25 Questions
State the mathematical operation that is indicated by the following symbols: a) + b) - c) x d) ÷ e) = f) ⁄
a) Addition, b) Subtraction, c) Multiplication, d) Division, e) Equality, f) No specific mathematical operation for this symbol
State the meaning of the equal sign and give an example of its use.
The equal sign indicates that the values on either side of the sign are equivalent. Example: 5 + 3 = 8.
Explain how to add whole numbers. Provide an example.
When adding whole numbers, align the units, tens, hundreds, etc., columns and start adding from the rightmost column. Carry over if the sum is more than 9. Example: 452 + 107 = 559.
Describe the process of adding decimal numbers. Give an example.
To add decimal numbers, line up the decimals vertically and add as you would with whole numbers. Example: 0.875 + 1.2 + 375.007 + 71.1357 + 735 = 1183.2177.
Explain how to add fractions. Mention the importance of having a common denominator.
When adding fractions, ensure they have a common denominator; find the common denominator by multiplying the individual denominators. Example: 1/2 + 3/4 = 5/4 with a common denominator of 4.
What is the common method for converting fractions to the common denominator?
Divide the original denominator into the common denominator, and then multiply both the top and bottom by this value.
What is the lowest common denominator for the fractions provided in the example?
24
How can a mixed number be converted to an improper fraction?
Multiply the whole number by the denominator and add the numerator as the new numerator. The denominator remains the same.
Subtract 20 from 430.
410
When subtracting whole numbers, borrow one unit when necessary.
True
What is the value of I in Objective Five Exercise Answer 1?
2
What is the value of P in Objective Five Exercise Answer 2?
500
What is the value of V in Objective Five Exercise Answer 3?
68.92
What is the result of 2 × 4 + 6 − 3?
11
What is the result of 30 ÷ 15 + 200 + 10 − 10 × 20?
180
Simplify [20 + (30 + 15 × 2) ÷ 40]?
21
Calculate 30(5 + 15 − 20 + 2 × 20) ÷ 50?
18
What is the result of 8 ÷ 4 × 2 + 6(100 ÷ 50) + 7?
25
How much cable is left on the reel if 150 m of cable is used for the job with three runs of 15 m and two runs of 18 m?
105 m
What is the total horsepower load of the machine shop with three 3/8 hp motors, five 11/4 hp motors, and seven 11/2 hp motors?
20 3/8 hp
How do you multiply decimal numbers?
Place the larger number over the smaller one, align the right-hand digits, multiply as whole numbers, count the total number of decimal places and place the decimal in the answer.
What is the process of cancellation when multiplying fractions?
It is the simplification process where one denominator and one numerator are divided evenly by the same number.
When dividing fractions, one should invert and __________.
multiply
Explain the order of operations using BEDMAS.
Perform operations in the order of brackets, exponents, division, multiplication, addition, and subtraction.
What rules should you follow when multiplying fractions?
- Multiply the numerators. 2. Multiply the denominators. 3. Reduce the answer to lowest terms.
Study Notes
First Period Math Applications
- This module covers basic mathematical skills required for electricians, including solving trade-related problems using arithmetic operations.
- The objectives of this module are to:
- Recognize basic arithmetic symbols
- Add and subtract whole, decimal, and fractional numbers
- Multiply and divide whole, decimal, and fractional numbers
- State the correct sequence of arithmetic operations and solve equations
- Apply math skills to transpose equations related to Ohm's Law
Objective One: Arithmetic Symbols
- Arithmetic symbols are shorthand marks representing mathematical operations:
-
- for addition
-
- for subtraction
- × for multiplication
- ÷ for division
- = for equality
-
- Examples of arithmetic symbols in use:
- 6 + 2 = 8
- 17 - 12 = 5
- 16 × 12 = 192
- 28 ÷ 4 = 7
Objective Two: Addition and Subtraction
- Addition of whole numbers:
- Line up units, tens, and hundreds columns
- Add columns from top to bottom
- Carry or add digits to the next column if the sum is more than 10
- Examples of adding whole numbers:
- 452 + 107 = 559
- 2157 + 845 + 34 = 3036
- Addition of decimal numbers:
- Line up decimal points
- Add columns from top to bottom
- Keep the decimal point in the same vertical line
- Examples of adding decimal numbers:
- 0.875 + 1.2 + 375.007 + 71.1357 + 735 = 1183.2177
- Subtraction of whole numbers:
- Line up units, tens, and hundreds columns
- Subtract columns from top to bottom
- Borrow from the next column if the subtraction is negative
- Examples of subtracting whole numbers:
- 623 - 254 = 369
- 430 - 20 = 410
Objective Three: Multiplication and Division
- Multiplication of whole numbers:
- Multiply numbers as usual
- Examples of multiplying whole numbers:
- 16 × 12 = 192
- Division of whole numbers:
- Divide numbers as usual
