Multiplying Fractions - Fast And Easy Math Learning Videos
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Title: Multiplying Fractions - Fast And Easy Math Learning Videos
When we multiply two fractions, we can show the multiplication using the same array we’ve used before, like this.
Since we’re dealing with fractions of numbers, we need whole units that are bigger than these that we’ve used before. We can zoom in a little like this.
Now we can see each whole unit in more detail.
We start by showing the first fraction in the problem, two-fifths, on this scale.
So, we divide each unit into five equal parts to show fifths.
We show the second fraction on this scale.
So, we divide each unit into four equal parts to show fourths.
Next, two show the first fraction, we count two-fifths here, and show the second fraction by counting three-fourths here.
The product of these fractions is shown by this array.
We’re multiplying fractions, so the first thing we need to know is how many parts are in each whole unit in the answer. A whole unit is shown here
We have five parts per unit times four parts per unit.
When we multiply these two numbers, we see that we have twenty parts in a whole unit.
This means the denominator of the answer is 20.
Next, we need to know how many of these parts we have in the array we created by multiplying the fractions. Two parts are counted on this side, and three parts are counted on this side.
Two times three is six, so when we connect the lines we see that the array has six of these parts in all.
This means the numerator of the answer is 6.
Again, there are twenty parts in each whole unit, so the denominator is 20.
We have six parts in the array, so the numerator is six.
So the product of the two fractions is six-twentieths.
Now notice that the numerator, six, is equal to the product of the two numerators in the fractions we multiplied.
Two times three equals six.
Also notice that the denominator, twenty, is equal to the product of the two denominators in the fractions we multiplied.
Five times four equals twenty.
Here’s another example.
We can show the problem in an array.
We will show two-thirds on this side.
So, we divide the whole units into thirds, and count up two-thirds.
We will show the second fraction, 5/2 on this side.
So, we divide the whole units into halves, and count up five-halves.
The array for our problem looks like this.
So now we have whole units that have three parts times two parts.
So, we have six parts in each whole unit.
This means the denominator in the answer is 6.
To find the numerator of the answer, we count two parts times five parts.
So, there are a total of 10 parts counted in the array.
This means the numerator is 10.
Again, each unit is divided into six parts, so the denominator is six.
We count ten of these parts.
So, the numerator is ten.
Again, notice that the numerator in the answer is the product of the numerators in the fractions we multiplied.
The denominator is the product of the denominators in the fractions we multiplied.
We could solve every multiplication problem with fractions using diagrams like this. But, that would take a long time. In every case, the answer would be the same as we get if we just multiplied the numerators and denominators as we did in these examples.
We saw that when we multiply the denominators, we find how many parts are in each whole unit, which tells us the size of the parts in the array that represents the answer.
When we multiply the numerators, we find how many parts we have in the array.
Now that we know what multiplying fractions means, we can use these facts to solve all multiplication problems with fractions.
Here we have four-fifths times one-half. To multiply these two fractions, first we multiply the numerators.
Four times one equals 4.
Next, we multiply the denominators.
Five times two equals ten.
So the answer is four-tenths.
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