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12 ÷ 3 = 4
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48 × 0.15 = 2.4 × 3
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2.4 ÷ 0.3 = 8
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48 ÷ 3 = 2.4 ÷ 0.15
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1.2 ÷ 0.3 = 4
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2.4 ÷ 0.15 = 16
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3 apples and 4 pears cost £1.55
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I know the cost of an apple
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I know the cost of a pear
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6 apples and 8 pears cost £3.10
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I know which costs more, one apple or one pear
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6 apples and 11 pears cost £3.70
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Every perfect cube is a multiple of 9, or 1 more or 1 less than a multiple of 9
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… = … = 38
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(3n – 1)3 ≡ 27n3 – 27n2 + 9n – 1 and (3n + 1)3 ≡ 27n3 + 27n2 + 9n + 1
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Every integer is a multiple of 3, or 1 more or 1 less than a multiple of 3
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12,345,689 is not a perfect cube
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(3n)3 ≡ 27n3
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n2 + 2n + 1 ≡ (n + 1)2
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n2 + n + 1 < n2 + 2n + 1
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n is positive
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The value of n2 + n + 1 is never a perfect square
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n2 + n + 1 > n2
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The value of n2 + n + 1 is between the value of n2 and the value of (n + 1)2
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a + d = ½ cm2 4a + d = 1 cm2
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d 2 cm b a e c 2 cm
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e = ½ cm2 a + d + e = 1 cm2 a + e + c = 1 cm2 b + c = 1 cm2
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b = ⅔ cm2
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3a = ½ cm2
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These triangles are similar, length ratio 1:2
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