# Big numbers and the four operations · Grade 5

> Big numbers and the four operations, Grade 5: Numbers beyond a million and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Big numbers and the four operations (Grade 5) you practise 9 skills: Numbers beyond a million · Column addition and subtraction · Long multiplication · Long and short division · Order of operations · Clever strategies · Equations and inequalities · Estimating · Word problems.

Read numbers beyond a million in groups of three from the right: the units, the thousands, then the millions. So 45,302,018 is forty-five million, three hundred and two thousand and eighteen. There is no greatest whole number: you can always add 1 and get a bigger one.

In long multiplication and division you split a number by the value of its digits: multiply each part and add the results, or take away multiples of the divisor place by place. Estimate before you work it out, and at the end check that your answer is close to the estimate.

There are clever ways to work things out. To work out 28 × 5, multiply by 10 and halve. In a division you can multiply or divide both numbers by the same number and the answer does not change: 4,800 ÷ 16 equals 2,400 ÷ 8. And multiplication and division undo each other, so use one to find a missing number in the other.

**Tip:** Before you answer a word problem, check that it gives you enough information. Sometimes a fact is missing, and then you cannot know the answer.

## What you learn

### Numbers beyond a million

- Example: How do you read this number? 90,123,000
- Options: ninety million, one hundred and twenty-three thousand ninety million, one hundred and twenty-three thousand. · nine hundred and one million, two hundred and thirty thousand nine hundred and one million, two hundred and thirty thousand. · ninety million, one hundred and twenty thousand ninety million, one hundred and twenty thousand. · ninety million, one hundred and thirty-two thousand ninety million, one hundred and thirty-two thousand.
- Answer: ninety million, one hundred and twenty-three thousand
- Solution: 90,123,000 ninety million, one hundred and twenty-three thousand.

### Column addition and subtraction

- Example: Work out: 9,556 + 2,287
- Answer: 11843
- Solution: Write the numbers one under the other, units under units, and work column by column from the right:    9,556 +  2,287 ────────   11,843 9,556 + 2,287 = 11,843

### Long multiplication

- Example: Work out: 33 × 6
- Answer: 198
- Solution: Split the first number by place value and multiply each part: 33 × 6 = 30 × 6 + 3 × 6 30 × 6 = 180 3 × 6 = 18 180 + 18 = 198

### Long and short division

- Example: Work out: 234 ÷ 9
- Answer: 26
- Solution: Take multiples of 9 away from 234, largest first: 9 × 20 = 180 234 − 180 = 54 9 × 6 = 54 54 − 54 = 0 Add up all the numbers we multiplied by: 20 + 6 = 26 The quotient is 26, with no remainder. Check: 26 × 9 = 234

### 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

### Clever strategies

- Example: Fill in the missing number: 753,788 + 145,995 = 753,783 + ☐
- Answer: 146000
- Solution: 5 was taken from the first number, so add 5 to the second: 145,995 + 5 = 146,000 753,788 + 145,995 = 753,783 + 146,000 = 899,783

### Equations and inequalities

- Example: Find the missing number: 1,420 = 71 × ☐
- Answer: 20
- Solution: To find a missing factor, divide the product by the known factor: 1,420 ÷ 71 = 20 Check: 1,420 = 71 × 20

### Estimating

- 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.

### Word problems

- Example: A factory packs 6 pencils in each box. Today it packed 127 boxes. How many pencils did it pack today?
- Answer: 762
- Solution: 127 × 6 = 762

## Not on the site yet

- Negative numbers
- Writing a story for a calculation
- How many whole number solutions

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 5 topics](https://kixplo.com/il/en/math/grade-5/2023/)