Question

self test
integers: perform indicated operation.
1.) $-6 + -7 =$
2.) $-4 + 1 =$
3.) $3 + -2 =$
4.) $-8 + 5 =$
5.) $6 - 11 =$
6.) $8 - (-10) =$
7.) $-9 - 3 =$
8.) $-5 - (-6) =$
9.) $-8( 3) =$
10.) $(-3)(-8) =$
11.) $9(-7) =$
12.) $-81 \div 9 =$
13.) $-12 \div -12 =$
14.) $\frac{48}{-6} =$
15.) $\frac{-27}{-9} =$
plot each point and label by letter.
16.) a $(-4, 2)$
17.) b $(5,0)$
18.) c $(1, -3)$
19.) d $(0, -4)$
20.) a _______
21.) b _______
22.) c _______
23.) d _______

Explanation:

Step1: Solve -6 + -7

When adding two negative numbers, we add their absolute values and keep the negative sign. So, \(|-6| + |-7| = 6 + 7 = 13\), and since both are negative, the result is \(-13\).

Step2: Solve -4 + 1

When adding a negative and a positive number, we subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value. \(|-4| = 4\), \(|1| = 1\), \(4 - 1 = 3\), and since -4 has the larger absolute value, the result is \(-3\).

Step3: Solve 3 + -2

Subtract the absolute values: \(|3| - |-2| = 3 - 2 = 1\). The positive number has the larger absolute value, so the result is \(1\).

Step4: Solve -8 + 5

Subtract the absolute values: \(|-8| - |5| = 8 - 5 = 3\). The negative number has the larger absolute value, so the result is \(-3\).

Step5: Solve 6 - 11

Rewrite as \(6 + (-11)\). Then, \(|-11| - |6| = 11 - 6 = 5\), and since -11 has the larger absolute value, the result is \(-5\).

Step6: Solve 8 - (-10)

Subtracting a negative is like adding the positive, so \(8 + 10 = 18\).

Step7: Solve -9 - 3

Rewrite as \(-9 + (-3)\). Add the absolute values: \(9 + 3 = 12\), so the result is \(-12\).

Step8: Solve -5 - (-6)

Subtracting a negative is adding the positive: \(-5 + 6 = 1\) (since \(6 - 5 = 1\) and 6 is positive).

Step9: Solve -8(3)

Multiply the absolute values: \(8 \times 3 = 24\), and since one number is negative, the result is \(-24\).

Step10: Solve (-3)(-8)

Multiply the absolute values: \(3 \times 8 = 24\), and since both are negative, the result is \(24\) (negative times negative is positive).

Step11: Solve 9(-7)

Multiply the absolute values: \(9 \times 7 = 63\), and since one number is negative, the result is \(-63\).

Step12: Solve -81 ÷ 9

Divide the absolute values: \(81 \div 9 = 9\), and since the dividend is negative, the result is \(-9\).

Step13: Solve -12 ÷ -12

Divide the absolute values: \(12 \div 12 = 1\), and since both are negative, the result is \(1\) (negative divided by negative is positive).

Step14: Solve \(\frac{48}{-6}\)

Divide the absolute values: \(48 \div 6 = 8\), and since the denominator is negative, the result is \(-8\).

Step15: Solve \(\frac{-27}{-9}\)

Divide the absolute values: \(27 \div 9 = 3\), and since both are negative, the result is \(3\) (negative divided by negative is positive).

Step16: Plot A(-4, 2)

Move 4 units left on the x - axis (since x = -4) and 2 units up on the y - axis (since y = 2) and mark the point as A.

Step17: Plot B(5, 0)

Move 5 units right on the x - axis (x = 5) and 0 units on the y - axis (y = 0, which is on the x - axis) and mark the point as B.

Step18: Plot C(1, -3)

Move 1 unit right on the x - axis (x = 1) and 3 units down on the y - axis (y = -3) and mark the point as C.

Step19: Plot D(0, -4)

Move 0 units on the x - axis (x = 0, which is the y - axis) and 4 units down on the y - axis (y = -4) and mark the point as D.

Step20: Find coordinates of A in the second graph

Looking at the second graph, point A is at (2, 1) (2 units right on x, 1 unit up on y).

Step21: Find coordinates of B in the second graph

Point B is at (-1, 2) (-1 unit left on x, 2 units up on y).

Step22: Find coordinates of C in the second graph

Point C is at (-2, 0) (-2 units left on x, 0 units on y).

Step23: Find coordinates of D in the second graph

Point D is at (1, -1) (1 unit right on x, 1 unit down on y).

Answer:

1. \(-13\)
2. \(-3\)
3. \(1\)
4. \(-3\)
5. \(-5\)
6. \(18\)
7. \(-12\)
8. \(1\)
9. \(-24\)
10. \(24\)
11. \(-63\)
12. \(-9\)
13. \(1\)
14. \(-8\)
15. \(3\)
16. (Plot as described)
17. (Plot as described)
18. (Plot as described)
19. (Plot as described)
20. \((2, 1)\)
21. \((-1, 2)\)
22. \((-2, 0)\)
23. \((1, -1)\)