Posts tagged foundations of math
How to determine whether a number is a prime or composite number

You’ve already learned several ways to classify a whole number: as positive, negative, or 0; as the opposite of a number, in terms of the whole numbers by which it’s divisible, and in terms of its multiples. Another way to classify a whole number greater than 1 is as either a “prime” number or a “composite” number. A whole number will either be a prime number or a composite number, but it can’t be both.

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Divisibility rules for the numbers 2 through 10 (Is a number divisible by 2? By 3? By 4? etc.)

When we talk about the “divisibility” of a whole number, we’re just talking about the whole numbers that divide evenly into it. As an example, 5 divides evenly into 15 three times, since 15/5=3, which means we can say that 15 is “divisible” by 5. In this lesson we’ll look at divisibility rules for the numbers 2-10.

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Using unit multipliers to convert between different units

Unit multipliers are what we use to convert one set of units to another. A really easy example is using a unit multiplier to convert feet to inches. We’ll be multiplying by fractions, remembering to put on the top (the numerator) the units we want to keep, and we put on the bottom (the denominator) the units we want to get rid of.

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What are opposite numbers?

When we talk about the “opposite of a number,” we’re specifically talking about the positive and negative versions of the same number. Now that’s not a technical definition by any means, so let me show you what I mean.

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How to multiply signed numbers (positive and negative numbers)

As a reminder, signed numbers are positive and negative numbers. When we multiply signed numbers, therefore, there are three possible combinations. Multiplying numbers with the same sign will give a positive result, but multiplying numbers with different signs will give a negative result.

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How to divide positive and negative numbers

Use the sign rules for division and check answers by multiplying. See what happens when zero is the dividend or the divisor.

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How to add and subtract mixed numbers with unlike denominators

Find a common denominator, add or subtract mixed numbers, and regroup a whole when the fraction on top is smaller.

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What is a radical? Square roots, cube roots, and fractional powers

Identify the index and radicand, evaluate square and cube roots, and connect roots to fractional exponents.

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How to simplify fractions by canceling common factors

Reduce a fraction to lowest terms by dividing its numerator and denominator by the same factor. Work through 630/945 step by step.

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