- Examples of dividing whole numbers:
- 28 ÷ 4 = 7
Objective Four: Sequence of Arithmetic Operations
- The correct sequence of arithmetic operations is:
- Parentheses (brackets)
- Exponents (none in this module)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Objective Five: Equations and Transposition
- Equations are statements with equal signs (=)
- Examples of equations:
- 2x + 3 = 5
- Transposition of equations:
- Rearrange equations to solve for a specific variable
- Use Ohm's Law equations (not covered in this module)
Exercises and Answers
- Exercises for each objective are provided
- Answers are provided at the end of the module### Objective Three: Multiplication and Division
- Multiply whole numbers by following the multiplication of whole numbers method
- Multiply decimal numbers by following these steps:
- Place the larger number over the smaller one with right-hand digits aligned
- Multiply using the whole numbers method
- Count the total number of decimal places found in both numbers
- Set the decimal point in the answer at the same number of decimal places
- Multiply fractions by following these steps:
- Multiply the numerators to obtain a product of numerators
- Multiply the denominators to obtain a product of denominators
- Reduce the answer to lowest terms
- Divide whole numbers by dividing the dividend by the divisor
- Divide decimal numbers by dividing the dividend by the divisor
- Divide fractions by using the reciprocal of a fraction and multiplication
- Change the divide sign to a multiplication sign and invert the last fraction
- Multiply the numerators and denominators
- Give the answer as a mixed number reduced to lowest terms
Objective Four: Sequence of Arithmetic Operations
- Follow the order of operations (BEDMAS) to solve mathematical statements:
- Perform operations within brackets first
- Apply exponents
- Perform multiplication and division from left to right
- Perform addition and subtraction from left to right
- Use BEDMAS to solve equations with multiple operations
- Apply the rules to equations with brackets, exponents, multiplication, division, addition, and subtraction
Objective Five: Transposition of Equations (Ohm's Law)
-
An equation is a mathematical statement with two expressions equal in value
-
Equations can be balanced by adding, subtracting, multiplying, or dividing both sides by the same value
-
Transpose equations to find an unknown value by doing the same operation to each side
-
Apply transposition to equations such as Ohm's Law (E = I×R) to solve for an unknown value### Solving Equations
-
To solve an equation with fractions on both sides, use cross-multiplication: multiply the numerator of one fraction by the denominator of the other fraction and vice versa.
-
When cross-multiplying, change the sign of the expression being moved from one side of the equation to the other (e.g., from positive to negative or negative to positive).
Example 1: Solving for E.R
- Given the equation P = E²/R, solve for E.R by multiplying each side by R, canceling the Rs on the right side, and taking the square root of each side.
- Result: E.R = √R × P or E = √R × P.
Fractions and Cross-Multiplication
- If one side of an equation is not in fraction form, it can be made so by placing it over 1.
- This enables cross-multiplication, which involves multiplying the numerators and denominators of the fractions.
Solving for P
- Example: given the equation 2P = 10, solve for P by cross-multiplying and dividing each side by 2.
- Result: P = 5.
Equations with Expressions
- Equations can also be solved by moving an expression from one side to the other.
- When doing so, change the sign of the expression (e.g., from positive to negative or negative to positive).
Example 2: Solving for P
- Given the equation 2P + 4 = 8, solve for P by subtracting 4 from both sides and dividing each side by 2.
- Result: P = 2.
Example 3: Solving for R2
- Given the equation R1 + R2 = RT, transpose to find R2 by subtracting R1 from both sides.
- Result: R2 = RT - R1.
Formula Transposition
- To transpose a formula, move an expression from one side to the other and change its function (e.g., from multiplication to division).
Examples of Formula Transposition
- Example 1: given the equation 3A = 9, solve for A by dividing each side by 3.
- Example 2: given the equation B/10 = 25, solve for B by multiplying each side by 10.
Taking the Root of Both Sides
- Taking the root of both sides of an equation by a common term maintains the balance of the equation.
- Example: given the equation 22 = 4, solve for the square root of each side.
- Result: 2 = 2.
Objective Exercises
- Exercises include solving for I, V, P, R, and other variables using various equations and formulas.
- Answers are provided for each exercise.
Test your knowledge of circuit fundamentals with this quiz designed for electrician students. Topics covered include applications and first period math.
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