Adding and Subtracting Rational Numbers Worksheets

This is one of those topics that everyone needs a little refresher of before they are ready to go full at it. We are working with signed values (positive or negative) in several different forms (whole numbers, decimals, fractions, and percentages). The goal is to help students become proficient with performing addition or subtraction operations with all different types of rational numbers in all types of different scenarios. These worksheets and lessons help students become really comfortable with all different forms of rational numbers and the operations between them.

Aligned Standard: HSN.RN.B.3

• Decimal Step-by-step Lesson- This one is made to help students build confidence. Since the operations involved are only addition and subtraction, we will process the operations left to right.
• Fraction Step-by-step Lesson- These basically just add an extra step for students. Rewrite all the fractions with a common base and then process the operations.
• Guided Lesson - We cover all the number forms you will see for this level. Process them as they come.
• Guided Lesson Explanation - Make sure that you are processing the operations in the correct order. Addition and subtraction are at the same priority level, so they must be processed left to right.
• Practice Worksheet - We provide solid hints in a helper box. We are working with decimals and fractions here.

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

Homework Sheets

The homework sheets provide problems that grow in difficulty as they go on.

• Homework 1 - Find each sum or difference. Fraction answers must be proper and in simplest terms. Signed Numbers: Change all operation to addition. KEEP - CHANGE - OPPOSITE.
• Homework 2 - Decimals: Align the decimal points then add or subtract. Fractions: Get common denominators, add or subtract, then simplify.

Practice Worksheets

Answer keys can be found on the last page of each file.

• Practice 2 - Some of the problems on this worksheet are in whole number form, others are decimals, and yet we still have some fractions.
• Practice 3 - Remember that since everything is undergoing complementary operations, you process everything left to right.

Math Skill Quizzes

This section allows us to assess how far we got with this topic. You will know what you know and that which you do not.

• Quiz 1 - Rewrite all the fractions with a common base. Therefore we process the operations left to right.
• Quiz 2 - Once again we come across common operations that are only addition and subtraction. This means that we process each of the operations from left to right.

The Rules of Adding and Subtracting Rational Numbers

Adding Same Signed Numbers - We make sure to add their absolute values. Your final sum should have the same sign as your addends.

Example: 4 + 7 = 11. Both addends are positive values, the sum must be too.

Example: -6 + -2 = -8. Both addends are negative values, the sum must be too.

Adding Different Signed Numbers - To perform this subtract the lesser absolute value from the greater absolute value.

Example: -5 + 9 = 4. Since 9 has larger absolute value, the sum stays positive.

Example: 3 + -8 = -5. Since -8 has larger absolute value, the sum stays negative.

Subtracting Rational Numbers - When we want to subtract bottom heavy rational numbers, add the additive inverse. This comes in handy when subtracting from a negative number.

Example: 6 – 12. We can rewrite this as the additive inverse. 6 + (-12) = -6

Example: -9 – 15. We do it again. -9 + (-15) = -24

Applying This Skill to Word Problems

When starting to learn word problems, kids encounter a single addition or single-step subtraction problem. Such problems are easier to understand and master. However, as children progress, word problems get complicated. They no more have to do a single addition or subtraction. They are given problems that involve multistep addition, subtraction or in some cases both. These problems, if not understood properly, can hinder students from understanding further advanced mathematical concepts.

Let us consider a multistep problem: John buys ten chocolates for himself. On his way home, he gives three to the kid. When he reaches home, he finds out that his father has bought five more chocolates for him. How many chocolates does John have now?

In the above problem, John initially has ten to start, and then he gave away three of them to a kid. The first step is to focus on the words being used here. Words like take away or gave away indicates subtraction. So, in the first step, you need to subtract the number of given away chocolates from the total population.

10 - 3 = 7

Later, John reaches home and finds out that his father has 5 more chocolates for him. Here the word more indicates something that needs to be added. So, in the next step, we have to perform addition.

7 + 5 = 12

Initially, John has 10 chocolates; he gave away three of them. Later he got 5 more and he ended up with 12 chocolates in total.