# Ordering For Rational Numbers Worksheets

We often need to organize values to either explain them to other people or simply make sense of them for ourselves. At this point students should have a very solid understanding of how to take positive integers and order them least to greatest or vice versa. Where a little confusion comes into play is when students begin working with fractions, decimals, and negative numbers or a mixture of all three. We encourage students to always start by making sure that all values are in the same notation system and then proceed from there. We need to remember that the more negative a value is, the further that it moves to left on a number line. These worksheets and lessons will help students learn how to give order to rational numbers.

### Aligned Standard: Grade 6 Numbers - 6.NS.C.7b

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

### How to Compare Negative Values of Decimals and Fractions

Fractions and decimals belong to the family of rational numbers, which are numbers that are expressed in the form of ratios. Integers, on the other hand, are any whole number or its opposite and are also rational numbers. There will be times where we will need to compare fractions and decimals. There may even be times that we need to compare these values to whole numbers and negative values.

In an example, let's say you have a set of 4 numbers and are asked to place them in order from least to greatest: 0.4, -8.2, 2.4, -2 1/2

The first step is we need to make is to get everything in the same notation system. In this case we have 3 in decimal form and 1 value in fractional form. We need to convert 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. The decimal equivalent is 2.5. The remaining numbers are: 0.4, -8.2, 2.4, -2.5

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. We know the positive values are greater than both of those. So, we move the negative values to the left and the positive values to the right: -8.2, -2.5, 2.4, 0.4. 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.