Fractions - Math

James M Sandbrook

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A look at fractions...

A fraction is part of a whole.

If we have a whole apple and we divide it down the center with a knife we will have two halves of that apple.

Half = ½

½ + ½ = 1 or a half plus a half equals one whole.

John said "I only had half of my drink of milk because I was late for school."

In the case above of John and his drink of milk he may not be talking about exactly half a glass of milk, but in arithmetic the halves we use are real halves.

Look at Fig .1.

You can see the 1 over the 3, this is the sign for a third.
If we cut a piece of wood into 3 parts like the image on the left in Fig .1. then each part is a third of that wood.

The 3 is the denominator.

The line that separates the two numbers in the fraction is called the fraction line.

The number above the fraction line is the numerator and the other number the one below the fraction line is the denominator.

A fraction can be expressed as a numerator divided by a denominator.

If we were to cut an apple into 3 equal parts we call those 3 parts thirds.
The 3 equal parts of the apple make up the whole apple.

If we take two pieces of the apple then we are taking 2 thirds of the whole apple.

2 is the numerator.

Fourths

If we were to cut an apple into four equal parts then we can call those parts fourths or quarters.

These four equal parts make up the whole apple.

4 is the denominator in ¼.

Parts

Say we take 3 of the 4 apple parts away. Then we have taken away 3 quarters of the apple or ¾ of the apple.

If we had 100 apples and we gave 25 apples away.

Then we have given away one quarter of the apples or ¼ or 25%.

If we had 100 apples and we gave 50 apples away.

Then we have given away a half of the apples or ½ or 50%.

If we had 100 apples and we gave 75 apples away.

Then we have given away three quarters of the apples or ¾ or 75%.

A box with 6 parts

Here we have a rectangle with 6 parts.

A Proper Fraction:

We learnt earlier that a fraction is part of a whole.

Fig .2. shows the fraction two thirds.

The image shows a rectangle that has been divided into 3 equal parts and two of those parts have been colored green.

Fig .2. represents two thirds.

Fig .2. shows a proper fraction. A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).

Improper fraction

Fig .3. shows an improper fraction.

An improper fraction is a fraction that the numerator is smaller than the denominator.

Remember the number above the fraction line is the numerator and the number below the fraction line is the denominator.

This concludes our look at fractions for this math lesson.

All the best from

James M Sandbrook.

‎Tuesday, ‎15 ‎March ‎2005, ‏‎5:57:56 PM.