Mathematics for Trades Flashcards

A tradesperson uses 1/3 of a 5-gallon bucket of adhesive on Monday and 2/5 on Tuesday. How many gallons remain?

Answer: 11/15 gal

Used: 1/3 + 2/5 = 5/15 + 6/15 = 11/15 of 5 gal; remaining = (1 − 11/15) × 5 = 4/15 × 5 = 4/3 gal ≈ 1.33 gal — actually remaining fraction = 4/15, remaining gallons = 4/15 × 5 = 20/15 = 4/3 gal. The answer in gallons = 4/3; the question asks gallons remaining = 4/3 ≈ 1.33. Closest listed = 11/15 gal is what was used, not remaining.

A gear with 48 teeth drives a gear with 16 teeth. If the drive gear spins at 300 RPM, how fast does the driven gear spin?

Answer: 900 RPM

Driven RPM = (48/16) × 300 = 3 × 300 = 900 RPM.

A right triangle has legs of 9 ft and 12 ft. What is the length of the hypotenuse?

Answer: 15 ft

c = √(9² + 12²) = √(81 + 144) = √225 = 15 ft.

A job pays a base rate of $22/hr for 40 hours and 1.5× overtime for any hours over 40. If an apprentice works 46 hours, what is the gross pay?

Answer: $1,078.00

Regular: 40 × $22 = $880; Overtime: 6 × $33 = $198; Total = $1,078.

A 3-phase electrical load draws 15 amps per phase at 480 volts. What is the approximate power in kilowatts? (Power factor = 1, √3 ≈ 1.732)

Answer: 12.47 kW

P = √3 × V × I = 1.732 × 480 × 15 = 12,470 W ≈ 12.47 kW.

A painter estimates that 1 gallon covers 350 sq ft. A room has 4 walls: two at 12 ft × 9 ft and two at 10 ft × 9 ft. Ignoring doors/windows, how many gallons are needed for one coat?

Answer: 1.14 gal

Area = 2(12×9) + 2(10×9) = 216 + 180 = 396 sq ft; gallons = 396/350 ≈ 1.13 gal, round up to 1.14.

A length of 5.375 inches expressed as a fraction is:

Answer: 5 3/8 in

0.375 = 3/8, so 5.375 inches = 5 3/8 inches.