Use mental structure when numbers fit together
Some calculations are faster when we spot a useful pair or a simple scaling fact.
Look for factors that make 10, 100 or another easy number before you reach for a written method.
Year 7
Mental and written arithmetic with integers, decimals and fractions
Choose efficient methods for arithmetic, line up place value carefully, and connect fractions, decimals and whole-number structure.
Lesson overview
Number - integers, decimals and fractions
Year 7 arithmetic is not just about getting an answer. We choose whether a mental shortcut, a written layout or a fraction method is most sensible, then we explain why it works. Place value keeps decimals in line, and equivalent fractions help when denominators do not already match.
Line up decimals by place value
When adding or subtracting decimals, tenths must stay under tenths and hundredths under hundredths.
| Ones | Tenths | Hundredths |
|---|---|---|
| 3 | 6 | 0 |
| 2 | 4 | 5 |
| 6 | 0 | 5 |
Treat 3.6 as 3.60 so each digit sits in the correct column.
Equivalent fractions create a common denominator
To add 3/4 and 1/8, rewrite 3/4 in eighths first.
You can only add the numerators when the fractions name parts of the same size.
Worked example
Work out 2.45 + 1.8 + 0.37.
| Ones | Tenths | Hundredths |
|---|---|---|
| 2 | 4 | 5 |
| 1 | 8 | 0 |
| 0 | 3 | 7 |
| 4 | 6 | 2 |
- Rewrite 1.8 as 1.80 so the decimal places line up.
- Add the hundredths: 5 hundredths and 7 hundredths make 12 hundredths.
- Exchange 10 hundredths for 1 tenth, leaving 2 hundredths.
- Add the tenths and ones to get a total of 4.62.
Try it
Choose the method that fits the numbers, then answer carefully.
Question 1
Which answer is correct for 407 - 189?
Question 2
Which answer is correct for 3.6 + 2.45?
| Ones | Tenths | Hundredths |
|---|---|---|
| 3 | 6 | 0 |
| 2 | 4 | 5 |
Question 3
What is 3/4 + 1/8?
Question 4
Which calculation can be worked out most efficiently by spotting a useful pair?
Question 5
Which statement is correct?
one half
one quarter
combine the parts
Common mistakes
Watch for these when working through the lesson.
- Adding decimals without lining up the place values.
- Adding the numerator and denominator separately when working with fractions.
- Using a long written method for a calculation that has a quicker mental structure.
Related topics
These ideas fit closely with this lesson.
- Operations with negative numbers.
- Prime factorisation and factor pairs.
- Simplify linear expressions.