Proportions

S.W.B.A.T Write a proportion when given a word problem and solve for the variable

What are Proportions? A proportion is a name we give to a statement that two ratios are equal It can be written two ways To equal fractions Using a colon a:b = c:d

Cross Products When two ratios are equal, the cross products of the ratios are equal For the proportion a:b = c:d a (d) = b (c)

Reading Proportions The following proportion is read as “twenty is to twenty-five as four is to five.”

Cross Proportions In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion To find the cross products of a proportion, we multiply the other terms, called the extremes, and the middle terms, called the means

Cross Proportions In this proportion 20 and 5 are the extremes, and 20 and 4 are the means Cross Products: 20 (5) = 25 (4) 100 = 100 Since the cross products are both equal to 100, we know that these ratios are equal and that this is a true proportion

Word Problem In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long. However, a model was used for the beetle that was really only 20 inches long. A 30-inch tall model building was also used in the movie. How tall did the building seem in the movie?

Word Problem Solution Step 1: Write the proportion Step 2: Multiply to find the cross products 20 inches (x) = 50 feet (30 inches) Step 3: Divide to find x 20x = 50 (30) 20x = 1500 Divide by 20 X = 75