Summary: Representing Parts of a Whole as Fractions

Key Concepts

  • Property of One
    • Any number, except zero, divided by itself is one.   [latex]{\Large\frac{a}{a}}=1[/latex] , where [latex]a\ne 0[/latex]
  • Mixed Numbers
    • A mixed number consists of a whole number [latex]a[/latex] and a fraction [latex]{\Large\frac{b}{c}}[/latex] where [latex]c\ne 0[/latex]
    • It is written as follows: [latex]a{\Large\frac{b}{c}}\enspace c\ne 0[/latex]
  • Proper and Improper Fractions
    • The fraction [latex]ab[/latex] is a proper fraction if [latex]a<b[/latex] and an improper fraction if [latex]a\ge b[/latex] .
  • Convert an improper fraction to a mixed number.
    1. Divide the denominator into the numerator.
    2. Identify the quotient, remainder, and divisor.
    3. Write the mixed number as quotient [latex]{\large\frac{\text{remainder}}{\text{divisor}}}[/latex]
  • Convert a mixed number to an improper fraction.
    1. Multiply the whole number by the denominator.
    2. Add the numerator to the product found in Step 1.
    3. Write the final sum over the original denominator.
  • Equivalent Fractions Property
    • If [latex]\mathrm{a, b,}[/latex] and [latex]c[/latex] are numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] , then [latex]{\Large\frac{a}{b}}={\Large\frac{a\cdot c}{b\cdot c}}[/latex]


equivalent fractions
Equivalent fractions are two or more fractions that have the same value.
A fraction is written [latex]{\Large\frac{a}{b}}[/latex] . in a fraction, [latex]a[/latex] is the numerator and [latex]b[/latex] is the denominator. A fraction represents parts of a whole. The denominator [latex]b[/latex] is the number of equal parts the whole has been divided into, and the numerator [latex]a[/latex] indicates how many parts are included.
mixed number
A mixed number contains