<< Back to Lessons Index

7th Grade Math / Lesson 1B: Equivalent Relationships II

Equivalent Relationships
What will we be learning in this unit?


  • In this lesson you will learn find equivalent relationships between fractions, decimals, and percents

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


Equivalent Relationships
Converting Decimals to Fractions


To convert a decimal to a fraction you need to be familiar with the place values of the decimal.

  • 42.65 The five is in the hundredth place. So the fraction value of this number is 4265/100 which reduces to lower terms 853/20 (divide both numerator and denominator by 5)

    Examples: Convert the decimals to fractions

    1. 3.057
    2. 1.9
    3. .77

    *Hint: The number of digits passed the decimal point is how many zeros you need in the denominator.


  • Equivalent Relationships
    Converting Decimals to Fractions


    To convert a decimal to a fraction you need to be familiar with the place values of the decimal.

  • 42.65 The five is in the hundredth place. So the fraction value of this number is 4265/100 which reduces to lower terms 853/20 (divide both numerator and denominator by 5)

    Examples: Convert the decimals to fractions

    1. 3.057     3057/1000
    2. 1.9         19/10
    3. .77         77/100

    *Hint: The number of digits passed the decimal point is how many zeros you need in the denominator.


  • Equivalent Relationships
    Converting Fractions to Decimals


    To convert a fraction to a decimal you have to do division.

  • Take the numerator and divide it by the denominator.
         65/32   65/32 = 2.03125



    Examples: Convert the following into decimals.

    1. 32/45

    2. 12/7


  • Equivalent Relationships
    Converting Fractions to Decimals


    To convert a fraction to a decimal you have to do division.

  • Take the numerator and divide it by the denominator.
         65/32   65/32 = 2.03125



    Examples: Convert the following into decimals.

    1. 32/45   32 / 45 = .711 (This is a rounded answer)

    2. 12/7     12 / 7 = 1.714 (This is a rounded answer)


  • Equivalent Relationships
    Converting Percents

    Percents are based on the value 100.

    To convert a percent to a fraction: take the percent number and place it in the numerator (without the decimal point). The denominator will be 100. (Simplify if possible)
    Example: Change 45% to a fraction

    To convert a percent to a decimal: since percentages are based on 100, move the decimal place two places (two zeros) to the left.
    Example: Change 45% to a decimal


    Equivalent Relationships
    Converting Percents

    Percents are based on the value 100.

    To convert a percent to a fraction: take the percent number and place it in the numerator (without the decimal point). The denominator will be 100. (Simplify if possible)
    Example: Change 45% to a fraction      45/100=9/20

    To convert a percent to a decimal: since percentages are based on 100, move the decimal place two places (two zeros) to the left.
    Example: Change 45% to a decimal      .45


    Equivalent Relationships
    Converting Percents

    Percents are based on the value 100.

    To convert a decimal to a percent: Since percent is based on 100, (two zeros), move the decimal point two places to the right.
    Example: Change 7.435 to a percent

    To convert a fraction to a percent: change the fraction to a decimal and follow the above procedure for changing it to a percent.
    Example: Change 34/57 to a percent


    Equivalent Relationships
    Converting Percents

    Percents are based on the value 100.

    To convert a decimal to a percent: Since percent is based on 100, (two zeros), move the decimal point two places to the right.
    Example: Change 7.435 to a percent      743.5%

    To convert a fraction to a percent: change the fraction to a decimal and follow the above procedure for changing it to a percent.
    Example: Change 15/63 to a percent      15/63 = .238 (this is rounded)
                                                                     .238 = 23.8%