1 · The metric ladder
Metric units go by tens: 1 m = 100 cm, 1 km = 1,000 m, 1 kg = 1,000 g, 1 L = 1,000 mL.
Bigger unit to smaller unit: multiply. 6 m = 6 × 100 = 600 cm. Smaller to bigger: divide. 4,000 g = 4 kg.
2 · Mixed units
"How many grams are in 2 kg 400 g?" Convert the big part, then add the small part: 2 × 1,000 = 2,000, plus 400 = 2,400 g.
6 m 79 cm = 600 + 79 = 679 cm. 3 L 50 mL = 3,000 + 50 = 3,050 mL (watch the zero).
3 · Customary units
1 foot = 12 inches, 1 yard = 3 feet, 1 pound = 16 ounces, 1 gallon = 4 quarts.
5 feet 3 inches = 60 + 3 = 63 inches. 2 yards = 6 feet = 72 inches.
4 · Comparing in different units
Which is heavier, 1,500 g or 1 kg 250 g? Put both in grams: 1,500 vs 1,250. The 1,500 g wins.
Always convert to the same unit before comparing. Usually the smaller unit is easiest.
5 · How many fit?
"A wall is 6 m long. Tiles are 40 cm wide. How many tiles fit along the wall?" Same unit first: 6 m = 600 cm. Then 600 ÷ 40 = 15 tiles.
"A 2 L jug fills 250 mL cups." 2,000 ÷ 250 = 8 cups.
6 · Elapsed time: hop the hours, then the minutes
"A show starts at 6:45 p.m. and lasts 4 hours 35 minutes." Hop 4 hours: 10:45. Then 15 minutes to 11:00, and 20 more: 11:20 p.m.
Split the minutes at the next o'clock so you never go past 60.
7 · How long between two times?
From 8:50 a.m. to 1:15 p.m.: 8:50 → 9:00 is 10 min. 9:00 → 1:00 is 4 h. 1:00 → 1:15 is 15 min. Total 4 h 25 min.
Crossing noon is fine: 11 → 12 → 1 is two hours.
8 · Working back to a start time
"A class ends at 3:10 and lasted 1 hour 45 minutes. When did it start?" Go backwards: 3:10 − 1 h = 2:10. 2:10 − 10 min = 2:00. 2:00 − 35 min = 1:25.
9 · Minutes and hours
1 h = 60 min. 150 minutes = 2 h 30 min (60 + 60 + 30). 3 h 20 min = 200 minutes.
A day is 24 hours, a week is 7 days, a year is 12 months or 52 weeks.
10 · Money with decimals
Money is written with two decimal places: $7.50 is 7 dollars and 50 cents. Line up the decimal points to add: $2.75 + $4.00 = $6.75.
2 books at $2.75: $2.75 + $2.75 = $5.50. Add the $4.00 pen: $9.50.
11 · Change from a bill
"A book costs $7.50. Sam buys 2 and pays with $20." Total 2 × $7.50 = $15.00. Count up: $15 → $20 is $5.00 change.
"A book costs $9.80. Leo buys 2, pays $20." Total $19.60. Count up 40¢: change $0.40.
12 · Sharing a total
"Each ticket costs $15. A group spends $90. How many tickets?" 90 ÷ 15 = 6. Count by 15s: 15, 30, 45, 60, 75, 90.
"$150 shared by 6 friends": $150 ÷ 6 = $25 each. You are ready for the test! 🎉
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