Learn on PengiSaxon Math, Course 3Chapter 4: Algebra • Measurement

Lesson 33: Subtracting Integers

New Concept This course builds your math foundation step by step. You will master core skills and connect them, preparing you for all future math challenges. What’s next This card introduces the big picture. Now, we'll dive into our first specific skill: subtracting integers by transforming them into addition problems.

Section 1

📘 Subtracting Integers

New Concept

This course builds your math foundation step-by-step. You will master core skills and connect them, preparing you for all future math challenges.

What’s next

This card introduces the big picture. Now, we'll dive into our first specific skill: subtracting integers by transforming them into addition problems.

Section 2

Subtracting By Adding The Opposite

Property

Instead of subtracting a number, add its opposite.

Examples

(15)(5)=(15)+(+5)=10(-15) - (-5) = (-15) + (+5) = -10
9(+12)=9+(12)=39 - (+12) = 9 + (-12) = -3

Explanation

Why make subtraction hard? Just flip the sign of the number you are subtracting and turn the problem into simple addition! It’s the ultimate math uno reverse card, changing the game from subtraction to a friendly round of adding. Now you are an addition wizard!

Section 3

Adding With Same Signs

Property

To find the sum of addends with the same sign: 1. Add the absolute values of the addends. 2. Take the sign of the addends.

Examples

(7)+(6)=13(-7) + (-6) = -13
(+11)+(+4)=+15(+11) + (+4) = +15

Explanation

Think of it as teamwork! When two positives or two negatives get together, they join forces to make an even bigger number with the same sign. Everyone is on the same team here, so just add them up and keep their sign!

Section 4

Adding With Different Signs

Property

To find the sum of addends with different signs: 1. Subtract the absolute values of the addends. 2. Take the sign of the addend with the greater absolute value.

Examples

(18)+(+8)=10(-18) + (+8) = -10
(22)+(5)=17(22) + (-5) = 17

Explanation

This is an epic tug-of-war! Find the difference between the numbers' strengths. The stronger number, the one with the bigger absolute value, wins the battle and plants its sign on the final answer! May the biggest number win!

Section 5

Integers In Your Wallet

Property

Use positive integers for income, rebates, or deposits and negative integers for bills or withdrawals to calculate a final balance.

Examples

You start with 150 dollars, get a 30 dollars rebate, and pay a 100 dollars bill: 150+30100=80150 + 30 - 100 = 80 dollars.
With a 400 dollars balance, you deposit 50 dollars and withdraw 90 dollars: 400+50+(90)=360400 + 50 + (-90) = 360 dollars.

Explanation

Your bank account is a real-life number line! Getting paid is a positive jump, and paying bills is a negative one. Integer math helps you track your cash flow, so you always know if you have enough for that new video game.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Algebra • Measurement

  1. Lesson 1

    Lesson 31: Adding Integers and Collecting Like Terms

  2. Lesson 2

    Lesson 32: Probability

  3. Lesson 3Current

    Lesson 33: Subtracting Integers

  4. Lesson 4

    Lesson 34: Proportions and Ratio Word Problems

  5. Lesson 5

    Lesson 35: Similar and Congruent Polygons

  6. Lesson 6

    Lesson 36: Multiplying and Dividing Integers and Multiplying and Dividing Terms

  7. Lesson 7

    Lesson 37: Areas of Combined Polygons

  8. Lesson 8

    Lesson 38: Using Properties of Equality to Solve Equations

  9. Lesson 9

    Lesson 39: Circumference of a Circle

  10. Lesson 10

    Lesson 40: Area of a Circle

  11. Lesson 11

    Lesson 11: Investigation 4: Drawing Geometric Solids

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Subtracting Integers

New Concept

This course builds your math foundation step-by-step. You will master core skills and connect them, preparing you for all future math challenges.

What’s next

This card introduces the big picture. Now, we'll dive into our first specific skill: subtracting integers by transforming them into addition problems.

Section 2

Subtracting By Adding The Opposite

Property

Instead of subtracting a number, add its opposite.

Examples

(15)(5)=(15)+(+5)=10(-15) - (-5) = (-15) + (+5) = -10
9(+12)=9+(12)=39 - (+12) = 9 + (-12) = -3

Explanation

Why make subtraction hard? Just flip the sign of the number you are subtracting and turn the problem into simple addition! It’s the ultimate math uno reverse card, changing the game from subtraction to a friendly round of adding. Now you are an addition wizard!

Section 3

Adding With Same Signs

Property

To find the sum of addends with the same sign: 1. Add the absolute values of the addends. 2. Take the sign of the addends.

Examples

(7)+(6)=13(-7) + (-6) = -13
(+11)+(+4)=+15(+11) + (+4) = +15

Explanation

Think of it as teamwork! When two positives or two negatives get together, they join forces to make an even bigger number with the same sign. Everyone is on the same team here, so just add them up and keep their sign!

Section 4

Adding With Different Signs

Property

To find the sum of addends with different signs: 1. Subtract the absolute values of the addends. 2. Take the sign of the addend with the greater absolute value.

Examples

(18)+(+8)=10(-18) + (+8) = -10
(22)+(5)=17(22) + (-5) = 17

Explanation

This is an epic tug-of-war! Find the difference between the numbers' strengths. The stronger number, the one with the bigger absolute value, wins the battle and plants its sign on the final answer! May the biggest number win!

Section 5

Integers In Your Wallet

Property

Use positive integers for income, rebates, or deposits and negative integers for bills or withdrawals to calculate a final balance.

Examples

You start with 150 dollars, get a 30 dollars rebate, and pay a 100 dollars bill: 150+30100=80150 + 30 - 100 = 80 dollars.
With a 400 dollars balance, you deposit 50 dollars and withdraw 90 dollars: 400+50+(90)=360400 + 50 + (-90) = 360 dollars.

Explanation

Your bank account is a real-life number line! Getting paid is a positive jump, and paying bills is a negative one. Integer math helps you track your cash flow, so you always know if you have enough for that new video game.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Algebra • Measurement

  1. Lesson 1

    Lesson 31: Adding Integers and Collecting Like Terms

  2. Lesson 2

    Lesson 32: Probability

  3. Lesson 3Current

    Lesson 33: Subtracting Integers

  4. Lesson 4

    Lesson 34: Proportions and Ratio Word Problems

  5. Lesson 5

    Lesson 35: Similar and Congruent Polygons

  6. Lesson 6

    Lesson 36: Multiplying and Dividing Integers and Multiplying and Dividing Terms

  7. Lesson 7

    Lesson 37: Areas of Combined Polygons

  8. Lesson 8

    Lesson 38: Using Properties of Equality to Solve Equations

  9. Lesson 9

    Lesson 39: Circumference of a Circle

  10. Lesson 10

    Lesson 40: Area of a Circle

  11. Lesson 11

    Lesson 11: Investigation 4: Drawing Geometric Solids