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© Boardworks Ltd of 42 KS3 Mathematics N2 Negative numbers

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© Boardworks Ltd of 42 A A A A Contents N2 Negative numbers N2.1 Ordering integers N2.4 Multiplying and dividing integers N2.2 Adding and subtracting integers N2.3 Using negative numbers in context

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© Boardworks Ltd of 42 Introducing integers A positive or negative whole number, including zero, is called an integer. –3 is an example of an integer. –3 is read as ‘negative three’. This can also be written as –3 or (–3). It is 3 less than 0. 0 – 3 =–3 Or in words, ‘zero minus three equals negative three’.

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© Boardworks Ltd of 42 Positive and negative integers can be shown on a number line. Positive integersNegative integers We can use the number line to compare integers. For example: –3–8 –3 > –8 –3 ‘is greater than’ –8 Integers on a number line

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© Boardworks Ltd of 42 Ordering negative numbers Write the integers –2, 8, 2, –6, –9 and 5 in order from smallest to largest. We can also use a number line to help us write integers in order. Look at the position of the integers on the number line: –9–9–6–6–2–2258 So, the integers in order are: –9, –6, –2, 2, 5, and 8

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© Boardworks Ltd of 42 Ordered Paths

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© Boardworks Ltd of 42 Contents N2 Negative numbers A A A A N2.2 Adding and subtracting integers N2.4 Multiplying and dividing integers N2.1 Ordering integers N2.3 Using negative numbers in context

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© Boardworks Ltd of 42 Mid-points

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© Boardworks Ltd of 42 Adding integers We can use a number line to help us add positive and negative integers. –2 + 5 = -23 = 3 To add a positive integer we move forwards up the number line.

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© Boardworks Ltd of 42 We can use a number line to help us add positive and negative integers. To add a negative integer we move backwards down the number line. –3 + –4 = = – –3 + –4is the same as–3 – 4 Adding integers

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© Boardworks Ltd of 42 Ordered addition square

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© Boardworks Ltd of 42 Mixed addition square

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© Boardworks Ltd of Subtracting integers We can use a number line to help us subtract positive and negative integers. 5 – 8 == –3 To subtract a positive integer we move backwards down the number line.

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© Boardworks Ltd of 42 3 – –6 = 39 = 9 We can use a number line to help us subtract positive and negative integers. To subtract a negative integer we move forwards up the number line. 3 – –6is the same as3 + 6 Subtracting integers

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© Boardworks Ltd of 42 We can use a number line to help us subtract positive and negative integers. –4 – –7 = -43 = 3 To subtract a negative integers we move forwards up the number line. –4 – –7is the same as–4 + 7 Subtracting integers

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© Boardworks Ltd of 42 Using a number line

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© Boardworks Ltd of 42 Ordered subtraction square

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© Boardworks Ltd of 42 Mixed subtraction square

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© Boardworks Ltd of 42 Complete this table

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© Boardworks Ltd of 42 Integer cards - addition and subtraction

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© Boardworks Ltd of 42 Magic Square

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© Boardworks Ltd of 42 Chequered sums

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© Boardworks Ltd of 42 Integer circle sums

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© Boardworks Ltd of 42 Adding and subtracting integers summary To add a positive integer we move forwards up the number line. To add a negative integer we move backwards down the number line. To subtract a positive integer we move backwards down the number line. To subtract a negative integer we move forwards up the number line. a + – b is the same as a – b. a – – b is the same as a + b.

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© Boardworks Ltd of 42 A A A A N2.3 Using negative numbers in context Contents N2 Negative numbers N2.4 Multiplying and dividing integers N2.1 Ordering integers N2.2 Adding and subtracting integers

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© Boardworks Ltd of 42 Negative numbers in context There are many real life situations which use negative numbers. Temperature Balance -£34.52 Bank balances Games with negative scores. Measurements taken below sea level

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© Boardworks Ltd of 42 Sea level

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© Boardworks Ltd of 42 Temperatures

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© Boardworks Ltd of 42 Ordering temperatures

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© Boardworks Ltd of 42 Comparing temperatures

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© Boardworks Ltd of 42 Contents N2 Negative numbers A A A A N2.4 Multiplying and dividing integers N2.1 Ordering integers N2.2 Adding and subtracting integers N2.3 Using negative numbers in context

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© Boardworks Ltd of 42 –3 + –3 + –3 + –3 + –3 = 0–3–6–9–9–12 –3 –15 5 × –3= –15 A positive number × a negative number = a negative number Multiplying and dividing integers –3

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© Boardworks Ltd of 42 –7 × 3 == 3 × –7 = 0 –7 –14 –7 –21 A negative number × a positive number = a negative number Multiplying and dividing negative numbers

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© Boardworks Ltd of 42 –4 × –6 = 0 – – – –6 18 – –6 24 A negative number × a negative number = a positive number Multiplying and dividing negative numbers

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© Boardworks Ltd of 42 Ordered multiplication square

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© Boardworks Ltd of 42 When multiplying negative numbers remember: Rules for multiplying and dividing Dividing is the inverse operation to multiplying. When we are dividing negative numbers similar rules apply: +×+=+ –+×= – –+×=– –+×=– +÷+=+ –+÷= – –+÷=– –+÷=–

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© Boardworks Ltd of 42 Multiplying and dividing integers Complete the following: –3 × 8 = –24 42 ÷ = –6 –7 × –8 = 96–12 47 × = –72 ÷ –6 =12 –36 ÷ = –4 9 ÷ –90 = –6540 –7 × = 175 –25 –4 × –5 × –8 =–160 3 × –8 ÷ = 1.5 –16

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© Boardworks Ltd of 42 Using a calculator We can enter negative numbers into a calculator by using the sign change key: (–)(–) For example: –417 ÷ –0.6 can be entered as: (–)(–)417 ÷ (–)(–)0.6 = The answer will be displayed as 695. Always make sure that answers given by a calculator are sensible.

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© Boardworks Ltd of 42 Mixed multiplication square

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© Boardworks Ltd of 42 Mixed division square

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© Boardworks Ltd of 42 Integer cards – multiplication and division

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© Boardworks Ltd of 42 Number spiral 3 –7–7 –4–4 ×2×2 –8–8 –2–2 –10 ÷ –5 2 × –1 –2– ÷ –2 –3–3 × 5 – –11 – 5 –

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