Chapter 4 Reason mathematically Write down the next three numbers in each number sequence. a –1, –2, –4, –8, …, …, …, b –1, 3, –9, 27, …, …, …, a Multiplying by 2 each time to give missing numbers –16, –32, –64 b Multiplying by –3 each time to give missing numbers –81, 243, –729
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11 Write down the next three numbers in each number sequence. a 1, –2, 4, –8, …, …, … b –1, –3, –9, –27, …, …, … 1, –4, 16, –64, …, …, … c –1, 5, –25, 125, …, …, … d 12 This is Tim’s solution to a problem: (7 – 11) × (3 – 8) = 4 × 5 = 20 He has the correct answer but made some errors. Explain where he has made errors. Solve problems
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Peter asked Kath to think of two integers smaller than eight and tell her their product. Kath said, ‘The product is –12’.
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Peter said, ‘There are four different possible sets of numbers that give that product.’
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Write down the four possible pairs of numbers Kath could have been thinking of. To have a negative product, one number must be positive while the other is negative. To have a product of 12, you can have 3 × 4 or 2 × 6 only using integers less than eight. So the four sets are –3 × 4, 3 × –4, –2 × 6, 2 × –6 12 Julie asked Chris to think of two integers less than ten with a product of –24. Write down the four different possible pairs of numbers Chris could have.
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13 a I n each brick wall, work out the number to write in an empty brick by multiplying the numbers in the two bricks below it. Copy and complete each brick wall. ii i 4
–2
–1
1
–4
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b Andy said: ‘You will always have a positive number at the top of the brick wall if there is one negative number in the bottom layer.’ Is Andy correct? Explain your answer.
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