Whole numbers and zero · Year 7
In Whole numbers and zero (Year 7) you practise 5 skills: The decimal system · Clever computing · Divisibility · Order of operations · Estimating and checking. The decimal system has ten digits, from 0 to 9. The value of a digit depends on its place: each place to the left is 10 times as big as the place on its right. So a 7 in the millions place is worth 100 times as much as a 7 in the ten thousands place.
The laws of arithmetic let you work things out the easy way: the commutative law changes the order of the factors, the associative law changes the groups, and the distributive law splits a number into parts. If you know the answer to one calculation, you can find the answers to related calculations without starting again. Divisibility rules let you check without dividing: a number is divisible by 5 when its ones digit is 0 or 5, by 3 or 9 when the sum of its digits is divisible by 3 or 9, by 4 when its last two digits make a number divisible by 4, and by 6 when it is even and divisible by 3. With no brackets, multiply and divide before you add and subtract. With brackets, work out what is inside them first. Before you calculate, estimate the answer, and afterwards check that your answer is close to the estimate.
Tip: To check whether a number is divisible by 3, add up its digits and check the sum.
What you learn
The decimal system
For example: How many symbols (digits) does the decimal system use?
Answer and solution
The answer: 10
In the decimal system, every number is written with the digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 That is 10 symbols.
Clever computing
For example: Work it out the easy way: 9 × 35
Answer and solution
The answer: 315
By the distributive law, split the number into tens and ones: 9 × 35 = 9 × 30 + 9 × 5 9 × 30 + 9 × 5 = 270 + 45 = 315
Divisibility
For example: Is 22 divisible by 3?
- No
- Yes
Answer and solution
The answer: No
The sum of the digits: 2 + 2 = 4 4 is not divisible by 3. So 22 is not divisible by 3. The answer: no.
Order of operations
For example: Work out: 4 × 10 ÷ 5
Answer and solution
The answer: 8
Each line does one operation: 4 × 10 ÷ 5 = 40 ÷ 5 40 ÷ 5 = 8
Estimating and checking
For example: Round 2,288 to the nearest thousand.
Answer and solution
The answer: 2000
The deciding digit is 2, so round down. 2,288 rounded to the nearest thousand is 2,000.
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).