Can somebody please explain 'Ratios' to me?

Question

Yeahh, I know it sounds pretty basic, but for like the past 5 weeks of my extra numeracy class I haven't been paying alot of attention... anyways we have a big test tomorrow, so would someone be able to explain the basic Ratio system and how to simlify them?

Thanks guys x*x

Answer 1

A ratio is a comparison of two numbers by division.

Ratios are unitless when they relate quantities of the same dimensions. When the two quantities being compared are of different types, the units are the first quantity "per" unit of the second — for example, a speed or velocity can be expressed in "miles per hour". If the second unit is a measure of time, we call this type of ratio a rate.

Fractions and percentages are both specific applications of ratios. Fractions relate the part (the numerator) to the whole (the denominator) while percentages indicate parts per 100.

A ratio of 2:3 ("two to three") means that the whole is made up of 2 parts of one thing and 3 parts of another — thus, the whole contains five parts in all. To be specific, if a basket contains 2 apples and 3 oranges, then the ratio of apples to oranges is 2:3. If another 2 apples and 3 oranges are added to the basket, then it will contain 4 apples and 6 oranges, resulting in a ratio of 4:6, which is equivalent to a ratio of 2:3 (thus ratios reduce like regular fractions). In this case, 2/5 or 40% of the fruit are apples and 3/5 or 60% are oranges in the basket.

Note that in the previous example the proportion of apples in the basket is 2/5 ("two of five" fruits, "two out of five" fruits, "two fifths" of the fruits, or 40% of the fruits). Thus a proportion compares part to whole instead of part to part.

Answer 2

Ratios are pretty simple. They're generally written as x:y, where x and y are two related values. For example, if you were making a cake and you wanted to add 2 cups of flour for every cup of water, the cake would contain a 2:1 flour-to-water ratio. (Or a 1:2 water-to-flour ratio.)

Simplifying ratios is just as easy. Say you were making a particularly large cake, but with a different recipe. You added 12 cups of flour and 9 cups of water. The cake would contain a flour-to-water ratio of 12:9. Note, however, that 12 and 9 have a common factor, 3. You can divide both sides of the ratio by this value to reduce the ratio, in this case to 4:3. Since 4 and 3 have no common whole factors, this is the simplest form of the ratio.