Читать книгу Algebra I All-in-One For Dummies - Mary Jane Sterling, Mary Sterling Jane - Страница 80

A proportion is an equation with two fractions equal to one another. Proportions have some wonderful properties that make them useful for solving problems — especially when you’re comparing one quantity to another or one percentage to another.

Given the proportion , the following are also true:

 . (The cross-products form an equation.)

 . (The “flip” is an equation.)

 . (You can reduce either fraction vertically.)

 . (You can reduce the numerator or denominator horizontally.)

Q. Find the missing value in the following proportion:

A. The numerator and denominator in the fraction on the left have a common factor of 6. Multiply each by . Flip the proportion to get the unknown in the numerator of the right-hand fraction. Then you see that the two bottom numbers both have a common factor of 7. Divide each by 7. Finally, cross-multiply to get your answer:

Q. If Agnes can type 60 words per minute, how long will it take her to type a manuscript containing 4,020 words (if she can keep typing at the same rate)?

A. Set up a proportion with words in the two numerators and the corresponding number of minutes in the denominators:

Divide both numerators by 60 and then cross-multiply to solve for x.

It will take her 67 minutes — just over an hour.

15 Solve for x:

16 Solve for x:

17 Solve for x:

18 Solve for x:

19 A recipe calls for 2 teaspoons of cinnamon and 4 cups of flour. You need to increase the flour to 6 cups. To keep the ingredients proportional, how many teaspoons of cinnamon should you use?

20 A factory produces two faulty tablets for every 500 tablets it produces. How many faulty tablets would you expect to find in a shipment of 1,250?