How to Use Input/output Tables to Add and Subtract Integers?

A step-by-step guide to using input/output tables to add and subtract integers

Here is a step-by-step guide on how to use input/output tables to add and subtract integers:

Step 1: Understand the Table An input/output table is a table that shows the relationship between two sets of numbers. The input values are listed in one column, and the corresponding output values are listed in another column. It is important to understand the table’s structure and how the input and output values are related.

Step 2: Identify the Operation Look at the table to determine whether you are adding or subtracting integers. This will help you decide which sign to use when you write the expressions.

Step 3: Write the Expressions Write the expressions for each row in the table using the input value and the operation. For example, if the operation is addition, the expression would be:

\(input\) \(+ n =\) \(output\)

Where ‘\(n\)’ is the integer that needs to be added to the input to get the output.

Step 4: Solve for the Unknown Use algebraic methods to solve for the unknown integer ‘\(n\)’ in each row. You can do this by isolating ‘\(n\)’ on one side of the equation. For example, if the equation is:

\(input\) \(+ n =\) \(output\)

You can solve for ‘\(n\)’ by subtracting the input from both sides:

\(n = output – input\)

Step 5: Check Your Work Once you have solved for ‘\(n\)’ in each row, check your work by plugging in the input and ‘n’ values into the equation to see if they produce the correct output value.

Pre-Algebra for Beginners 2027 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

Step 6: Practice, Practice, Practice! The more you practice using input/output tables to add and subtract integers, the easier it will become. Try creating your tables with different input and output values to challenge yourself.

Here’s an example to help illustrate these steps:

Example: Use an input/output table to add \(5\) to each input value.

Step 1: Understand the Table This is an input/output table with the input values listed in the left column and the output values to be determined in the right column.

Step 2: Identify the Operation The operation is addition, so we will be adding \(5\) to each input value.

Step 3: Write the Expressions We can write the expressions for each row as:

\(-4 + 5 = output -2 + 5 = output 1 + 5 = output 6 + 5 = output\)

Step 4: Solve for the Unknown Solving for ‘\(n\)’ in each equation, we get:

\(-4 + 5 = 1, -2 + 5 = 3,1 + 5 = 6, 6 + 5 = 11\)

The Ultimate Algebra Bundle 2027 From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

So the completed table looks like this:

Step 5: Check Your Work We can plug in the input and ‘\(n\)’ values into each equation to verify that they produce the correct output value. For example:

\(-4 + 5 = 1\)

Step 6: Practice, Practice, Practice! Try creating your own input/output tables with different operations and input/output values to further practice your skills.

Using Input/output Tables to Add and Subtract Integers, Example 1

Find out the rule to complete the table.
Solution:
Start with the number in the In column.
Figure out the rule to know whether you have to subtract or add to give the value shown in the Out column.
\(10-…. =-4\)
\(10+4=14\)
So, \(5-14=-9, 0-14=-14, -5-14=-19\)
The rule is IN\(-14=\)Out

Using Input/output Tables to Add and Subtract Integers, Example 2

Find out the rule to complete the table.
Solution:
Start with the number in the In column.
Figure out the rule to know whether you have to subtract or add to give the value shown in the Out column.
\(-7+…. =-2\)
\(-7+(-2)=5\)
So, \(-4+5=1, -1+5=4, 1+5=6\)
The rule is IN\(+5=\)Out

Recommended EffortlessMath Books

For a workbook that builds input/output tables into broader function thinking, the Pre-Algebra for Beginners covers tables, patterns, and integer operations with worked examples. For early algebra coverage of functions and rules, the Algebra I for Beginners connects input/output tables to linear equations.

Frequently Asked Questions

How do you complete an input output table?

Find the rule, then apply it to every input. If the rule is “add −6,” an input of 4 gives 4 + (−6) = −2, and an input of −3 gives −3 + (−6) = −9. If the rule is not given, use a row that already has both numbers to work it out first. Then fill in each blank output and recheck the signs on negative integers.

How do you find the rule for input output tables?

Pick a row with both values and subtract: output − input. If the input is 5 and the output is 2, then 2 − 5 = −3, so the rule is “add −3” (or “subtract 3”). Test the rule on a second row before trusting it. If the difference is not the same in every row, the rule is not simple addition or subtraction, so try multiplication instead.

How do you read input output tables?

Read each row from left to right: the input goes into the rule and the output comes out. In a table with the rule “subtract −2,” the row 7 → 9 means 7 − (−2) = 9. Tables can also be written in two rows instead of two columns, with inputs on top. Either way, each input is matched with exactly one output.

How do you graph input output tables?

Turn each row into an ordered pair (input, output) and plot it on a coordinate plane, with the input on the x-axis. For the rule “add −4,” the rows 0 → −4, 2 → −2 and 5 → 1 give the points (0, −4), (2, −2) and (5, 1). For addition and subtraction rules, the points always fall on a straight line with a slope of 1.

How do you teach input output tables?

Begin with a “function machine” game: a student secretly picks a rule like “add 3,” classmates call out inputs, and everyone guesses the rule from the outputs. Once the idea is clear, add negative inputs and then negative rules such as “subtract −5.” Having students explain the rule in words before writing it with symbols builds both integer skills and early algebra thinking.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to apply integer addition and subtraction rules
• How to solve integer addition and subtraction word problems
• Order of operations (PEMDAS)
• How to solve linear equations
• How to find the slope of a line