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Math Formulas and Definitions for Basic Calculations

Learn essential math formulas and definitions, including area, perimeter, simple interest, density, and more for practical applications. Practice problems and step-by-step solutions provided.

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Math Formulas and Definitions for Basic Calculations

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  1. FORMULAS

  2. Definitions • Area • Perimeter/Circumference • Surface Area • Volume • Distance / Rate • Simple Interest • Density

  3. Distance = Rate x Time How far did you travel if you drove at a rate of 60 miles per hour for 5 hours? D = rt D = 60 x 5 D = 300 Answer: 300 miles

  4. Time = Distance / Rate How much time did it take for you to travel 300 miles at a rate of 60 miles per hour? T = D/r T = 300 / 50 D = 5 Answer: 5 hours

  5. D = rt Find D if r = 12 and t = 8 D = rt D = 12 x 8 D = 96 Find r if D = 240 and t = 8 D = rt 240 = r x 8 Solve backwards 240 / 8 = r 30 = r D = rt 240 = 8r 8 8 30 = r

  6. Simple Interest I = PRT Interest = Principle x Rate x Time How much interest would you make if you deposited $500 at the bank at a rate of 10% per year for 4 years? I = 500 x .10 x 4 I = $200

  7. Simple Interest I = PRT Interest = Principle x Rate x Time How much time did you keep your money in the bank if you made $400 in interest at a rate of 5% with an initial deposit of $800 ( principle)? • 400 = 800 x .05 x t • = 40 x t • 400 / 40 = 10 years

  8. Simple Interest I = PRT How much time did you keep your money in the bank if you made $400 in interest at a rate of 5% with an initial deposit of $800 ( principle)? • I = PRT • 400 = 800 x .05 x t • = 40 t • 400 = 40 t • 40 40 • 10 = t

  9. Circumference of a Circle PI TIMES DIAMETER PI TIMES DOUBLE THE RADIUS 3.14 d

  10. Circumference of a Circle C = 3.14 d Find C if d = 10 31.4 units Find C if d = 5 15.7 units Find C if r = 5 31.4 units

  11. Circumference of a Circle C = 3.14 d Find d if C = 400 20 units • C = 3.14 d • 400 = 3.14 d • = 3.14 d • 3.14 3.14 Substitute 400 for C Solve backwards 3.14 times what is 400 Divide 400 by 3.14 20 = d

  12. Area of a Circle • PI TIMES RADIUS TO SECOND POWER • A = 3.14 r 2 • A = 3.14 x r x r

  13. Area of a Circle A = 3.14 r 2 Find A if r = 10 314 square units Find A if r = 5 78.5 square units Find A if r = 20 1256 square units

  14. Area of a Circle A = 3.14 r 2 Find r if A = 2826 sq units 30 units 2826 = 3.14 x r2 Work backwards Undo operations Step by step Divide by 3.14 Square Root • A = 3.14 r2 • = 3.14 r2 • 2826 = 3.14 r2 • 3.14 3.14 • = r2 • 30 = r

  15. Surface Area of a Rectangular Prism SA is double the area of the front + double the area of the side + double the area of the top SA = 2 lw + 2 lh + 2 wh

  16. SA = 2 lw + 2 lh + 2 wh H = 6 cm W = 5 cm L = 10 cm SA = 280 square centimeters

  17. Surface Area Hint: use every combination 6 cm 5 cm 10 cm SA = 2lw+2lh +2wh SA = 2*10*5 + 2*10*6 + 2*5*6 SA = 100 + 120 + 60 SA = 280 square centimeters

  18. Surface Area

  19. Volume of a Rectangular Prism V = lwh H = 6 inches W = 4 inches L = 25 inches 600 cubic inches

  20. Volume 4 inches 6 inches 25 inches V = lwh V = 25 * 4 * 6 V = 600 cubic inches 600 cubic inches

  21. Volume of a Rectangular Prism

  22. Density = Mass / Volume Take a look at the two boxes above. Each box has the same volume. If each ball has the same mass, which box would weigh more? Why? The box that has more balls has more mass per unit of volume. This property of matter is called density. The density of a material helps to distinguish it from other materials. Since mass is usually expressed in grams and volume in cubic centimeters, density is expressed in grams/cubic centimeter.

  23. Density = Mass / Volume 6 cm 5 cm 4 cm V = 120 cc 1. Calculate Volume: V = lwh • Calculate Mass: • Each marble weighs 10 grams • Box 1 contains 24 marbles • Box 2 contains 12 marbles M = 240 g M = 120 g

  24. Density = Mass / Volume 6 cm 5 cm 4 cm Calculate Density: Volume = 120 cc Mass 1 = 250 g Mass 2 = 130 g Calculate Density: D = M/V D = 240/120 D = 120/120 D = 1 D = 2

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