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Top-Heavy Fractions and Mixed Numbers

# Top-Heavy Fractions and Mixed Numbers

### Top-Heavy Fractions and Mixed Numbers

When the fraction is top-heavy (when the numerator is larger than the denominator), you can express it as a mixed number.

1

Here we have three halves of cake. How would you write this as a fraction?

2

Here we have three halves or $\dfrac{3}{2}$ of cake.

This is a top heavy fraction.

3

We can see that $\dfrac{3}{2}$ of cake is more than one whole cake. What is an alternative way of writing $\dfrac{3}{2}$?

What do you think we call numbers like $1\dfrac{1}{2}$?

1

Each of these pizzas was divided into five slices. How many slices are left?

2

We know we have more than one pizza so we can expect a top heavy fraction. How do we write the eight slices as a top heavy fraction?

3

We have $\dfrac{8}{5}$ of pizza, but how would you write it as a mixed number?

4

So there are $\dfrac{8}{5}$ pizzas here which we can also write as $1\dfrac{3}{5}$.

But how did we get from $\dfrac{8}{5}$ to $1\dfrac{3}{5}$?

1

The whole pizza is divided into five slices and all five are still on the plate. How do we write this part as a fraction?

2

So we've taken $\dfrac{5}{5}$ and replaced it with $1$.

We started with $\dfrac{8}{5}$, after taking five away there are three left and that's how we get $1\dfrac{3}{5}$.

1

Try this one. The amount of cake as a top heavy fraction is $\dfrac{5}{3}$. How would you write it as a mixed number?

How would you write $\dfrac{7}{4}$ as a mixed number?

Try another one: what is $\dfrac{9}{2}$ as a mixed number?

1

We have converted top heavy fractions to mixed numbers.

This time we will go the other way and convert a mixed number into a top heavy fraction.

2

Looking at the image we can see we have two whole pizzas and a fraction of a pizza. What is this as a mixed number?

3

Our mixed number is $2\frac{2}{5}$ .To convert into a top heavy fraction, we need to know how many slices there are in the two whole pizzas. Write this as a top heavy fraction.

4

We have seen that we can replace our two whole pizzas or the $2$ with$\frac{10}{5}$

We add the $\dfrac{10}{5}$ to the $\dfrac{2}{5}$ to give a total of $\dfrac{12}{5}$.

5

We started with a mixed number $2\dfrac{2}{5}$ and found out how many slices are in the two whole pizzas.

This gave us the answer that $2\dfrac{2}{5}=\dfrac{12}{5}$.

How do you write the mixed number $3\dfrac{2}{3}$ as a top heavy fraction?

1

Summary! Fractions can be top heavy

That means the numerator is bigger than the denominator, for example $\dfrac{7}{6}$

2

Top heavy fractions and mixed numbers are greater than $1$

For example, $\dfrac{6}{6}$ is the same as $1$, so $\dfrac{7}{6}$ has a whole and an "extra" sixth.

3

You can turn top heavy fractions into mixed numbers

For example, $\dfrac{7}{6}$ is the same as the mixed number $1\dfrac{1}{6}$.

4

We can turn mixed numbers into top heavy fractions.

For example, $2\dfrac{2}{5}$ is the same as the top heavy fraction $\dfrac{12}{5}$.