Integer — Grade 7 Accelerated, what it means and where it is taught
A whole number, positive, negative, or zero.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Rational — Any number writable as ab with integers a and b, b ≠ 0.
- Prime polynomial — One that will not factor any further over the integers.
Practise this idea
9 questions in the course bank use Integer, in Reasoning with Equations & Inequalities, Solving Inequalities, Real Numbers, Slope & the Forms of a Line, Factoring, Logarithms. The first 8 are below; the rest are in those units.
Problem 1
The sum of two consecutive integers is 47. Find the smaller one.
Worked answer
23
n + (n + 1) = 47
2n + 1 = 47
2n = 46, so n = 23 and the other is 24.
Problem 2
The sum of three consecutive even integers is 84. Find the smallest.
Worked answer
26
n + (n+2) + (n+4) = 84
3n + 6 = 84
3n = 78, so n = 26. The three are 26, 28, 30 ✓
Problem 3
How many integers satisfy -7 ≤ 2x - 1 < 9?
Worked answer
8
Add 1 everywhere: -6 ≤ 2x < 10
Divide by 2: -3 ≤ x < 5
Integers: -3, -2, -1, 0, 1, 2, 3, 4
That is 8 values — note 5 is excluded.
Problem 4
Is -5 an integer?
- Yes
- No
Worked answer
Yes
Integers are the whole numbers and their negatives, so yes.
Problem 5
Which describes 0?
- Integer and rational
- Irrational
- Neither
Worked answer
Integer and rational
0 is a whole number and an integer
It is rational because 0 = 01.
Problem 6
√150 lies between two consecutive integers. What is the smaller one?
Worked answer
12
144 < 150 < 169
So 12 < √150 < 13
Problem 7
Write y = 23x - 4 in standard form Ax + By = C with integer coefficients.
Worked answer
2x - 3y = 12
3y = 2x - 12
2x - 3y = 12
Problem 8
Which expression will not factor over the integers?
- x2 + 9
- x2 - 9
- x2 + 6x + 9
- x2 - 6x + 9
Worked answer
x2 + 9
x2 + 9 is a sum of squares
It has no real factors