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Mastering Adding and Subtracting Integers: Word Problems Worksheet with Answers
Understanding how to add and subtract integers is a fundamental skill in mathematics, essential for solving real-world problems. This comprehensive guide will help you master these concepts through engaging word problems and provide a worksheet with answers to reinforce your learning.
#### Why Learn About Adding and Subtracting Integers?
Integers are whole numbers that can be positive, negative, or zero. They are used in various real-life scenarios, such as calculating temperatures, financial transactions, and elevations. Learning to add and subtract integers helps students develop critical thinking and problem-solving skills.
#### Key Concepts in Adding and Subtracting Integers
1. **Positive and Negative Numbers**: Positive numbers are greater than zero, while negative numbers are less than zero. Zero is neutral.
2. **Addition of Integers**:
- **Same Sign**: Add the absolute values and keep the common sign.
- **Different Signs**: Subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
3. **Subtraction of Integers**: Subtracting an integer is the same as adding its opposite. For example, \(5 - (-3)\) is the same as \(5 + 3\).
#### Practical Applications of Adding and Subtracting Integers
1. **Temperature Changes**: Calculating the difference in temperatures over time.
2. **Financial Transactions**: Managing credits and debits in bank accounts.
3. **Elevation Levels**: Determining the difference in heights between two points.
#### Sample Word Problems
1. **Temperature Change**:
- Problem: The temperature was \(10^\circ C\) in the morning. By evening, it dropped by \(15^\circ C\). What is the temperature in the evening?
- Solution: \(10 + (-15) = -5^\circ C\)
2. **Financial Transaction**:
- Problem: Sarah has \$50 in her bank account. She withdraws \$70. What is her account balance?
- Solution: \(50 - 70 = -20\)
3. **Elevation Difference**:
- Problem: A submarine is at \(200\) feet below sea level. It ascends \(150\) feet. What is its new position?
- Solution: \(-200 + 150 = -50\) feet
#### Worksheet: Adding and Subtracting Integers Word Problems
**Instructions**: Solve the following word problems. Show your work and write the final answer.
1. **Temperature Drop**:
- Problem: The temperature was \(25^\circ C\) in the afternoon. By night, it dropped by \(30^\circ C\). What is the temperature at night?
- Solution: \(25 + (-30) = -5^\circ C\)
2. **Bank Account Balance**:
- Problem: John has \$100 in his bank account. He writes a check for \$150. What is his new balance?
- Solution: \(100 - 150 = -50\)
3. **Mountain Climb**:
- Problem: A hiker is at \(500\) meters above sea level. He descends \(600\) meters. What is his new elevation?
- Solution: \(500 + (-600) = -100\) meters
4. **Football Yardage**:
- Problem: A football team gains \(20\) yards on one play and loses \(35\) yards on the next. What is the net yardage?
- Solution: \(20 + (-35) = -15\) yards
5. **Debt Calculation**:
- Problem: Maria owes \$40 to her friend. She borrows another \$60. What is her total debt?
- Solution: \(-40 + (-60) = -100\)
6. **Temperature Increase**:
- Problem: The temperature was \(-10^\circ C\) in the morning. By noon, it increased by \(15^\circ C\). What is the temperature at noon?
- Solution: \(-10 + 15 = 5^\circ C\)
7. **Elevation Change**:
- Problem: A diver is \(50\) feet below sea level. He dives another \(30\) feet deeper. What is his new depth?
- Solution: \(-50 + (-30) = -80\) feet
8. **Profit and Loss**:
- Problem: A shopkeeper made a profit of \$200 on Monday and a loss of \$250 on Tuesday. What is the net profit or loss?
- Solution: \(200 + (-250) = -50\)
9. **Temperature Fluctuation**:
- Problem: The temperature was \(5^\circ C\) in the morning. It dropped by \(8^\circ C\) and then rose by \(3^\circ C\). What is the final temperature?
- Solution: \(5 + (-8) + 3 = 0^\circ C\)
10. **Bank Withdrawal**:
- Problem: Alex has \$300 in his bank account. He withdraws \$450. What is his new balance?
- Solution: \(300 - 450 = -150\)
#### Answer Key
1. \(-5^\circ C\)
2. \(-50\)
3. \(-100\) meters
4. \(-15\) yards
5. \(-100\)
6. \(5^\circ C\)
7. \(-80\) feet
8. \(-50\)
9. \(0^\circ C\)
10. \(-150\)
#### Conclusion
Mastering the addition and subtraction of integers through word problems is crucial for developing mathematical proficiency. By practicing these problems, students can enhance their problem-solving skills and apply mathematical concepts to real-world situations. Use the provided worksheet to test your understanding and check your answers to ensure accuracy.
