Negative Fractions

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 4: Negative Numbers, Zero, Absolute Values, and Opposites

Negative Numbers Negative numbers are something new and interesting to think about. What do they mean? They arose from changing the order in which we subtracted two numbers. While we usually think of a "difference" by starting our thought process with the larger number, when we fail to do that and try to "take away" …

Algebra Intro 7: Properties of Multiplication

Properties Of Multiplication Do the patterns that applied to addition also apply to multiplication... do the following all produce the same result? $latex 3 \cdot 5 \cdot 7 \\*~\\*3 \cdot (5 \cdot 7) \\*~\\*(3 \cdot 5) \cdot 7&s=2&bg=ffffff&fg=000000$ After carefully following the order of operations, we see that they all result in a value of 105. …

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 …

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: …

Inverse Musings: * and /

Inverse operations and functions are wonderful things. Without them, solving equations would be much more challenging. Yet inverse operations can also be odd beasts. My previous "inverses" post pondered addition and subtraction, which led us (as young students) to expand our initial universe of counting numbers into the integers. Addition and subtraction are operations that …