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7th Grade Math / Lesson 1A: Equivalent Relationships

Equivalent Relationships
What will we be learning in this unit?


  • This lesson will compare and order fractions and decimals.

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


Equivalent Relationships
Fractions


Putting fractions in order:

  1. Find the least common denominator. Least common denominator is the smallest number that all denominators can go into.
  2. Make new fractions by multiplying the numerators by the same value the denominator changed by.
  3. Compare the numerators and put the fractions in the appropriate order.


Equivalent Relationships
Fractions

Example 1: Put the following fractions in order from least to greatest.

5/6     2/3     7/9

Least common denominator: 18     (6, 3, and 9 all go into 18 evenly)

Make new fractions: 5*3 = 15     2*6   = 12          7*2 14
                                  6*3 = 18      3*6  = 18          9*2 =  18

Compare the new fractions and put them in order 12/18    14/18  15/18   

Solution: 2/3 7/9  5/6

 


Equivalent Relationships
Fractions

Click the site below for practice with fractions. When you finish the problems, you can return to the lesson slides by clicking on the x in the top right corner to close the page.

Practice with fractions - click HERE

 


Equivalent Relationships
Decimals

Putting decimals in order

  • First compare the whole number (to the left of the decimal point). Put the numbers in order.
  • Then compare to the right of the decimal. Look one place at a time beginning with the tenths place.

543.21098
5: hundred
4: ten
3:one
Decimal point
2: tenth
1: hundredth
0: thousandth
9: ten-thousandth
8: hundred-thousandth


Equivalent Relationships
Decimals

Example 2:
Put in order from least to greatest:
12.871     12.781     12.71     12.178

Solution:

  • All of the numbers have a twelve to the left of the decimal.
  • Compare the first digit to the right of the decimal place (the tenth place). The last number has a "1" there. This is the smallest number.
  • The second and third numbers have a "7" in the tenth place. So we look to the hundredth place. The second number contains an "8" and the third number contains a "1" in the hundredth place. Therefore 12.71 is the next smallest number followed by 12.781.
  • The only remaining decimal number is 12.871, which is the largest of the four.
The numbers ordered least to greatest:
12.178     12.71      12.781      12.871


Equivalent Relationships
Decimals

Click on the site below for practice with decimals. When you finish the problems, you can return to the lesson slides by clicking on the x in the top right corner to close the page.

Practice with fractions - click HERE