Place value, primes and integers
What each digit in a number is worth, and numbers in expanded notation. Primes have exactly two factors; composite numbers have more. Read one part at a time and tap “I know this”. Then test yourself in the quiz.
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Every digit has a place
The place of a digit gives its value. In Grade 7 you work with numbers of at least 9 digits (up to the hundred millions).
| Place | Value |
|---|---|
| units (U) | 1 |
| tens (T) | 10 |
| hundreds (H) | 100 |
| thousands (Th) | 1 000 |
| ten thousands (TTh) | 10 000 |
| hundred thousands (HTh) | 100 000 |
| millions (M) | 1 000 000 |
| ten millions (TM) | 10 000 000 |
| hundred millions (HM) | 100 000 000 |
Expanded notation
Write a number as the sum of the values of its digits: 4 352 = 4 000 + 300 + 50 + 2.
A zero holds a place open: 4 052 = 4 000 + 50 + 2 (no hundreds).
Read big numbers in groups of three from the right: 2 506 381 = two million five hundred and six thousand three hundred and eighty-one.
Prime numbers
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors.
Primes up to 100 (25 primes): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
1 is not prime (only one factor). 2 is the only even prime.
Careful: 91 looks prime, but 91 = 7 × 13, so it is composite.
Prime factors
Break a number into primes with a factor tree: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
Positive and negative
Integers are the numbers …, −3, −2, −1, 0, 1, 2, 3, …: the whole numbers (0, 1, 2, 3, …) and their negatives. Negative numbers are less than 0, like temperatures below freezing.
- On a number line left is always smaller: −7 < −3.
- The opposite of 5 is −5; their sum is 0.
Calculating with integers
| Rule | Example |
|---|---|
| plus a negative = minus | 5 + (−3) = 2 |
| minus a negative = plus | 5 − (−3) = 8 |
| same signs × or ÷ → positive | (−4) × (−3) = 12 |
| different signs × or ÷ → negative | (−4) × 3 = −12 |
- On the number line: adding a positive number moves you right; subtracting a positive number moves you left.
- −3 + (−4) = −7: start at −3 and move 4 to the left.
- −2 − 5 = −7: start at −2 and move 5 to the left.
- −6 + 9 = 3: start at −6 and move 9 to the right.
Think of money: −3 is a debt of R3. If someone takes your debt away, you are better off: −(−3) = +3.
Remember this and test yourself
- The place of a digit gives its value.
- Prime: exactly two factors (1 and itself).
- Negative numbers are less than 0.
- U, T, H, Th: units, tens, hundreds, thousands.
- 1 is not prime; 2 is the only even prime.
- Left on the number line is smaller.
Write these points in your book. Read them again the night before the test.
Every step to the left is worth ten times more.
Important words
First say the answer yourself, then turn the card over.
Match column A to column B
Tap a word in column A, then its meaning in column B. You can also start in column B.
True or false?
Read the question and the answer. Is the answer right? Tap True or False.
Now the real quiz!
The quiz has many more questions on this topic. Every question shows straight away whether you are right and explains why.
Take the quiz: Place value, primes and integers- Let your child work the examples on paper and explain them to you.
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Follows CAPS for Grade 7 Mathematics. Always check your teacher’s notes and textbook too.