- Key Concepts on Subtracting Signed Numbers
- Different forms of Subtracting Signed Numbers?
- How do you teach students to Subtract Signed Numbers?
- Step 1: Rewrite subtraction problem as addition
- Step 2: Determine the sign of the answer
- Step 3: Add the values
- Examples on Subtracting Signed Numbers
- Example 1: Subtracting different signed fractions
- Example 2: Subtracting one negative number and one positive number
- Example 3: Subtracting two positive numbers with the smaller number being the minuend.
- Why Teach Subtracting Signed Numbers this way?
- Vocabulary for teaching Subtracting signed numbers
- Misconceptions and Errors on Subtracting Signed Numbers
- Resources on Subtracting Signed Numbers:
- Frequently asked questions on teaching Subtracting Signed Numbers
Key Concepts on Subtracting Signed Numbers
It is important for students to learn how to subtract signed numbers so that they are familiar and prepared to simplify expressions with signed numbers and variables. Students can subtract signed numbers by rewriting the subtraction equation with addition.
Different forms of Subtracting Signed Numbers?
There are a few different forms of subtracting signed number problems.
- Two positive numbers with the smaller value being the minuend.
- 62 – 85
- Two negative numbers
- -32 – (-5)
- One negative number and one positive number
- 4 – (-7)
- -15 – 13
How do you teach students to Subtract Signed Numbers?
Using
Step 1: Rewrite subtraction problem as addition
Have students rewrite each subtraction expression with addition. Remind students that subtracting a negative is the same as adding a positive and subtracting a positive is the same as adding a negative.
What is -32 – (-5) rewritten with addition?
-32 + 5
Step 2: Determine the sign of the answer
Have students determine the sign of the rewritten addition expression. Remind students that if the signs of the rewritten addition problem are different AND if the one with the larger absolute value is negative, the final sign will be negative.
If the signs of the rewritten addition problem are different AND if the one with the larger absolute value is positive, the final sign will be positive. If the signs of the rewritten addition problem are both negative, the final sign will be negative.
In the expression -32 + 5, the signs of the rewritten addition problem are different, and the value with the larger absolute value is negative, so the final sign will be negative.
Step 3: Add the values
Have the student add the values. Since -32 and 5 have different signs, we should do 32 – 5. Remember to always write the number with the greater absolute value first.
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32 – 5 = 17
Remember, the final answer will be negative.
-17
Examples on Subtracting Signed Numbers
Example 1: Subtracting different signed fractions
Example 2: Subtracting one negative number and one positive number
What is 4 – (-7) = ?
Example 3: Subtracting two positive numbers with the smaller number being the minuend.
What is 62 – 85 = ?
Why Teach Subtracting Signed Numbers this way?
Subtracting signed numbers is useful for students to build their fluency for future skills including simplifying expressions and solving equations.
Vocabulary for teaching Subtracting signed numbers
Absolute Value: The distance a number is away from zero on a number line. Absolute value is always positive.
Negative: Any number to the left of zero (0) on the number line.
Positive: Any number to the right of zero (0) on the number line.
Misconceptions and Errors on Subtracting Signed Numbers
- Students may choose the wrong sign for the final answer.
- Rewrite expression incorrectly
- Students may choose the wrong operation once they find the absolute values of both numbers.
Resources on Subtracting Signed Numbers:
Downloadable worksheets for subtracting signed numbers
Quiz for assessing subtracting signed numbers
Frequently asked questions on teaching Subtracting Signed Numbers
What is the rule for subtracting signed numbers?
->Rewrite as an addition expression.
->If both numbers have the same sign: Add their absolute values and keep the same sign.
->If the numbers have different signs. Subtract their absolute values, then take the sign of the number with the greater absolute value.
How do you subtract numbers that have the same sign?
First, rewrite the subtraction expression with addition. If the numbers are both negative: Add their absolute values, then make your answer negative.
If the numbers are both positive: Add their absolute values, then make your answer positive.
How do you subtract numbers that have different signs?
First, rewrite the subtraction expression with addition. Then subtract their absolute values, then take the sign of the number with the greater absolute value.
How do you subtract positive and negative fractions?
->Rewrite subtraction expression with addition.
->Rewrite the fraction with a common denominator.
->If both numbers have the same sign: Add the absolute values of the numerator and keep the same sign.
->If the numbers have different signs. Subtract the absolute values of the numerator, then take the sign of the number with the greater absolute value.
->Keep the denominator the same.
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