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FRACTIONS AND RATIOS - Coggle Diagram
FRACTIONS AND RATIOS
I THINK OF A FRACTION AS REPRESENTING A PART OF A WHOLE. IS THERE ANY MORE TO IT THAN THAT?
mathematical notation used for a fraction might, in fact, be used in at least five different ways:
to represent a proportion of a whole or of a unit;
share or a part of something
to represent a point on a line;
As with all types of numbers, use the number line to represent fractions by dividing up the section of the number line from 0 to 1 into a number of equal parts.
to represent a proportion of a set;
to model a division problem;
The fraction 3/8 can also be used to represent the division of 3 by 8, thinking of division as ‘equal sharing between’
as a ratio.
WHAT ABOUT NUMERATORS, DENOMINATORS, VULGAR FRACTIONS, PROPER AND IMPROPER FRACTIONS, MIXED NUMBERS, AND SO ON?
The
numerator
and the
denominator
are simply the top number and the bottom number in the fraction notation
A fraction in which the top number is smaller than the bottom number, such as 3/8, is sometimes called a
proper fraction
fraction such as 11/8 being referred to as an
improper fraction
Sequences of
equivalent fractions
follow a very straightforward pattern.
For example, all these fractions are equivalent: 3/5, 6/10, 9/15, 12/20, 15/25, 18/30, 21/35, 24/40
HOW DO YOU SIMPLIFY FRACTIONS?
that you do not change the answer to a division calculation if you multiply or divide both numbers by the same thing.
cancelling
by dividing the top and bottom numbers by any common factors, we can reduce the fraction to its simplest form
HOW DOES THIS WORK WITH RATIOS?
The principle used for simplifying fractions applies to ratios, of course, because fractions can be interpreted as ratios. If you multiply or divide two numbers by the same thing, the ratio stays the same.
HOW DO YOU COMPARE ONE FRACTION WITH ANOTHER?
HOW IS A REMAINDER IN A DIVISION CALCULATION INTERPRETED AS A FRACTION?
30 ÷ 7 = 4 remainder 2. Depending on the context in which this division calculation arose, it may be possible to deal with the remainder here by dividing that by 7 as well. Using the idea that a fraction can represent a division, we know that 2 ÷ 7 is equal to 2/7.
HOW DO YOU ADD AND SUBTRACT FRACTIONS?
add two fractions with the same bottom number (denominator)
if you have o(1/8) of a chocolate bar and you add it to (3/8) of a chocolate bar, you have altogether (4/8) of a chocolate bar. So, clearly, 1/8 + 3/8 = 4/8.
simplified to 1/2 by cancelling 4.
result may be an improper fraction
3/8 + 5/8 + 7/8 = 15/8.
subtraction where the dominator is the same
example, , 7/8 – 5/8 = 2/8.
be simplified to 1/4 by cancelling 2
To add or subtract two fractions with different denominators
change one or both of them to equivalent fractions so that they finish up with the same bottom number
HOW DO YOU MULTIPLY TWO SIMPLE FRACTIONS?