Rational or Irrational
Is √25 rational or irrational?
Rational
Order: 1/2, 0.4, 0.45
0.4 < 0.45 < 1/2
Find three consecutive integers that add to 6.
1, 2, 3
x + 9 = 12
x = 3
2x + 5 = 11
x = 3
Is π rational or irrational?
Irrational
Which is larger: √2 or 1.41?
√2 (≈1.414)
Find three consecutive integers whose sum is 72.
23, 24, 25
x/5 = 8
x = 40
3x + 7 = 2x + 9
x = 2
Is 3.14159… repeating or non-repeating?
Non-repeating → Irrational
Place in order: –2.5, –3, –2.2
–3 < –2.5 < –2.2
The sum of three consecutive even integers is 54. Find them.
16, 18, 20
7x = –21
x = –3
6x – 4 = 4x + 8
x = 6
Is 4/7 rational or irrational?
Rational
Place √2, 1.4, 1.5 in order
1.4 < √2 < 1.5
The sum of four consecutive odd integers is 64. Find them.
13, 15, 17, 19
5x = –25
x = –5
4x + 5 = 3x + 9
x = 4
Explain why 0.232323… is rational.
It repeats → can be written as a fraction
Arrange: 2/3, 0.66, 0.67
0.66 < 2/3 < 0.67
The sum of four consecutive even integers is 100.
22, 24, 26, 28
–4x = 20
x = –5
5(2x + 1) = 3x + 10
x = 1