This chapter is about problem solving. During this chapter, you will use a variety of problem-solving strategies that will remain useful throughout this course, including:
- Collecting Data
- Finding Patterns
- Writing and Solving an Equation
- Drawing a Graph
- Working Backward
Diamond Problems:
In every Diamond Problem, the product of the two side numbers (left and right) is the top number and their sum is the bottom number. Proportions
Axes, Quadrants, and Graphing on an xy‑Coordinate Graph |
Proportional Relationships
A proportional relationship can be seen in a table: if one quantity is multiplied by an amount, the corresponding quantity is multiplied by the same amount. On a graph, a proportional relationship is linear and goes through the origin.
Cost ($) 0 7 14 21 28 REMEMBER: Fraction - Decimal - Percent Decimal to percent: Multiply the decimal by 100. Percent to decimal: Divide the percent by 100. Fraction to percent: Set up an equivalent fraction using 100 as the denominator. The numerator is the percent. Percent to fraction: Use 100 as the denominator. Use the digits in the percent as the numerator. Simplify as needed. Terminating decimal to fraction: Make the digits the numerator. Use the decimal place value as the denominator. Simplify as needed. Fraction to decimal: Divide the numerator by the denominator. If sets of digits repeat, then write just one of the repeating sets and place a “bar” over it. Independent and Dependent Variables |