THE TRANSITION LINE // FIELD NOTES // STOP 32
Solving equations and the data trio
Field Book
Lessons 121 to 124
Method
Pencil and paper. Calculators never.
Room 8 opens this stop. The last door before the end of the Line. Equations solve by isolating the variable with opposite operations applied to both sides, fractional percents reduce through the times-one-hundredth move, mean, median, and mode read a data set three ways, and like terms combine before anything else moves.
What you have to be able to do
- Solve equations formally
- Change fractional percents to fractions
- Find mean, median, and mode
- Combine like terms
The procedures
Solving formallyField Book Lesson 121
- Work to isolate the variable on one side of the equals sign.
- Perform the opposite operation, and do the same thing to both sides.
Fractional percentsField Book Lesson 122
- Rewrite the percent as an improper fractional percent.
- Multiply by 1100 and reduce.
Mean, median, modeField Book Lesson 123
- Mean adds all values and divides by the count.
- Median takes the middle of the ordered list. Mode takes the most frequent value.
Combining like termsField Book Lesson 124
- Combine variable terms with variable terms and constants with constants.
- Carry each sign with its own term.
Worked: both sides
- 6N - 13 = 35. Add 13 to both sides: 6N = 48.
- Divide both sides by 6: N = 8.
Worked: the trio
- Data: 4, 7, 7, 9, 13. The mean is 40 รท 5 = 8.
- The median is 7, and the mode is 7.
Terms on the record
| Term | Meaning |
|---|
| equation | a claim that two expressions have the same value |
| solve | to find the value of the variable that makes the equation true |
| mean | the sum of the values divided by their count |
| median | the middle value of the ordered list |
| mode | the most frequent value in the list |
| like terms | terms that carry the same variable part |