When we first thought about the number line, we counted only in whole numbers - we went straight from zero to one to two to three. But what if we wanted to stop in between the numbers?
If we stop halfway between 0 and 1, we call that number a half - 1/2 - one out of two parts of a whole number. If we stop halfway between 0 and 1/2, we call that number a quarter - 1/4 - one out of four parts of a whole number. If we stop halfway between 2 and 3, we call that number 2 1/2. Or we can call it 5/2 - five halves, instead of 2 1/2 whole numbers. Or we could call it 10/4 - ten quarters of a whole number.
When we write fractions this way, we call the top number the numerator and the bottom number the denominator.
Another way to write the numbers that come between whole numbers is as decimals.
How do you add fractions together? If the denominators are the same, it's easy: just add the top numbers (the numerators) together: 1/8 + 2/8 = 3/8. But what about if the denominators aren't the same? Then you need to find a common denominator, make the denominators the same, and then add the numerators together. One way to find a common denominator is to multiply the denominators together. So to add 1/4 and 1/3, you find that 12 is a common denominator for them. Convert 1/4 to 3/12 and 1/3 to 4/12, and then add 3/12 + 4/12 = 7/12.
Bibliography and further reading about numbers:
Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University
Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.
More about Professor Carr's work on the Portland State University website
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