Rational Numbers Subtracting Integers To subtract an integer, add its additive inverse. SUBTRACTING RATIONAL NUMBERS

RATIONAL NUMBERS~

SUBTRACTING RATIONAL NUMBERS

Rational Numbers

Subtracting IntegersTo subtract an integer, add its additive inverse.


Subtracting a smaller number from a larger number is the same as finding how far apart the two numbers are on a number line. Subtracting an integer is the same as adding its opposite.

How do I subtract Integers? Words Numbers Algebra

Change the subtraction sign to an addition

sign and change the sign of the

second number.

2 – 3 = 2 + (–3)4 – (–5) = 4 + 5

a – b = a + (–b)a – (–b) = a + b


Rules:

1. Change the SUBTRACTION sign to an ADDITION sign.

2. Change the sign of the SECOND addend to its OPPOSITE sign.

3. This is now an addition problem! Follow the rules for adding integers!


A. –7 – 4

–7 – 4 = –7 + (–4)

B. 8 – (–5)

8 – (–5) = 8 + 5

C. –6 – (–3)

–6 – (–3) = –6 + 3

= –11

= 13

= –3

Add the opposite of 4.

Add the opposite of –5.


Same sign; use the sign of the integers.


6 > 3; use the sign of 6.

Subtract.


Your Turn!

A. 3 – (–6)

3 – (–6) = 3 + 6

B. –4 – 1

–4 – 1 = –4 + (–1)

C. –7 – (–8)

–7 – (–8) = –7 + 8

= 9

= –5

= 1


Add the opposite of 1.


Same signs; use the sign of the integers.



Subtract.


A. 8 – j for j = –6

8 – j

8 – (–6) Substitute –6 for j.

Evaluate the expression for the given value of the variable.

= 8 + 6

= 14




B. –9 – y for y = –4

= –9 + 4

= –5


–9 – y

–9 – (–4) Substitute –4 for y.




A. 11 – m for m = –3

11 – m

11 – (–3) Substitute –3 for m.


= 11 + 3

= 14



Your Turn!


B. –5 – r for r = –2

= –5 + 2

= –3


–5 – r

–5 – (–2) Substitute –2 for r.



Your Turn!


The top of the Sears Tower in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top?

Architecture Application

1454 – (–43) Subtract the lowest level from the height.

1454 + 43 Add the opposite of (–43).

= 1497 Same sign; use the sign of the integers.

It is 1497 feet from the lowest level to the top.


The distance from the high dive to the swimming pool is 25 feet. The pool is 14 feet deep. What is the total distance from the high dive to the bottom of the pool?

Your Turn!

25 – (–14) Subtract the depth of the pool from the height of the high dive.

25 + 14 Add the opposite of (–14).

= 39 Same sign; use the sign of the integers.

It is 39 feet from the diving board to the bottom of the pool.


ExampleSolve each equation.a. n = 6 – (-4)



n = 6 – (-4) To subtract –4, add 4



n = 6 – (-4) To subtract –4, add 4n = 6 + 4



n = 6 – (-4) To subtract –4, add 4n = 6 + 4n = 10


ExampleSolve each equation.b. (-3) – (-7) = y



(-3) – (-7) = y To subtract –7, add 7



(-3) – (-7) = y To subtract –7, add 7 (-3) + 7 = y



(-3) – (-7) = y To subtract –7, add 7 (-3) + 7 = y 4 = y


STUDENT ACTIVITY

You will now receive a worksheet. Turn the worksheet in when completed.

Do Not DisturbWork In Progress

Documents

Rational Numbers Subtracting Integers To subtract an integer, add its additive inverse. SUBTRACTING RATIONAL NUMBERS