1 · Units to know
Length: 12 inches = 1 foot, 3 feet = 1 yard, 5,280 feet = 1 mile. 100 centimeters = 1 meter, 1,000 meters = 1 kilometer.
Weight and capacity: 16 ounces = 1 pound. 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon. 1,000 grams = 1 kilogram, 1,000 milliliters = 1 liter.
2 · Big unit to small unit: multiply
Going to a smaller unit gives a bigger number. 7 feet = 7 × 12 = 84 inches. 3 kilograms = 3 × 1,000 = 3,000 grams.
Going to a bigger unit gives a smaller number: 48 ounces = 48 ÷ 16 = 3 pounds.
3 · Conversions in two steps
How many cups are in 3 gallons? 3 gallons = 12 quarts = 24 pints = 48 cups. Each step doubles or multiplies, and stopping early is the trap.
A shortcut to remember: 1 gallon = 16 cups.
4 · Mixed units
"A board 5 feet 4 inches long is cut into 4 equal pieces." Change to one unit first: 5 feet 4 inches = 60 + 4 = 64 inches. Each piece is 64 ÷ 4 = 16 inches.
A foot is 12 inches, not 10. Treating 5 feet 4 inches as "54" is a common slip.
5 · Elapsed time
From 10:35 a.m. to 2:10 p.m.: count to the next hour (25 minutes to 11:00), then whole hours (11:00 to 2:00 is 3 hours), then the rest (10 minutes). Total 3 hours 35 minutes.
Crossing noon is where mistakes happen: 11 a.m. to 1 p.m. is 2 hours.
6 · Speed, distance, and time
distance = speed × time. A cyclist going 12 miles per hour for 3 hours rides 36 miles.
Find the speed first when it is hidden: "150 miles in 3 hours" is 50 miles per hour, so 5 hours covers 250 miles.
7 · Unit price and the better buy
Divide the price by the number of items to get the price of one. 6 for $4.20 is $0.70 each; 10 for $6.50 is $0.65 each, so the 10-pack is the better buy.
The pack with the lower total price is not always the better buy.
8 · Map scales
If 1 inch on a map stands for 20 miles, then 4 inches stands for 4 × 20 = 80 miles, and 4 ½ inches for 80 + 10 = 90 miles.
Backwards: 140 miles on the same map is 140 ÷ 20 = 7 inches.
9 · Working with rates
"A machine fills 45 bottles in 3 minutes. How many in 10 minutes?" One minute: 45 ÷ 3 = 15 bottles. Ten minutes: 150.
Always find the amount for one first. Then multiply.
10 · Choosing a sensible unit
The length of a pencil is about 18 centimeters; the distance between two cities is measured in kilometers or miles; a bathtub holds about 200 liters.
If an answer says a dog weighs 30 grams or a door is 2 kilometers tall, the unit is wrong.
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