Subtracting Integers 1
Use a number line to find 11 – 4.
Answer: 7
Find 3 – 12.
Answer: –9
Estimate –1 – 1.
Answer: –2
Find 2.4 – 5.6.
Answer: –3.2
Use a number line to find –3 – 9.
Answer: –12
Find –8 – (–13).
Answer: 5
Find:
-1 1/5 - (-3/5)
Answer:
- 3/5
Find 6.7 – 9.2.
Answer: –2.5
Use a number line to find 6 – (–5).
Answer: 11
Find 5 – (–4).
Answer: 9
Do the rules for subtracting integers apply to all rational numbers? Explain your reasoning.
Answer: Yes; subtraction can be rewritten as adding the opposite, the same rule used for integers
Evaluate –6 – 8 + 6
Use properties of addition, and explain how the Commutative and Associative Properties make this easier using mental math.
Answer: –8; reorder to group –6 and 6 together first using the Commutative Property, since –6 + 6 = 0, leaving just –8
Use a number line to find –2 – (–4).
Answer: 2
The air temperature outside an igloo is –8°C. The air temperature inside is 13°C warmer. Write an expression to find the temperature inside, then solve.
Answer: –8 + 13; the inside temperature is 5°C
Find:
5 2/3 + 7 2/5 + (-3 1/3)
Answer: Approximately 9⅔ (rewrite as a sum, group terms with common denominators, then simplify)
Evaluate [13 + (–28)] – 13 using properties of addition.
Answer: –28; regroup so that 13 and –13 cancel out, leaving –28
Explain how subtracting an integer is related to adding its opposite, using a number line to support your explanation.
Answer: To subtract an integer, add its opposite; on a number line this means moving the arrow the same distance but in the direction of adding rather than subtracting (e.g., –2 – 4 = –2 + (–4), moving 4 units left from –2 to land on –6)
North America's elevation range is 6,190 – (–86) and Africa's elevation range is 5,895 – (–155). Which continent has the greater range of elevations?
Answer: North America, with a range of 6,276 m compared to Africa's 6,050 m
Determine whether the Commutative and Associative Properties of Addition apply to expressions involving subtraction of rational numbers, and justify your reasoning with an example.
Answer: Yes; once subtraction is rewritten as adding the opposite, the properties apply the same way they do for addition of any rational numbers (e.g., –1⅕ – 5/7 can be rewritten as –1⅕ + (–5/7) and reordered)
A city recorded a temperature change from –6.1°C in the morning to a low of –8.75°C, then rose to 3.2°C by evening. Find the total change in temperature from the morning low to the evening high, and explain each step using properties of addition.
Answer: Total change is 11.95°C; rewrite the subtraction as adding the opposite (3.2 – (–8.75) = 3.2 + 8.75), then add to get 11.95