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Welcome to GCSE Edexcel Maths revision.

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Topic M 1: Integers, decimals and calculations.

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This video covers Foundation and Higher tiers.

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An integer is a whole number: and so on, minus 2, minus 1, 0, 1, 2, and so on.

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In 307.46, the 4 means four tenths and the 6 means six hundredths.

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Zeros can be essential place holders.

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Multiplying by 10, 100 or 1000 makes each digit worth 10, 100 or 1000 times as much.

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For example, 0.047 multiplied by 100 equals 4.7.

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Dividing reverses this; do not describe the decimal point as changing the number's place-value system.

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On a number line, values increase to the right: minus 7 is less than minus 2 is less than 0 is less than 0.4.

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The symbols is less than or equal to and is greater than or equal to include equality; is not equal to means not equal.

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Signed numbers on a number line

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Compare decimals by matching place values: 0.6 equals 0.60 is greater than 0.56.

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For fractions, use a common denominator or convert to decimals before ordering.

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Adding a positive number moves right; subtracting a positive number moves left. minus 3 plus 7 equals 4 and minus 3 minus 7 equals minus 10.

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Subtracting a negative adds its opposite: 5 minus open bracket minus 2 close bracket equals 7.

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For multiplication and division,

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equal signs give a positive result and different signs give a negative result: open bracket minus 4 close bracket multiplied by open bracket minus 3 close bracket equals 12;

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12 divided by open bracket minus 3 close bracket equals minus 4.

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This sign rule does not apply to addition.

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For column addition and subtraction, line up decimal points and matching place values. 7.35 plus 0.8 equals 8.15.

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Exchange between neighbouring columns when required; use zeros to make places clear.

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For long multiplication,

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multiply by each digit and account for its place value. 24 multiplied by 13 equals 24 multiplied by 10 plus 24 multiplied by 3 equals 240 plus 72 equals 312.

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For long division, divide, multiply, subtract and bring down the next digit. 156 divided by 12 equals 13 because 12 multiplied by 13 equals 156.

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A remainder may need to become a fraction or decimal in the context.

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To multiply decimals,

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first use whole numbers and then restore the total number of decimal places: 1.2 multiplied by 0.35 equals 0.42 because 12 multiplied by 35 equals 420 and there are three decimal places altogether.

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To divide by a decimal, multiply both numbers by the same power of 10: 4.8 divided by 0.06 equals 480 divided by 6 equals 80.

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Changing only the divisor changes the question.

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Use brackets first,

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then powers and roots,

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then multiplication and division from left to right,

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then addition and subtraction from left to right. 18 divided by 3 multiplied by 2 equals 12,

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not 3.

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The reciprocal of a non-zero number is 1 divided by that number.

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The reciprocal of 5 is 1 over 5 ; the reciprocal of 2 over 3 is 3 over 2 .

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A number times its reciprocal is 1.

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Worked example: 4 plus 3 multiplied by open bracket 7 minus 5 close bracket squared equals 4 plus 3 multiplied by 2 squared equals 4 plus 12 equals 16.

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Show each stage so the order is clear.

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Worked example: open bracket minus 3 close bracket squared equals 9, but minus 3 squared equals minus 9 because squaring happens before the minus sign outside the power.

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Brackets change which number is squared.

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Check arithmetic using an inverse operation or an estimate.

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If 6.2 multiplied by 4.9 is reported as 303.8, estimating 6 multiplied by 5 is approximately equal to 30 reveals the place-value error; the correct product is 30.38.

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That completes Integers, decimals and calculations.

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Revisit the notes and test yourself on the revision website.