This cheat sheet explains how to subtract integers using the Keep Change Change memory aid. It helps students turn every subtraction problem into an addition problem, which is usually easier to solve. Students in grades 6-8 need this skill for number sense, equations, coordinate grids, and later algebra.
The layout is designed as a calm printable reference with clear sections for the rule, number line meaning, and practice patterns.
The main idea is that subtracting an integer means adding its opposite, so . Keep the first number, change subtraction to addition, and change the sign of the second number. After rewriting, use integer addition rules, such as adding two negatives or finding the difference of opposite signs.
A number line can show why subtracting a positive moves left and subtracting a negative moves right.
Key Facts
- Keep Change Change means keep the first integer, change to , and change the second integer to its opposite.
- The main subtraction rule is .
- Subtracting a positive integer moves left on the number line, such as .
- Subtracting a negative integer moves right on the number line, such as .
- When adding integers with the same sign, add the absolute values and keep the common sign, such as .
- When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
- The opposite of is , and the opposite of is .
- A double negative in subtraction becomes addition, so .
Vocabulary
- Integer
- An integer is a whole number, its opposite, or zero, such as , , or .
- Opposite
- The opposite of a number is the number the same distance from on the other side of the number line.
- Additive inverse
- An additive inverse is a number that adds with another number to make , such as .
- Absolute value
- Absolute value is the distance a number is from , written as .
- Number line
- A number line is a visual model that shows numbers in order from left to right.
- Keep Change Change
- Keep Change Change is a memory aid for rewriting subtraction as addition of the opposite.
Common Mistakes to Avoid
- Changing both numbers is wrong because Keep Change Change only changes the operation and the second number. For example, becomes , not .
- Forgetting to change the subtraction sign is wrong because the problem has not been rewritten as addition. For example, should become .
- Treating as is wrong because subtracting a negative means adding the opposite. The correct rewrite is .
- Ignoring the sign with the larger absolute value is wrong when adding integers with different signs. For example, because is larger than .
- Reading the number line direction backward is wrong because subtracting a positive moves left and subtracting a negative moves right. For example, moves spaces left to .
Practice Questions
- 1 Use Keep Change Change to solve .
- 2 Rewrite and solve .
- 3 Evaluate and explain which direction you would move on a number line.
- 4 Explain why subtracting a negative integer gives the same result as adding a positive integer.
Understanding How to subtract integers (Keep Change Change) Memory Aid
A useful way to understand integer subtraction is to think about undoing rather than memorizing marks. Addition and subtraction are inverse operations. Adding a number and then adding its opposite brings the total back to zero.
For example, positive six paired with negative six has no net value. This cancellation idea explains why an opposite is needed when a quantity is being removed.
The changed sign is not a random trick. It represents the number that reverses the effect of the number being subtracted.
Parentheses matter because they show that a negative sign belongs to the second integer. In an expression such as negative two minus negative seven, the first negative describes the starting value. The subtraction sign tells what operation to perform.
The second negative describes the number being removed. These jobs are different. Students often lose track by reading two nearby signs as one symbol.
Rewrite one sign at a time, then pause before calculating. A clean rewrite makes errors easier to spot and prevents a negative value from disappearing.
This skill appears in situations involving change from a starting amount. Temperature can begin below zero and then change. Bank balances can include money owed.
Elevation can be measured above or below sea level. A football team can lose yards, then compare that loss with another result. Coordinate grids use negative positions to show locations left of the vertical axis or below the horizontal axis.
In each setting, subtraction compares values or removes a change. The result may be positive even when negative numbers appear, because removing a loss increases the total.
Checking is especially important when the signs look confusing. Use estimation first. If a negative amount is removed, expect the answer to be greater than the starting amount.
If a positive amount is removed, expect it to be less. You can then check by adding the subtracted integer back to the answer. If the original starting number returns, the calculation is consistent.
Number lines help at first, but they should support reasoning rather than replace it. Practice should include positive and negative starting values, zero, parentheses, and word problems. The goal is to recognize the structure of the expression and explain why the answer has its sign.