7th Grade Chapter 7
7-1 Solving Two Step Equations
To solve a two-step equation, the goal is to isolate the variable. Use the properties of equality to undo the addition or subtraction first. Then undo the multiplication or division.
7-2 Solving Multi-Step Equations
When appropriate, apply the Distributive Property to remove parentheses from an equation. Then combine all like terms on each side of the equal sign. Undo addition and/or subtraction, and then undo multiplication and/or division, as you did in simpler two-step equations.
7-3 Two-Step Equations with Fractions and Decimals
To clear a fraction from an equation, you essentially “get rid” of the denominator by making it 1. You do this by multiplying both sides of the equation by the denominator. When a fraction is the coefficient of the variable, you can multiply by the reciprocal of the fraction. This actually combines two steps: multiplying to eliminate the denominator and dividing by what would be the resulting coefficient.
7-4 Reasoning Strategy:
Write an Equation When you write the words to suggest an equation, you are stating a relationship in a clear and unambiguous way. You are also organizing what you know and what you want to find into a mathematical sentence. Represent what you want to find with a variable.
7-5 Solving Two-Step Inequalities
You solve two-step inequalities in almost the same manner that you solve two-step equations, with one important difference: when you multiply or divide each side of an inequality by a negative number, you must also reverse the inequality symbol. It is important to check the reasonableness of the solution by substituting it back into the original inequality. However, an estimate is sufficient sometimes.
7-6 Transforming Formulas
You transform formulas to make them more useful in the problems that you need to solve. Transforming a formula allows you to represent the desired quantity in terms of the others. The ability to transform formulas will minimize the need to memorize many different formulas.
7-7 Simple and Compound Interest
The rate for simple interest is the annual percentage rate (APR), or the precent used to calculate interest that is pain in one year. In simple interest calculations using the formula I=prt, t is the time in years, t can represent a fraction or more of a year. In the compound interest formula, B=p(1+r/n)^nt, r is the interest rate for each interest period, and n is the number of interest periods. You find r by dividing the annual interest rate by the number of interest periods in one year.
To solve a two-step equation, the goal is to isolate the variable. Use the properties of equality to undo the addition or subtraction first. Then undo the multiplication or division.
7-2 Solving Multi-Step Equations
When appropriate, apply the Distributive Property to remove parentheses from an equation. Then combine all like terms on each side of the equal sign. Undo addition and/or subtraction, and then undo multiplication and/or division, as you did in simpler two-step equations.
7-3 Two-Step Equations with Fractions and Decimals
To clear a fraction from an equation, you essentially “get rid” of the denominator by making it 1. You do this by multiplying both sides of the equation by the denominator. When a fraction is the coefficient of the variable, you can multiply by the reciprocal of the fraction. This actually combines two steps: multiplying to eliminate the denominator and dividing by what would be the resulting coefficient.
7-4 Reasoning Strategy:
Write an Equation When you write the words to suggest an equation, you are stating a relationship in a clear and unambiguous way. You are also organizing what you know and what you want to find into a mathematical sentence. Represent what you want to find with a variable.
7-5 Solving Two-Step Inequalities
You solve two-step inequalities in almost the same manner that you solve two-step equations, with one important difference: when you multiply or divide each side of an inequality by a negative number, you must also reverse the inequality symbol. It is important to check the reasonableness of the solution by substituting it back into the original inequality. However, an estimate is sufficient sometimes.
7-6 Transforming Formulas
You transform formulas to make them more useful in the problems that you need to solve. Transforming a formula allows you to represent the desired quantity in terms of the others. The ability to transform formulas will minimize the need to memorize many different formulas.
7-7 Simple and Compound Interest
The rate for simple interest is the annual percentage rate (APR), or the precent used to calculate interest that is pain in one year. In simple interest calculations using the formula I=prt, t is the time in years, t can represent a fraction or more of a year. In the compound interest formula, B=p(1+r/n)^nt, r is the interest rate for each interest period, and n is the number of interest periods. You find r by dividing the annual interest rate by the number of interest periods in one year.