Introduction
In this lesson we will learn how to multiply whole numbers by fractions, as well as how to solve such problems using rectangular models.
Solving FractionWhole Number Multiplication Using Models
Models allow us to quickly visualize the solutions to whole numberfraction multiplication problems.
Solving Whole Number Fraction Multiplication Using Models
Let's take a look at how to solve two times onequarter using rectangular models.
Since the denominator of our fraction is 4, we will slice this shape into 4 pieces.
Now lets identify what one quarter should look like.
Another way of saying two times a quarter is one quarter plus a quarter.
Since we want two times a quarter, we can shade in two of our smaller rectangles to find our solution.
We can summarize our method for solving using rectangular models as follows:
Start with a rectangle, then split it up into as many pieces as the denominator of the fraction we are multiplying by.
Multiply the whole number by the numerator of our fraction, then shade in our shape that many times.
Sometimes we will need to use multiple shapes.
Solving Whole Number Fraction Multiplication Using Models
Let's take a look at how to solve two times threequarters using rectangular models.
Since our denominator is 4, we will slice our shape up into 4 pieces
Now lets identify what one quarter should look like.
Multiply our whole number by the numerator of the fraction. We should have 6 pieces shaded in.
This is what our answer would look like represented pictorially. We can count the number of shaded segments and place them as a fraction over our initial denominator.
Multiplying whole numbers by fractions
When multiplying whole numbers by fractions, we can break down the process into three simple steps:
Step 1  Turn your whole number into a fraction with a denominator equal to one.
Step 2  Multiply the two numerators together and the two denominators together.
Step 3  Simplify the result.
Example: Multiplying a whole number by a fraction
Let's take a look at how to solve 8 times one sixteenth.
Step 1  Turn your whole number into a fraction with a denominator equal to one.
Step 2  Multiply the two numerators together and the two denominators together.
Combine the results as a new fraction.
Step 3  Simplify the result.
We can divide both the numerator and denominator by 8, so our fraction will simplify to one half.
Our final answer is that 8 times one sixteenth equals one half.
Occaisonally, We will have the situation where we are multiplying a whole number by fraction and the denominator is equal to our whole number.
Example: Multiplying a whole number by a fraction
Let's take a look at how to solve one eighth times 8.
In this situation, our denominator will cancel out our whole number.
We can still solve it using our method from earlier, but as a shortcut we can cancel out our eights from eachother.
Our problem will turn into 1 times 1.
Alternatively, we can use our previous method and turn the whole number into a fraction with denominator equal to one.
Simplify the result.
Our fraction will simplify to equal one.
If we use the method described above, we should have no problem finding the correct answer each time we multiply fractions and whole numbers.

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