Ratios, Proportions and Probability

Ratios, proportions, and probability are basic math operations that can be mastered with this simple reference guide for students of all ages.

Ratios

A ratio is a comparison of two quantities. A wall is 72 inches high; a pencil is 8 inches long. By dividing 8 into 72, you find it would take 9 pencils to equal the height of the wall. The ratio, or comparison, of the wall to the pencil can be written three ways: 1 to 9; 1:9; 1/9.

Picture this: 6 circles, 4 triangles, and 9 squares. The ratio of triangles to circles is 4:6. The ratio of circles to squares is 6:9. The ratio of triangles to squares is 4:9. These ratios will stay the same if we divide both numbers in the ratio by the same number. By reducing 4:6 and 6:9 to their lowest terms, they are the same-2:3. This means that 2:3, 4:6, and 6:9 are all equal ratios. You can also find equal ratios for all three by multiplying both numbers of the ratio by the same number.

You can find a missing number (n) in an equal ratio. First, figure out which number has already been multiplied to get the number you know.

Proportions

A proportion is a statement that has two ratios that are equal. To make sure ratios are equal, called a proportion, we multiply the cross products. For example: 1/5 = 2/10, ½ x 10/5 = 10/10. To find a missing number (n) in a proportion, multiply the cross products and divide. For example: n/30 = 1/6; n x 6 = 1 x 30, n x 6 = 30, n = 30/6, n=5.

Probability

Probability is the ratio of favorable outcomes to possible outcomes in an experiment. You can use probability (P) to figure out how likely something is to happen. For example, six cards are turned facedown-3 have stars, 2 have triangles, and 1 has a circle. To find the probability of using the circle, use the formula P=number of favorable outcomes/number of trials. P = 1/6 = 1:6. You have a 1 in 6 probability of picking the circle, a 2 in 6 probability of picking a triangle, and a 3 in 6 probability of picking a star. Picture 10 cards on a table labeled "win," "lose," "draw again," lose," "win," "lose," "draw again," "lose," "lose," and "draw again." Each card is called an outcome. There are 10 cards and 10 possible outcomes. Since you have the same chance of drawing any of the cards, the outcomes are equally likely. To find the probability of drawing a card that says "win," write the number of outcomes that say win (2) on the top of your equation, and the number of possible outcomes (10) on the bottom of the equation. Then simplify. The probability of drawing a card that says win is 1/5.

Notebook Math Fact Book