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Mathematics » Introducing Fractions » Add and Subtract Mixed Numbers

# Modeling Subtraction of Mixed Numbers

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## Modeling Subtraction of Mixed Numbers

Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.

We will use fraction circles (pizzas!) to help us visualize the process.

Algebraically, you would write:

## Example

Use a model to subtract: $$1-\frac{1}{3}.$$

### Solution

What if we start with more than one whole? Let’s find out.

## Example

Use a model to subtract: $$2-\frac{3}{4}.$$

### Solution

In the next example, we’ll subtract more than one whole.

## Example

Use a model to subtract: $$2-1\frac{2}{5}.$$

### Solution

What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a $$\text{\1}$$ bill and one quarter. What could you do? You could change the dollar bill into $$4$$ quarters. The value of $$4$$ quarters is the same as one dollar bill, but the $$4$$ quarters are more useful for the parking meter. Now, instead of having a $$\text{\1}$$ bill and one quarter, you have $$5$$ quarters and can put $$3$$ quarters in the meter.

This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.

We can also model this using fraction circles, much like we did for addition of mixed numbers.

## Example

Use a model to subtract: $$1\frac{1}{4}-\frac{3}{4}$$

### Solution

 Rewrite vertically. Start with one whole and one fourth. Since the fractions have denominator 4, cut the whole into 4 pieces. You now have $$\frac{4}{4}$$ and $$\frac{1}{4}$$ which is $$\frac{5}{4}$$. Take away $$\frac{3}{4}$$. There is $$\frac{1}{2}$$ left.