What is the traditional method for multiplying fractions?

When we multiply fractions, we do not have to have the same denominators. We multiply straight across. Let’s look at three fourths times one half. 2

Three times one is three… 3

…and 4 times 2 equals 8. The product is three eighths.

Let’s look at another problem, seven halves times two sevenths. 5

Seven times two is fourteen… 6

…and two times seven is fourteen. The product is fourteen fourteenths. 7

Here’s another problem, six eighths times three sevenths. 8

Six times three is eighteen… 9

…and eight times seven equals fifty-six …and eight times seven equals fifty-six. The product is eighteen fifty-sixths. 10

Let’s look at one more problem, six thirds times four halves. 11

Six times four equals twenty-four… 12

…and 3 times 2 equals 6. The product is twenty-four sixths. 13

Remember, adding or subtracting fractions is different Remember, adding or subtracting fractions is different. When we add or subtract fractions, we have to have the same denominator. Let's look at the problem one fourth plus 2/3.

The denominators are not the same, so we need to get the same fair shares. 15

We change one fourth to three twelfths… 16

…and two thirds to eight twelfths. 17

Now we can add. The sum is eleven twelfths. 18

Let's compare this one more time with multiplying fractions.

When we multiply these fractions, we are taking a portion of one of the fractions. When we multiply 2/3 by 1/2, we are taking 2/3…

…of one half. We can think of this as taking a fraction of a fraction.

We see that two thirds times one half equals two sixths.

We can simplify two sixths. Two sixths is the same as one third We can simplify two sixths. Two sixths is the same as one third. The answer is one third.

How do we simplify the answer?

In most cases, we need to simplify the answers to fraction problems In most cases, we need to simplify the answers to fraction problems. We break larger fractions down into simpler fractions. Let’s see how this works.

When we multiply three fourths…

…times two fourths…

…we get six sixteenths.

We can simplify this fraction by finding the greatest common factor of the numerator and denominator. What is the greatest common factor of six and sixteen?

It is two. We write this as a fraction equal to one, or two halves.

Now we think, what number times two is six?

We know the answer is three.

For the denominator, we think, what number times two equals sixteen?

The answer is eight.

We rewrite this as three eighths times one…

…or simply three eighths …or simply three eighths. The fraction six sixteenths simplifies to three eighths.

Sometimes the numerator is larger than the denominator, This is called an improper fraction. When we multiply three fourths times three halves, we get nine eighths.

Let’s simplify the improper fraction nine eighths Let’s simplify the improper fraction nine eighths. We need to find the whole number in the fraction…

…so we pull out a fraction equal to one, eight eighths …so we pull out a fraction equal to one, eight eighths. Nine eighths is the same as eight eighths…

…plus one eighth. Since we know that eight eighths equals one…

…we write the improper fraction as the mixed number one and one eighth.

When do we simplify more than once?

Sometimes we have to simplify more than once to get our answer in its simplest form. For example, when we multiply four fifths times three halves…

…we get the improper fraction twelve tenths.

We’ll start by changing the fraction to a mixed number.

We break twelve tenths into a fraction equal to one, ten tenths…

…plus a proper fraction, two tenths.

We write this as one and two tenths. Is the answer simplified?

No, we can simplify two tenths No, we can simplify two tenths. What is the greatest common factor of two and ten?

It is two. We write two halves, and then think, what number times two is two?

It is one. The numerator if the simplified fraction is one.

Now we look at the denominator. What number times two equals ten?

The answer is five.

We write this as one fifth times one…

…or one fifth.

We wrote the improper fraction twelve tenths as one and two tenths…

…and then simplified the fraction two tenths to one fifth.

We see that our final answer is one and one fifth.