Core Focus on Rational Numbers & Equations Subtracting Rational Numbers Lesson 3.3.

Core Focus onRational Numbers & Equations

Subtracting Rational Numbers

Lesson 3.3

Warm-UpFind the value of each expression.

1. −3 − 4

2. 10 − (−5)

3. −235 − 110

4. 45.2 − 8.3

5. 32

31 15

23

3

–7

15

–345

–36.9

Subtracting Rational Numbers

Subtract positive and negative fractions and decimals.

Lesson 3.3

Subtracting Positive and Negative

Numbers

1. Turn the subtraction symbol into an addition symbol by adding the opposite.

2. Follow the rules for adding fractions and decimals to determine the sum.

Explore! What’s the Difference?

Find the difference in each situation.

Step 1 Yoko had $34.86 in her checking account. She wrote a check that left her with a balance of −$12.89. Find the value of the check she wrote.

Step 2 The neighborhood bank was offering savings accounts in January that earn interest. In February, the interest rate dropped to . What number represents the interest rate change from January to February?

Step 3 Margaret found out that the lowest temperature ever recorded in Vermont was −50.1° F. The highest temperature ever recorded in Vermont is 105.1° F. What is the difference between these two temperatures?

%3 52 %2 10

9

Explore! What’s the Difference?

Step 5 What would you consider the most important thing to remember when adding positive and negative fractions or decimals? Why?

Step 4 R.J. dove into the ocean and reached an elevation of feet (the distance below sea level). On his second dive, he reached an elevation of feet. What was the difference between his two dives?

2126

4331

Example 1Find the value of .

Change the subtraction symbol to an addition symbol by adding the opposite

Convert each mixed number to an improper fraction

Create equivalent fractions using the least common denominator of 6.

Rewrite the expression with equivalent fractions.

Add the numerators.

Simplify

21

31 26

1 13 2

1 16 2 6 2

3 2

1 13 2

19 56 2

3 2

19 38 5 15

3 6 2 6

38 15

6 6

51 13 2 66 2 8

5

6

538

6

38 ( 15) 53

6 6

Example 2Bromine has a boiling point of 58.8º C and a melting point of –7.2º C. What is the difference between the boiling point and the melting point?

Write the expression to represent the situation:

Add the opposite:

Add by lining up the decimals.

The difference between the boiling point and melting point of Bromine is 66º C.

0.66

2.7

8.58

58.8 – (–7.2)

58.8 + 7.2

Communication PromptScience and math are related in many ways. What is one way you have observed that math and science overlap?

Exit ProblemsFind each difference.

1. 18.7 − (−2.8)

2.

3.

8

3

4

3

61

32 13

21.5

1

81

1

22