2. Show the following operations on a number line and simplify:
a. $(+3)+(+2)$
b. $(+6)+(-3)$
c. $(-7)+(+4)$
d. $(-5)+(-4)$
e. $(+6)-(+1)$
f. $(-5)-(-8)$
g. $(-4)-(-2)$
3. On a number line, if you start at +2 where do you land after a shift of
a. +3
b. +5
c. +1
d. -6
e. -2
f. -4
4. On a number line, if you start at -5 where do you land after a shift of
a. +1
b. +8
c. +4
d. -4
e. -3
f. -6
5. Simplify:
a. $(+8)+(+2)+(+3)$
b. $(+6)+(-3)+(+4)$
c. $(-8)+(+5)+(-4)$
d. $(-11)-(-9)+(+5)$
e. $(-10)-(-6)+(-7)$
f. $(+21)-(+18)-(-15)$
g. $(-35)+(+24)+(+10)$
h. $(-16)+(+50)+(-24)$
i. $(-18)-(-19)+(-4)-(+8)$
j. $(-13)+(+7)-8+14-50
Answer (1)
Perform addition and subtraction on a number line for question 2.
Determine the final position after shifts on a number line for questions 3 and 4.
Simplify arithmetic expressions involving positive and negative numbers for question 5.
The final answers are: 2. a. +5, b. +3, c. -3, d. -9, e. +5, f. +3, g. -2; 3. a. +5, b. +7, c. +3, d. -4, e. 0, f. -2; 4. a. -4, b. +3, c. -1, d. -9, e. -8, f. -11; 5. a. 13, b. 7, c. -7, d. 3, e. -11, f. 18, g. -1, h. 10, i. -11, j. -50.
Explanation
Introduction We will solve each question step by step, showing the operations on a number line where applicable and simplifying the expressions.
Question 2 Solution
Show the following operations on a number line and simplify: a. ( + 3 ) + ( + 2 ) : Start at +3 and move 2 units to the right. The result is +5. b. ( + 6 ) + ( − 3 ) : Start at +6 and move 3 units to the left. The result is +3. c. ( − 7 ) + ( + 4 ) : Start at -7 and move 4 units to the right. The result is -3. d. ( − 5 ) + ( − 4 ) : Start at -5 and move 4 units to the left. The result is -9. e. ( + 6 ) − ( + 1 ) : This is the same as ( + 6 ) + ( − 1 ) . Start at +6 and move 1 unit to the left. The result is +5. f. ( − 5 ) − ( − 8 ) : This is the same as ( − 5 ) + ( + 8 ) . Start at -5 and move 8 units to the right. The result is +3. g. ( − 4 ) − ( − 2 ) : This is the same as ( − 4 ) + ( + 2 ) . Start at -4 and move 2 units to the right. The result is -2.
Question 3 Solution
On a number line, if you start at +2 where do you land after a shift of: a. +3: Start at +2 and move 3 units to the right. The result is +5. b. +5: Start at +2 and move 5 units to the right. The result is +7. c. +1: Start at +2 and move 1 unit to the right. The result is +3. d. -6: Start at +2 and move 6 units to the left. The result is -4. e. -2: Start at +2 and move 2 units to the left. The result is 0. f. -4: Start at +2 and move 4 units to the left. The result is -2.
Question 4 Solution
On a number line, if you start at -5 where do you land after a shift of: a. +1: Start at -5 and move 1 unit to the right. The result is -4. b. +8: Start at -5 and move 8 units to the right. The result is +3. c. +4: Start at -5 and move 4 units to the right. The result is -1. d. -4: Start at -5 and move 4 units to the left. The result is -9. e. -3: Start at -5 and move 3 units to the left. The result is -8. f. -6: Start at -5 and move 6 units to the left. The result is -11.
Question 5 Solution
Simplify: a. ( + 8 ) + ( + 2 ) + ( + 3 ) = 8 + 2 + 3 = 13 b. ( + 6 ) + ( − 3 ) + ( + 4 ) = 6 − 3 + 4 = 7 c. ( − 8 ) + ( + 5 ) + ( − 4 ) = − 8 + 5 − 4 = − 7 d. ( − 11 ) − ( − 9 ) + ( + 5 ) = − 11 + 9 + 5 = 3 e. ( − 10 ) − ( − 6 ) + ( − 7 ) = − 10 + 6 − 7 = − 11 f. ( + 21 ) − ( + 18 ) − ( − 15 ) = 21 − 18 + 15 = 18 g. ( − 35 ) + ( + 24 ) + ( + 10 ) = − 35 + 24 + 10 = − 1 h. ( − 16 ) + ( + 50 ) + ( − 24 ) = − 16 + 50 − 24 = 10 i. ( − 18 ) − ( − 19 ) + ( − 4 ) − ( + 8 ) = − 18 + 19 − 4 − 8 = − 11 j. $(-13)+(+7)-8+14-50 = -13 + 7 - 8 + 14 - 50 = -50
Final Answer The solutions to the given problems are:
a. +5, b. +3, c. -3, d. -9, e. +5, f. +3, g. -2
a. +5, b. +7, c. +3, d. -4, e. 0, f. -2
a. -4, b. +3, c. -1, d. -9, e. -8, f. -11
a. 13, b. 7, c. -7, d. 3, e. -11, f. 18, g. -1, h. 10, i. -11, j. -50
Examples
Understanding operations with positive and negative numbers is crucial in many real-life situations. For instance, managing finances involves dealing with credits (positive numbers) and debts (negative numbers). If you have $50 in your account and spend $30, then receive $20, the expression (+50) - (+30) + (+20) = 40 shows you have $40 left. Similarly, in temperature calculations, understanding positive and negative values helps determine changes in temperature, such as a drop of 10 degrees followed by a rise of 5 degrees: (-10) + (+5) = -5, indicating a net decrease of 5 degrees.
