product of a number 5?

1 Expert Answer The product of a number of 5 is 5 x, where x can be any number.

What is product of a number?

The product is the multiplication of two or more integers together. Assume their are two integers 8 and 7 , then their product will be obtained when we multiply both the numbers together. 8 × 7 = 56 . The product of 8 and 7 is 56 .