Common fractions and decimals

Common fractions and decimals

In this lesson, we will learn:

  • How to convert between decimals and decimal fractions (tenths and hundredths)
  • How to convert between decimals and unit fractions
  • How to convert between decimals and fraction halves and quarters

Notes:

  • Decimals can be converted into fractions and vice versa
    • Recall that place values are related to their neighbors by a factor of 10

    • Common fractions and decimals

  • Decimals can be easily converted into decimal fractions
    • Decimal fractions have denominators that are powers of 10
    • Decimal tenths are fractions out of 10
      • Ex. 0.3 = 310\large \frac{3}{10} ; 3 tenths = 3 out of 10 Common fractions and decimals
    • Decimal hundredths are fractions out of 100
      • Ex. 0.22 = 22100\large \frac{22}{100} ; 22 hundredths = 22 out of 100 Common fractions and decimals
    • Decimal hundredths can also be expressed as a sum of fractions, because of equivalent decimals (i.e. 0.2 = 0.20)
      • 0.22 = 22100\large \frac{22}{100} = 20100\large \frac{20}{100} + 2100\large \frac{2}{100} = 210\large \frac{2}{10} + 2100\large \frac{2}{100}

  • Two type of common fractions have a denominator of 2 or 4

Type

Fraction

Decimal Value

"half"

12\frac{1}{2}


= 50100\frac{50}{100} = 510\frac{5}{10}

0.5

"quarter"

14\frac{1}{4}


= 25100\frac{25}{100}

0.25

Lessons

  • Introduction
    Introduction to Common Fractions and Decimals:
    a)
    How are decimals related to fractions?

    b)
    How to convert decimal tenths into decimal fractions (110\large \frac{1}{10})

    c)
    How to convert decimal hundredths into decimal fractions (1100\large \frac{1}{100})

    d)
    How to convert between decimals and common fraction halves (12\large \frac{1}{2})

    e)
    How to convert between decimals and common fraction quarters (14\large \frac{1}{4})


  • 1.
    Writing common fractions as decimals
    Write the following fractions as decimals
    a)
    Unit fractions:

    b)
    Decimal fractions:

    c)
    Common fractions related to 12\large \frac{1}{2} or 14\large \frac{1}{4} :


  • 2.
    Fraction and figure equivalents for decimals
    Complete the table for the equivalent decimal, fraction, and shaded in figure:
    a)
    Common fractions and decimals

    b)
    Common fractions and decimals

    c)
    Common fractions and decimals

    d)
    Common fractions and decimals


  • 3.
    Fraction and figure equivalents for decimals
    Complete the table for the equivalent decimal, fraction, and shaded in figure:
    a)
    0.28 = 100\large \frac{}{100} = 20100\large \frac{20}{100} + 100\large \frac{}{100} = 10\large \frac{}{10} + 100\large \frac{}{100}

    b)
    0.51 = 100\large \frac{}{100} = 50100\large \frac{50}{100} + 100\large \frac{}{100} = 10\large \frac{}{10} + 100\large \frac{}{100}

    c)
    0.73 = ??\large \frac{?}{?} = 100\large \frac{}{100} + 100\large \frac{}{100} = 10\large \frac{}{10} + 100\large \frac{}{100}

    d)
    0.49 = ??\large \frac{?}{?} = ??\large \frac{?}{?} + ??\large \frac{?}{?} = ??\large \frac{?}{?} + ??\large \frac{?}{?}


  • 4.
    Common fractions and decimal number lines
    Using common fractions and decimals:

    A:25100  \large \frac{25}{100} \qquad \; B:710  \large \frac{7}{10} \qquad \; C:90100  \large \frac{90}{100} \qquad \; D:510  \large \frac{5}{10} \qquad \; A:75100\large \frac{75}{100} \qquad
    a)
    Draw each fraction as a point on the number line. Label each point with its corresponding letter

    Common fractions and decimals

    b)
    Which fractions can be rewritten in lowest forms as common fraction halves and quarters?