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Ordering For Rational Numbers

6.NS.C.7b
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Aligned To Common Core Standard:

Grade 6 Numbers - 6.NS.C.7b

How to Compare Negative Values of Decimals and Fractions (i.e., Place the following numbers in order from least to greatest: -8.2, 0.4, -2 1/2, 2.4) Fractions and decimals belong to the concept of rational numbers, which is a number that is expressed in the form of ratios. Integers, on the other hand, are any whole number or its opposite and are also rational numbers. For comparing fractions and decimals all in the same exercise, you could follow some of the steps presented below. In an example, let's say you have a set of numbers -8.2,0.4,-2 1/2 2.4.. The first step is we need to make the whole number fraction to a decimal number. We could make the decimal numbers in fractions as well, but it is more difficult. Now, to convert the whole number fraction, we multiply the denominator 2 with the whole number 2. We get an answer of 4; now we just add 1 present in the numerator to make it 5/2. Its decimal equivalent is 2.5. The remaining numbers are -8.2,0.4,-2.5,2.4. We know that -8.2 is less than 2.5; since 2.5 is closest to zero and the negative integer, which is closest to the list, is the largest. While we know that 0.4 is less 2.4, but it is greater than -2.5. Therefore, the list now becomes -8.2,-2.5,0.4,2.4.

Printable Worksheets And Lessons


  • Advance Comparisons Step-by-step Lesson- Compare decimals and mixed numbers. Order them from least to greatest. In this we have to identify the sign. Negative numbers are smaller than non-negative numbers. The larger the value after the negative sign, the smaller the number.

  • Guided Lesson - Compare decimals, mixed numbers, and fractions. Place a >, <, or = symbol on each line to compare the rational numbers below.


  • Guided Lesson Explanation - These comparisons are much harder for students to navigate successful. Practice makes perfect! When the right-hand number is equal to the left-hand side then we use the = sign. When the left-hand side number is greater than the right-hand side number, we put a > sign.

  • Practice Worksheet - This is a little bit crunched together. This is the typically format of the practice tests we have seen going around. You will place the rational numbers in both least to greatest and vice versa.


  • Matching Worksheet - I really didn't get too creative with this one. There are many more to follow. Match the word problems to their answers. Write the letter of the answer that matches the problem.


Homework Sheets

Decimals, fractions, negatives, just about all that and the kitchen sink too! These homework worksheets will help you make sense of this topic quickly.

  • Homework 1 - Place the following numbers in order from least to greatest. The larger the value after the negative sign, the smaller the number. We can see that -.8 and -2 are our smallest numbers. -2 is the largest negative number and -.8 our smallest number
  • Homework 2 - In this we have to identify the sign. Negative numbers are smaller than non-negative numbers. The larger the value after the negative sign, the smaller the number.
  • Homework 3 - Place a >, <, or = symbol on each line to compare the rational numbers below. We bring order to this system quickly.



Practice Worksheets

I start this section with a basic greater than, less than, or equal comparison. I feel it's important that they get the practice.

  • Practice 1 - We come at this from a decimal angle. If you remember just to point the arrow towards the smaller of the two values, you will have mastered this skill. That is off course outside of equal values.
  • Practice 2 - This mixes it up more. We shift between values that include three pieces and four pieces of data.
  • Practice 3 - The fourth problem is always the toughest. It is most likely due to the complication of decimals and mixed numbers being present in the same data set.



Math Skill Quizzes

I had many reports that quiz 3 was copied by a national testing center and used for a state test. Guess I'm doing something right.

  • Quiz 1 - Decimal and whole values in there. Students need to just consider everything before they make a choice.
  • Quiz 2 - This is symbol focused. Remember that negative values are less than postive decimal values.
  • Quiz 3 - The fractions may make it little more difficult. There are some top heavy mixed numbers that will need your assistance for a bit.