#7 Ratios, Rates, Proportions, and Units

Tip-Off Clues

• “at this rate”
• “per” or “for every” (both translate to division)
• repetition of units/items
• scale model/drawing

Proportions (x1/y1=x2/y2)

• ex. Every 3 days, Kumar rides his bike 180 kilometers. At this rate, how many kilometers will Kumar ride in 3 weeks?
  • Write all knowns in the appropriate slots; 3days/180 km =21 days/x km
  • Solve for the unknown; 3x=3780 > x=1260 km

Ratios

The ratio of “x to y” can be expressed as

• x to y
• x:y
• x/y

Ratios and Totals

• ex. In a student body election, 245 students voted for Evelyn. If only juniors and seniors voted, and the ratio of juniors to seniors is 2:5, how many more seniors voted for Evelyn?
  • 2jrs:5srs
  • 2/245 = 2/7 x 245 =70 jrs
  • 5/7 x 245 = 175 jrs
  • 175-70=105 more seniors

Unit Conversions

If you have/are taking chemistry, this should be very familiar to you. College Board gives you the numbers required to convert units, so all you need to know is HOW. One important thing to remember is that when you’re trying to get RID of a unit, you divide, and when you’re trying to CREATE one, you multiply

Single Unit Conversions

• given units x (desired units/starting units)
• ex. 25 minutes to hours
  • 25min x 1 hour/60min = .4 hours

Multi-Step Conversions

• given units x (linking unit/starting unit) x (desired unit/linking unit)
• ex. 650mm to feet (1 centimeter = .39in; 1 centimeter = 10mm)
  • 650mm x 1cm/10mm x .39in/cm x 1foot/12in = 2.1 feet