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Intermediate Algebra: Fractions and Real Numbers

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이 집합의 용어 (15)

  • How do you convert a mixed number to an improper fraction?

    Multiply the denominator by the whole number, add the numerator, then place the result over the original denominator.

  • Convert the mixed number \(2\frac{3}{4}\) to an improper fraction.

    \(\frac{11}{4}\)

  • How do you convert an improper fraction to a mixed number?

    Divide the numerator by the denominator; the quotient is the whole number, and the remainder is the new numerator over the original denominator.

  • Convert the improper fraction \(\frac{8}{5}\) to a mixed number.

    \(1\frac{3}{5}\)

  • What is the first step when multiplying or dividing mixed numbers?

    Change mixed numbers to improper fractions before multiplying or dividing.

  • What is the first step when adding or subtracting mixed numbers?

    Line up the mixed numbers vertically to align like terms.

  • What are the main subsets of the Real Number System?

    Natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

  • Define natural numbers.

    Counting numbers starting from 1, 2, 3, and so on.

  • Define whole numbers.

    Natural numbers including zero: 0, 1, 2, 3, ...

  • Define integers.

    Whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...

  • What are rational numbers?

    Numbers that can be expressed as a fraction of two integers, including integers, fractions, and terminating or repeating decimals.

  • What are irrational numbers?

    Numbers that cannot be expressed as a fraction, with non-terminating, non-repeating decimals, like \(\pi\) and \(\sqrt{2}\).

  • Use roster notation to name the set of all letters in the word 'mathematics.'

    { m, a, t, h, e, i, c, s }

  • Use roster notation to name the set of all odd whole numbers less than 11.

    { 1, 3, 5, 7, 9 }

  • What is set-builder notation?

    A way to describe a set by stating the properties that its members must satisfy.