Firefighter Entrance Math Exam Assistance
Basic Math, Addition & Subtraction
Addition and subtraction are opposite operations. Multiplication and Division are opposite operations. When dealing with several operations, the operations must be done in a specific order. First: Do all operations within parentheses first, follow the below order: (3 + 7) x 4 = ? (10) x 4 = 40. Second: Do all exponential operations next: (3 + 7)² x 42 = ? (10)² x 42 = ? (100) x 42 = 4200. Third: Do all multiplication and divisions before addition or subtractions. (3 + 7) x 4 - 2 = ? (10) x 4 -2 = ? (40) -2 = 38 (3 + 7) ÷ 2 - 2 = ? (10) ÷ 2 - 2 = ? (5) -2 = 3 (3 + 7)² x 16 -2 = ? (10)² x 16 -2 = ? (100) x 16 -2 = ? (1600) - 2 = 1598. Lastly: Do all addition or subtractions outside of parentheses. Any operations which contain a multiplication or division by zero (0) is 0. (3 + 7) x 42 x 0 = ? (10) x 42 x 0 = (420) x 0 = 0. 7 + 12 +(4 x 0) = ? 7 + 12 + (0) = 19 7 + 12 + (4 ÷ 0) = ? 7 + 12 + (0) = 19 (7 + 12) x (4 ÷ 0) = ? (19) x (0) = 0
Parallel Lines are lines that never meet. Perpendicular are lines that cross at right angles (90 angle) Know the basic
Square Root Numbers Know your squares! This will assist in square root problems 1 Squared = 1, 2 Squared = 4, 3 Squared = 9, etc.
Fractions are essentially parts of a whole. If you have half of something, then you have one of the two equal parts of that something. The denominator indicates how many of the whole will be divided into. The numerator tells how many parts you are dealing with. A coffee cake is cut into 8 parts. You eat one piece. The denominator in this cake is 8 pieces. The numerator references what's left and what has been eaten. There are 7/8 of the cake left and 1/8 of the cake is gone. When ever the numerator (top number) is less than the denominator (bottom number) the fraction is considered a "proper" fraction such as 1/8 or 7/8. An "improper" fraction occurs when the numerator exceeds or equals the denominator such as 9/8 or 8/8 . (Note: 8/8 has the value of 1) Numerator - Denominator A mixed number has a whole number and a fraction such as 2 1/2. In math, sometimes the mixed number must become an improper fraction to perform a calculation. To do this multiply the whole number by the denominator and add to the numerator. Example: 2 1/6 changed to an improper fraction becomes 13/6. To convert back divide the numerator by the denominator, the remainder becomes the numerator of a proper fraction within the mixed number such as 13/6 becomes 2 and 1/6 remaining. (2 1/6) Adding and Subtracting Fractions When add or subtract fractions, you must be convert the fractions to a common denominator before a calculation can be done. In the example: 1/2 + 1/4 = ? The fraction 1/2 must be converted to 2/4 before adding. (1/2= 2/4) The common denominator in this case was four.
To find the lowest common denominator, sometimes it may be necessary to multiply the denominators to find the lowest common denominator (LCD) In the example 2/3 + 2/7 = ? Multiply 3 x 7 = 21, which is the LCD. To convert the fractions divide the selected denominator (21) by the fraction denominator 21÷ 3 = 7. Multiply the numerator by 7 to get the proper fraction. (2/3 becomes 14/21 and 1/7 becomes 3/21) : Example: 2/3 + 2/7 = 14/21 + 6/21= 20/21 The answer 17/21 cannot be reduced any further. Multiplying Fractions There is no need to convert fractions to the LCD when multiplying fractions. Simply multiply the numerators, then multiply the denominators. Example: 2/5 x 3/7 = (2 x 3 =6) and (5 x 7 = 35)] = 6/35 LCD Example: 3 x 2 1/2 x 3 3/4 = 3/1 x 5/2 x 15/4 = (3 x 5 x 15) / (1 x 2 x 4) = 225/8 = 28 1/8 LCD Dividing Fractions Remember when dividing by a fraction invert the fraction then multiply. Whole numbers are also fractions! Example: Divide 30 by 1/2. 30 ÷ 1/2 = 30/1 x 2/1 (Inverted) = 60 (Note NOT in half.) Example: Divide 30 by 2. 30 ÷ 2 = 30/1 x 1/2 (Inverted) = 15 |