Fractions whose numerator and denominator share a common factor can be simplified. See why this is the case, with multiple examples to demonstrate the process.
Math problems often include negative differences. Familiarity with ways of manipulating them will help to both avoid common errors and recognize equivalent expressions.
Explanation of why a negative sign can be placed, or moved to, in front of a fraction, in front of its numerator, or in front of its denominator, without changing the value of the fraction.
Algebra Intro 9: Fractions, Reciprocals, and Properties of Division
Exploration of fractions as ratios, division problems, and the inverse of multiplication. What they look like, what they mean, and their lack of algebraic properties (associative, commutative).
Algebra Intro 10: Fractions and Multiplication
Exploration of ways to think about, and approach, fractions that are useful when working with them. What does a product of fractions mean, and what alternatives are there for evaluating it?
Algebra Intro 11: Dividing Fractions, Equivalent Fractions
Once a person is comfortable with multiplying fractions, dividing one fraction by another becomes fairly straightforward. Dividing Fractions An alternative to division by any number (not just a fraction) is “multiplying by the reciprocal”. Dividing by two has the same effect as multiplying by one half. Multiplying by the reciprocal of a number will always produce…… Continue reading Algebra Intro 11: Dividing Fractions, Equivalent Fractions
Algebra Intro 12: Adding and Subtracting Fractions
Once someone knows how to multiply fractions, and is comfortable creating equivalent fractions by multiplying by a fraction that equals 1, they have to tools needed to add and subtract fractions. Why Can’t I Just Add Two Fractions As Written? Consider the fraction “two thirds.” The phrase as written can be represented in two ways:…… Continue reading Algebra Intro 12: Adding and Subtracting Fractions