Integers 1a
Pupil Notes and worked examples
Key Skill 1: Write a number in words given the number in figures and vice-versa
You can be given a number in figures (numbers) and be asked to write this number using
words
You can also be given a number in words and be asked to write this number in figures.
e.g.
six thousand, three hundred and sixteen
=
6 316
one hundred and three thousand, six hundred and four
=
103 604
seventy thousand and ninety four
=
70 094
two million, four hundred and six thousand, three hundred
=
2 406 300
seven million, seventeen thousand and eighty nine
=
7 017 089
eighteen million and thirteen
=
18 000 013
two billion
= 2 000 000 000
Key Skill 2: Identify that numbers less than zero are negative
Whole numbers are the numbers 0, 1, 2, 3, 4, 5, etc…
Integers are the whole numbers and their negatives …-4, -3, -2, -1, 0, 1, 2, 3, 4 …
Positive integers are those integers greater than zero
Negative integers are those integers less than zero.
e.g.
Positive integers:
2, 6, 19, 75, 234, 9 876,
Negative integers: -2, -6, -19, -75, -234, -9 876,
1 000 000
-1 000 000
Key Skill 3: Appreciate that negative numbers are always smaller than positive numbers
Key Skill 4: Arrange a list of numbers, positive and negative, on a number line
You can be given a list of integers, positive and negative, and asked to put them in order from
smallest to largest.
The most negative integer should be first in the list (if there are any negatives)
The most positive integer being last in the last (if there are any positives).
e.g.
Put the following integers in order from smallest to largest
23,
56,
-34,
-17,
-88,
45,
-6
Solution
23
_
-6
_
-17
-34
-88
So required order is:
-88,
-34,
-17,
-6,
23,
45,
56
45
56
Key Skill 5: Round to a suitable degree of accuracy
Integers can be rounded off to the nearest ten, hundred, thousand, ten thousand, hundred
thousand, million and so on.
e.g.
Round to the nearest ten:
43 40,
465470,
(If the ‘units’ digit is 5 or more round up otherwise round down)
23472350
Round to the nearest hundred:
445  400,
34573500,
(If the ‘tens’ digit is 5 or more round up otherwise round down)
6458664600
Round to the nearest thousand: 34563000,
2352824000,
(If the ‘hundreds’ digit is 5 or more round up otherwise round down)
23456782346000
Round to the nearest million:
2 345 6782 000 000
17 911 576  18 000 000
(If the ‘hundred thousands’ digit is 5 or more round up otherwise round down)
Key Skill 6: Use rounding to estimate answers
Before performing a calculation, numbers can be rounded to make the calculation easier, however
the answer would be an estimate as the exact numbers were not used in the calculation.
e.g.
2 257 689 + 3 875 000 ?
Now 2 257 689 rounds to 2 000 000 to the nearest million
and 3 875 000 rounds to 4 000 000 to the nearest million
so
2 257 689 + 3 875 000 ≈ 2 000 000 + 4 000 000
so
2 257 689 + 3 875 000 ≈ 6 000 000, which is an estimate for the original calculation
6 768 – 2 345 ?
Now 6 768 rounds to 6 800 to the nearest hundred
and 2 345 rounds to 2 300 to the nearest hundred
so
6 768 – 2 345 ≈ 6 800 – 2 300
so
6 768 – 2 345 ≈ 4 500, which is an estimate for the original calculation
Key Skill 7: Perform calculations involving negative numbers
We use a number line to help us decide how to add and subtract positive and negative integers.
Adding positive integers – From your starting position move ‘right’ along the number line.
Adding negative integers – Do the opposite of ‘adding positive integers’ so move ‘left’
e.g.
5 + 6 = 11
-10 + 4 = -6
-20 + 42 = 22
-17 + 14 = -3
5 + (-6) = -1
-10 + (-4) = -14
-20 + (-42) = -62
-17 + (-14) = -31
Subtracting positive integers - From your starting position move ‘left’ along the number line.
Subtracting negative integers - Do the opposite of ‘subtracting positive integers’ so move ‘right ’
e.g.
8–5=3
6 – 10 = -4
-3 – 7 = -10
-5 – 18 = -23
8 – (-5) = 13
6 – (-10) = 16
-3 – (-7) = 4
-5 – (-18) = 13
Key Skill 8: Make correct use of the ‘less than’ and ‘greater than’ symbols
<
is the
less than
symbol
>
is the
more than
symbol
These are used to compare the size of positive and negative integers.
The sign always points to the smaller integer.
e.g.
4
<5
-7
<9
6
< 10
-3
< -7
-33
-9
<3
< -32
6>2
19 > 17
6 > -6
16 > -11
12 > - 17
-64 > -67
Hint:
This graphic helps you remember which way the sign goes.
ess than