Solve the following number patterns, comparisons, and integer addition problems.

Here are the solutions to the questions.

Question 1

• 1.1 Fill in the missing values of the following number patterns.

  • 1.1.1 The pattern is adding 4 to the previous number. $$-28; \mathbf{-24}; -20; -16; \mathbf{-12}$$
  • 1.1.2 The pattern is subtracting 12 from the previous number. $$24; 12; 0; \mathbf{-12}; \mathbf{-24}; \mathbf{-36}$$
  • 1.1.3 The differences are 11 (from $-36$ to $-25$) and 9 (from $-25$ to $-16$). The difference decreases by 2 each time. So the next difference is 7. $$-36; -25; -16; \mathbf{-9}$$

• 1.2 Write the correct sign between the numbers: greater than, less than or = equal to.

  • 1.2.1 $-9 = - \frac{9}{1}$
  • 1.2.2 $-30 < 30$
  • 1.2.3 $-100 < 101$
  • 1.2.4 $-26 < 62$

• 1.3 Arrange these numbers in ascending order: $300; -320; 302; -300; -302; 320$.

  $$-320; -302; -300; 300; 302; 320$$

• 1.4 Arrange these numbers in descending order: $-15; -51; 0; -115; 15; 51$.

  $$51; 15; 0; -15; -51; -115$$

Question 2
Add the integers without using a calculator.

• 2.1 $$(-15) + (-6) = -15 - 6 = \boxed{-21}$$
• 2.2 $$-8 + 12 = \boxed{4}$$
• 2.3 $$11 + (-15) = 11 - 15 = \boxed{-4}$$
• 2.4 $$(-6) + (-8) = -6 - 8 = \boxed{-14}$$
• 2.5 $$(-5) + 5 = \boxed{0}$$

Question 3
Subtract the integers without using a calculator.

• 3.1 $$12 - (-14) = 12 + 14 = \boxed{26}$$
• 3.2 $$-10 - 2 = \boxed{-12}$$
• 3.3 $$7 - (-13) = 7 + 13 = \boxed{20}$$
• 3.4 $$-9 - 5 = \boxed{-14}$$
• 3.5 $$(-12) - 5 = \boxed{-17}$$

Question 4

• 4.1 Use the properties of integers to complete the statements.

  • 4.1.1 $$8 + (-3) = \mathbf{-3} + 8$$
  • 4.1.2 $$(-6 + 2) + 4 = (-6 + 4) + \mathbf{2}$$

• 4.2 State which property was used:

  • 4.2.1 in 4.1.1: Commutative Property of Addition
  • 4.2.2 in 4.1.2: Associative Property of Addition