Strategies for operations properties can be used to add, subtract, factor, and expand linear expressions with rational coefficients. By rewriting an expression in different contexts, we can gain better insight into the problem and the relationships between the quantities. Using the formula a + 0.05a = 1.05a, we understand that increasing by 5% is the identical to multiplying by 1.05.

Complex mathematics and real-life problems involving positive and negative rational numbers can be solved using numbers in any form with the appropriate tools. For proper calculations, convert various forms; assess the validity of results by mental computing and estimating. Example: If a woman gets a 10% raise on her $25 hourly wage, that translates to an additional $2.50, raising her hourly wage to $27.50.

Word problems leading to px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers can be solved with fluency; you can also compare the algebraic solution to an arithmetic one. For example, to calculate the width of a rectangle with a perimeter of 54 cm and length of 6 cm.

Solutions can be found and