Multiplying Fractions and Whole Numbers - Fast And Easy Math Learning Videos
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Title: Multiplying Fractions and Whole Numbers - Fast And Easy Math Learning Videos
When we multiply whole numbers, we can show the multiplication using an array like the one shown here. This array shows the multiplication, 2 times 3.
The array is two blocks tall and three blocks wide.
We can show multiplication of a fraction times a whole number using the same kind of array.
Let’s change the first factor in this multiplication to a fraction.
Here we have the fraction 3 halves times the whole number 3. To show the fraction 3 halves, we start by dividing each whole unit on this side into halves, like this.
We show 3 halves here.
We show the whole number 3 here.
Now we draw the array.
We have three halves here, another three halves here, and three more halves here.
We can show that using repeated addition like this.
When we do the addition, we get 9 halves. That means that 3 halves times 3 is 9 halves.
Another example. Two times one third.
Here we have 2 blocks tall times one third of a block wide.
This can also be written as repeated addition. This time, we have the fraction one third, two times.
We write that like this.
One third plus one third.
We know this is equal to 2 thirds.
So, 2 times one third is two thirds.
Another example.
Six fifths times 4. We write this as repeated addition like this.
When we add, we get 24 fifths.
So six fifths times 4 is 24 fifths.
You probably noticed a pattern here. When we do the repeated addition in each case, the result of adding the numerators is the same result as multiplying the numerator of the fraction by the whole number.
Here, we added the numerator three, three times, and got 9.
That’s the same as multiplying 3 times 3 which is also nine.
Here, we added the numerator one, two times, and got 2.
That’s the same as multiplying 1 times 2, which is also 2.
Here, we added the numerator 6, four times and got 24.
That’s the same as multiplying 6 times 4, which is also 24.
So, to multiply fractions, we don’t have to do the repeated addition, we can just multiply the numerator times the whole number.
That gives us the numerator of the result.
The denominator stays the same.
Here’s an example. Four times three fifths. We multiply the numerator, which is three, times the whole number four, which gives us a numerator of 12.
And we keep the denominator.
So 4 times 3 fifths is 12 fifths.
Last example. Two fifths times 3. We multiply the numerator, 2, times the whole number 3, which gives us a numerator of 6, and the denominator stays the same.
The result is 6 fifths.
In the remainder of this lesson you’ll multiply whole numbers and fractions like these.
http://[a]www.ilearn.com%2Ffractions[/a]
https://youtu.be/BV-T6b7S9dc
