# Whole numbers and zero · Grade 6

> Whole numbers and zero, Grade 6: The decimal system, Clever computing and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Whole numbers and zero (Grade 6) 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

- Example: How many symbols (digits) does the decimal system use?
- Answer: 10
- Solution: 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

- Example: Work it out the easy way: 9 × 35
- Answer: 315
- Solution: 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

- Example: Is 22 divisible by 3?
- Options: No · Yes
- Answer: No
- Solution: 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

- Example: Work out: 4 × 10 ÷ 5
- Answer: 8
- Solution: Each line does one operation: 4 × 10 ÷ 5 = 40 ÷ 5 40 ÷ 5 = 8

### Estimating and checking

- Example: Round 2,288 to the nearest thousand.
- Answer: 2000
- Solution: The deciding digit is 2, so round down. 2,288 rounded to the nearest thousand is 2,000.

## Not on the site yet

- Negative numbers
- Other counting systems
- Writing a story for a calculation
- Choosing two numbers whose sum is as close as possible to a given number
- Questions with more than one right answer

The exercises are made by rules and the answers are worked out in code. The topic follows the new Israeli elementary programme (2023).

[Practise on the site](https://kixplo.com/il/en/) · [All Grade 6 topics](https://kixplo.com/il/en/math/grade-6/2023/)