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Number Patterns can be used to illustrate addition and subtraction rules for integers. • Patterns P and Q confirm that adding a negative number has the same effect as subtracting a natural …
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12. The numbers in this sequence increase by the same amount each time 13. Dani drives 4.8 miles to Bristol and then further 6.7 miles to Bath.
MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW
Integers Review 1.1 Integer Operations: Patterns fdfdsfs MathLinks: Grade 8 (Student Packet 1) 1 INTEGER OPERATIONS: PATTERNS Summary (Ready) We will use patterns to revisit the …
Mathematics (Linear) 1MA0 ADDITION AND SUBTRACTION
Check your answers if you have time at the end. 1. There were 34 coins in a bag. Jim took 15 coins out of the bag. Rose put 17 coins into the bag. How many coins are now in the bag? .....
Adding and subtracting rational numbers word problems …
Adding and subtracting rational numbers word problems worksheet pdf These free equations and word problems worksheets will help your students to practice writing and solve equations that …
I. Model Problems. II. Practice III. Challenge Problems IV.
I. Model Problems In these examples you will combine like terms. Example 1: Simplify . First change subtraction to add the opposite. Next group like terms. Add the coefficients of the like …
Adding Integers - Practice Problems - BHNmath
6) a) Sonu claims that adding two positive integers always results in a positive integer. Is Sonu’s claim correct? Explain. b) Addy stated that adding two negative integers can result in a …
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Practice Workbook - McGraw Hill Education
TO THE STUDENTThis Practice Workbook gives you additional examples and problems ... 1-4 Adding Integers ... 1-5 Subtracting Integers .....5 1-6 Multiplying and Dividing Integers .....6 1-7 …
Subtraction of integers - K5 Learning
Grade 6 Integers Worksheet - Subtraction of integers Author: K5 Learning Subject: Grade 6 Integers Worksheet Keywords: Grade 6 Integers Worksheet - Subtraction of integers math …
Adding and Subtracting Decimals Word Problems …
Adding and Subtracting Decimals Word Problems Homework Read each word problem carefully. Show all your work and answer in a complete sentence. 1. You spend $6.50 on a pair of …
DECIMALS PRACTICE BOOKLET TABLE OF CONTENTS
Word form is writing the decimals in words, such as three and fifty-two hundredths. EXAMPLE A: Name the place value of the underlined digit. 14.234 3 is in the hundredths place value …
Grade 6 Integers Worksheet - Addition of Integers (-10 to …
Title: Grade 6 Integers Worksheet - Addition of Integers (-10 to +10) Author: K5 Learning Subject: Grade 6 Integers Worksheet Keywords: Grade 6 Integers Worksheet - Addition of Integers ( …
Adding And Subtracting Integers Word Problems [PDF]
Adding And Subtracting Integers Word Problems Adding And Subtracting Integers Word Problems Deborah Ann Carey Subtraction and Addition Rebecca Wingard-Nelson,2014-01-01 Readers …
Adding and Subtracting Positive and Negative Numbers …
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Adding and subtracting scientific notation word problems worksheet answers Advertisement Advertisement Advertisement Fifth-grade math students may have memorized multiplication …
Adding and subtracting fractions - K5 Learning
Adding and subtracting fractions Grade 4 Word Problems Worksheet Mr. Bobbins manages an acre of mango farm. The mango farm has been open to visitors for a week. 1. Mr. Bobbins …
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Adding and Subtracting Positive and Negative Numbers Date_____ Period____ Evaluate each expression. 1) (−2) + 3 2) (−14) + (−7) 3) 3 − ... 0 j xAnlmln Yr3i bggh mt4s L nrge UsUeCr Cv …
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Addition and Subtraction Workbook - Bromley Educational Trust
column with no carrying answers Adding two 3 digit numbers in a column with carrying answers worksheet Subtracting 3 digit numbers from 3 digit numbers in a column with no ... Addition …
York Region District School Board
Worksheet Booklet The following worksheets are designed to help students practice and review key concepts and ... Adding and Subtracting Mixed Fractions (A) Find the value of each …
Adding and Subtracting Integers Worksheets 7th Grade
WWW.CUEMATH.COM • An integer can be negative, zero or positive. • A number if expressed in a fractional form is not an integer. • There are infinite real numbers between any two integers. …
Adding and subtracting fractions - K5 Learning
Answers 1. 51 7 −25 7 =23 7 There were 23 7 boxes of nails left in his toolbox. 2. 21 4 +31 4 =52 4 ... Adding and subtracting fractions word problems worksheet Author: K5 Learning Subject: …
Adding And Subtracting Integers Practice Worksheet
2. Effective Design of an Adding and Subtracting Integers Practice Worksheet The effectiveness of an "adding and subtracting integers practice worksheet" is not merely a matter of including …
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Adding And Subtracting Integers Word Problems …
Adding And Subtracting Integers Word Problems Worksheet: ... effective Word problems are included with each day to promote higher level thinking and answers are listed in the back of …
