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Transcript of Order
The IntegersThe IntegersThe IntegersThe IntegersOrderOrder
Think about the game!
• When working a problem on paper, think about what it means in the MathGym-1D game.
• Which direction does the answer move something? (Is answer is positive or negative?)
• How far does it move it? (What is the size of the answer? )
Order
• Order has to do with what comes first. 5 comes after 3 because it is 2 more than 3. We write either 5 > 3, read as “5 is greater than 3”
or 3 < 5, read as “3 is less than 5”
• Likewise, -3 comes after -5 since it is 2 more than -5, so
-3 > -5 and -5 < -3
Order
-2-3 0-1 1 2 3
Definition:x < y means y – x is positivex < y and y > x mean the same
thing
... ... 3 2 1 0 1 2 3
Do not get order mixed up with size.-5 < -3, but size-wise |-5| > |-3|
On the number line, if x is to the left of y, then x < y.
True or False!
T 7 < 12 12 – 7 = 527) – (-109) = 2
True or False!
T 7 < 12 12 – 7 = 5
True or False!
T 7 < 12 12 – 7 = 5
True or False!
F 3 < -6 (-6) – 3 = --27) – (-109) =
True or False!
F 3 < -6 (-6) – 3 = -9
True or False!
F 3 < -6 (-6) – 3 = -9
True or False!
T -107 > -105 (-107) - (-105) = -(-27) –
True or False!
T -107 > -105 (-107) - (-105) = -2
True or False!
F -107 > -105 (-107) - (-105) = -2
True or False!
T -27 > -109 (-27) – (-109) = 82
True or False!
T -27 > -109 (-27) – (-109) = 82
True or False!
T -27 > -109 (-27) – (-109) = 82
Sort the numbers in increasing order
4, -5, -7, 3, 2, -1, 0
All the negatives are less than the positives with 0 in between.
-5, -7, -1, 0, 4, 3, 2
Now sort the positives in increasing size and the negatives in the decreasing size
-7, -5, -1, 0, 2, 3, 4
Sort the numbers in increasing order
4, -5, -7, 3, 2, -1, 0
All the negatives are less than the positives with 0 in between.
-5, -7, -1, 0, 4, 3, 2
Now sort the positives in increasing size and the negatives in the decreasing size
-7, -5, -1, 0, 2, 3, 4
Sort the numbers in increasing order
4, -5, -7, 3, 2, -1, 0
All the negatives are less than the positives with 0 in between.
-5, -7, -1, 0, 4, 3, 2
Now sort the positives in increasing size and the negatives in the decreasing size
-7, -5, -1, 0, 2, 3, 4
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0, so(c – b) + (b – a) > 0, butc – a = (c – b) + (b – a)
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0.The sum of positives is positive, so(c – b) + (b – a) > 0. Butc – a = (c – b) + (b – a).So c – a > 0.
Therefor a < c.
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0.The sum of positives is positive. So (c – b) + (b – a) > 0. Butc – a = (c – b) + (b – a).So c – a > 0.
Therefor a < c.
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0.The sum of positives is positive. So (c – b) + (b – a) > 0. Butc – a = (c – b) + (b – a).So c – a > 0.
Therefor a < c.
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0.The sum of positives is positive, so(c – b) + (b – a) > 0. Butc – a = (c – b) + (b – a).So c – a > 0.
Therefor a < c.
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0.The sum of positives is positive, so(c – b) + (b – a) > 0. Butc – a = (c – b) + (b – a).So c – a > 0.
Therefor a < c.
Prove it!Theorem If a < b and b < c, then a < c
Proof:b – a > 0 and c – b > 0.The sum of positives is positive, so(c – b) + (b – a) > 0. Butc – a = (c – b) + (b – a).So c – a > 0.
Therefor a < c. TA DAH