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"Practice makes perfect. After a long time of practicing, our work will become natural, skillfull, swift, and steady." ~ Bruce Lee

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Check your answers!

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7 4

(seven-fourths or seven-quarters)

An Improper Fraction has a top number larger than (or equal to) the bottom number.

More Examples

See how the top number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions).

Three Types of Fractions

There are three types of fraction:

Fractions

A Fraction (such as ) has two numbers:

The top number (the Numerator) is the number of parts we have.
The bottom number (the Denominator) is the number of parts the whole is divided into.

So we can define the three types of fractions like this:

Improper Fraction

So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy.

4 4

Can be Equal

What about when the numerator is equal to the denominator? For example ?

Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

Improper Fractions or Mixed Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

Divide the numerator by the denominator.

Write down the whole number answer

Then write down any remainder above the denominator.

Example: Convert to a mixed fraction.

Divide:

Write down the 2 and then write down the remainder (3) above the denominator (4).

Answer:

That example can be written like this:

Example: Convert to a mixed fraction.

Answer:

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

Multiply the whole number part by the fraction's denominator.

Add that to the numerator

Then write the result on top of the denominator.

Example: Convert 3 to an improper fraction.

Multiply the whole number part by the denominator:

Add that to the numerator:

Then write that result above the denominator:

We can do the numerator in one go:

Example: Convert 2 to an improper fraction.

Are Improper Fractions Bad ?

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

Mixed Fraction:

What is:

Is it:

1 + 2 + 1 4

= 3 1 4 ?

Or is it:

1 + 2 × 1 4

= 1 1 2 ?

Improper Fraction:

What is:

It is:

4 9 13 4 4 = 4 +

But, for everyday use, people understand mixed fractions better.

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7 4 (seven-fourths or seven-quarters) An Improper Fraction has a top number larger than (or equal to) the bottom number. See how the top number is bigger than (or equal to) the bottom number? That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions).

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More help!

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Math Help for Fractions: Easy-to-understand lessons for kids, parents and teachers. Practice what you learn with games and quizzes.

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How to add and subtract fractions

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Cool look at how people started representing fractions

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Before studying this lesson about history of fractions, I recommend that you become familiar with Egyptian numeration system.

An extensive treatment of fractions appeared around 1600 B.C. in the Rhind Papyrus, which contained the work of Egyptians mathematicians.

The Egyptians did not express fractions as ratios such as 2:5 or 2/5.

Instead, they expressed ratios in unit fractions. What are unit fractions?

A unit fraction is a fraction that has a numerator of 1 and the denominator is a positive integer.

For example, 1/2, 1/5, and 1/5 are unit fractions. The figure above in the beginning of the lesson shows how the Egyptians wrote the unit fraction 1/18.

Notice also that there is a shape that looks like an open mouth (the ellipse). It refers to a fraction.

Now, what about adding fractions? How did they show it?

The Egyptians would then write 2/5 as 1/3 + 1/15

Of course, the Egyptians used their symbols to represent this fraction.
1/3 + 1/15 would be represented as shown below:

Notice that all we care about is the man's feet. Feet pointing toward the direction of writing means add. Otherwise, it means subtract.

In this case, since it is pointing towards the direction of writing, it means to add.

The history of fractions and the way we write fractions today.

The way we represent fractions today probably came from the Hindus.

Around A.D. 630, Brahmagupta would write the fraction two-fourths without the bar as

Then, the Arabs came up with the bar. However, the notation 2/4 was mostly used due to typesetting constraints.

The notion of numerator and denominator came from Latin writers. Up to the sixteenth century, the common denominator was found by multiplying the denominators.

In the seventh century, the least common multiple was used extensively when adding and subtracting fractions.

Multiplication of fractions as we know it today stayed the same for centuries.

Division of fractions however, was carried out in a way that is completely different to the way we perform this operation today.

The first way was to look for a common denominator although today we never look for a common denominator when dividing fractions.

4/2 ÷ 2/3 = 12/6 ÷ 4/6 = 12/4 = 3

The second way was to perform cross-multiplication.

4 × 3 = 12 and 2 × 2 = 4, so 12/4 = 3

This concludes our brief history of fractions

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Before studying this lesson about history of fractions, I recommend that you become familiar with Egyptian numeration system. An extensive treatment of fractions appeared around 1600 B.C. in the Rhind Papyrus, which contained the work of Egyptians mathematicians. The Egyptians did not express fractions as ratios such as 2:5 or 2/5.

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Fractions Mixed Operations more practice:

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Answer Key to More Practice continued

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Answer Key to More Practice