AccelePrep for the ACT Test 2nd Edition Student Text

98 • S URGE TO S UCCESS ! M ATH T EST P REP

PROPORTIONS

Simply put, a proportion is a statement that two fractions are equal. 4 2 12 6 Since 4 2 equals 2 1 and 12 6 equals 2 true. One of the amazing things about the world is that many situations can be described using proportions: Lourdes uses 3 gallons of gas to drive 105 miles. How much gas will she use to drive 315 miles? (The farther Lourdes drives, the more gas she uses.) Hector is building a wall. If 12 bricks weigh 40 pounds, how many bricks are there in a stack that weighs 60 pounds? (The more bricks there are in a stack, the more the stack weighs.) ‘•‡’Š Šƒ• ’Žƒ–‡† ͸Ͳ ƒ…”‡• ‘ˆ…‘” –Šƒ– Š‡ ‡‡†• –‘ ˆ‡”–‹Ž‹œ‡Ǥ ˆ ƒ tanker truck of liquid fertilizer is used for 12 acres, how many tanker –”—…• ‘ˆ Ž‹“—‹† ˆ‡”–‹Ž‹œ‡” ™‹ŽŽ ‘•‡’Š ‡‡†ǫ ȋ Š‡ ‘”‡ ƒ…”‡• –‘ „‡ fertilized, the more truckloads are required.) Each of these situations can be represented with a proportion. Set up a proportion to calculate how much gas Lourdes needs to drive 315 miles: Gas Gas Used Used gal —•– •‘Ž˜‡ ˆ‘” x (by cross-multiplying and dividing): x 105 3 315 ] g x = 9 Now calculate how many bricks are in a stack that weighs 60 pounds: 1 , we know the above statement is Miles Driven Miles Driven 1 1 2 2 gal miles x 105 3 315 miles

Example:

Example:

REVIEW Proportions represent a similar change in a given relationship: More Input, More Output Less Input, Less Output

STRATEGY ALERT A proportion is a comparison of two ratios. Typically a question stem will give you enough information to complete one ratio. The second ratio will have a missing element, x . After you have set these ratios equal to one another, check that the units of the two numerators match and that the units of the two denominators match.

bricks x

12 bricks

pounds 60

40

pounds

x 40 720 x = 18 ‹ƒŽŽ›ǡ…ƒŽ…—Žƒ–‡ Š‘™ ƒ› –ƒ‡” –”—…• ‘•‡’Š ™‹ŽŽ ‡‡†ǣ truck acres x 12 1 60 acres trucks 12 x = 60 x = 5