3.2: Addition and Subtraction

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Amy Lagusker
College of the Canyons

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The Three Methods of Subtraction

Example $\PageIndex{1}$

The Three methods:

Missing Addends
1. Represent with an algebraic equation
2. Example: “Mary has seven bananas, but she needs ten. How many more bananas does she need to purchase?”
3. 7+x=10 →x=3
Take-Away
1. Straight forward subtraction
2. Example: “Jennifer has ten oranges. She sold three of them. How many oranges does she have left?”
3. 10-3=7
Comparison
1. Comparing Separate Quantities
2. Example: “Cory has ten oranges and seven bananas. How many more oranges does Cory have than bananas?”
3. 10-7=3

Partner Activity 1

By yourself, solve 354-89, any way you like. Then compare and contrast your method to your partner’s method. Be prepared to share your method with the class.

Partner Activity 2

Consider the work of nine 2nd graders, all solving 354-89, just like you did a minute ago. Grade each student, as if you were their teacher, using a scale from 1 – 5, 5 being the best. Having the correct answer is only one point out of five. The other four points come from the students’ procedure and thoughts. Remember, even if you do not understand HOW they arrived at their correct answer, does not make their procedure incorrect.

Example $\PageIndex{2}$

Here is a real-life example of needing to subtract, but actually using addition:

Lance buys some supplies totaling $7.32. He hands the cashier a ten-dollar bill. His change is $2.68.

Solution

Instead of subtracting 10 – 7.32, the cashier will count UP:

“$7.32 + $1 + $1 + 25¢ + 25¢ + 10¢ + 5¢ + 1¢ + 1¢ + 1¢ = $10.00”

Example $\PageIndex{3}$

Subtract 342 – 186 = 156 using a number line and count UP.

Solution

Why are the above examples in the Mental Math section of this textbook? Because doing these problems on paper enough times will train your brain to subtract with mental math and without borrowing.

Partner Activity 3

Subtract the following problems using the methods from either Example 2 or Example 3 above.

753 – 345 = ________
421 – 175 = ________

Practice Problems

Explain how to solve the following problems using mental math:

56 + 81
1000 – 284
94 + 801
762 – 451