Edexcel · GCSE Maths · 1MA1 · Foundation and Higher
M1 · Integers, decimals and calculations
Revision notes, worked examples and methods for integers, decimals and calculations.
Notes and quizzes ready · 50 questions · Video coming soon.
Foundation shows shared notes and questions. Higher includes the shared content and labelled Higher extensions. Changing tier starts the notes and a new quiz set.
Revise the key ideas
Place value and signed numbers
An integer is a whole number: …, −2, −1, 0, 1, 2, …. In 307.46, the 4 means four tenths and the 6 means six hundredths. Zeros can be essential place holders.
Multiplying by 10, 100 or 1000 makes each digit worth 10, 100 or 1000 times as much. For example, 0.047 × 100 = 4.7. Dividing reverses this; do not describe the decimal point as changing the number's place-value system.
On a number line, values increase to the right: −7 < −2 < 0 < 0.4. The symbols ≤ and ≥ include equality; ≠ means not equal. Signed numbers on a number line
Compare decimals by matching place values: 0.6 = 0.60 > 0.56. For fractions, use a common denominator or convert to decimals before ordering.
Adding a positive number moves right; subtracting a positive number moves left. −3 + 7 = 4 and −3 − 7 = −10. Subtracting a negative adds its opposite: 5 − (−2) = 7.
For multiplication and division, equal signs give a positive result and different signs give a negative result: (−4) × (−3) = 12; 12 ÷ (−3) = −4. This sign rule does not apply to addition.
Written methods and order
For column addition and subtraction, line up decimal points and matching place values. 7.35 + 0.8 = 8.15. Exchange between neighbouring columns when required; use zeros to make places clear.
For long multiplication, multiply by each digit and account for its place value. 24 × 13 = 24 × 10 + 24 × 3 = 240 + 72 = 312.
For long division, divide, multiply, subtract and bring down the next digit. 156 ÷ 12 = 13 because 12 × 13 = 156. A remainder may need to become a fraction or decimal in the context.
To multiply decimals, first use whole numbers and then restore the total number of decimal places: 1.2 × 0.35 = 0.42 because 12 × 35 = 420 and there are three decimal places altogether.
To divide by a decimal, multiply both numbers by the same power of 10: 4.8 ÷ 0.06 = 480 ÷ 6 = 80. Changing only the divisor changes the question.
Use brackets first, then powers and roots, then multiplication/division from left to right, then addition/subtraction from left to right. 18 ÷ 3 × 2 = 12, not 3.
The reciprocal of a non-zero number is 1 divided by that number. The reciprocal of 5 is 15; the reciprocal of 23 is 32. A number times its reciprocal is 1.
Worked examples and checking
Worked example: 4 + 3 × (7 − 5)2 = 4 + 3 × 22 = 4 + 12 = 16. Show each stage so the order is clear.
Worked example: (−3)2 = 9, but −32 = −9 because squaring happens before the minus sign outside the power. Brackets change which number is squared.
Check arithmetic using an inverse operation or an estimate. If 6.2 × 4.9 is reported as 303.8, estimating 6 × 5 ≈ 30 reveals the place-value error; the correct product is 30.38.
Test yourself
50 questions · Sets of 10 from the selected tier. For fractions, use / when typing; for powers, use superscripts or ^. Follow each question's answer format. These quick checks support revision; practise full written solutions and proofs too.
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