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8 (a) Write down (i) the number twenty-seven million, three hundred sixty thousand, forty-five in figures, (ii) the six factors of 20, (iii) a fraction that is equivalent to 7/9, (iv) a prime number between 30 and 40. 9 Work out (a) -6 + +12 (b) +5 - -7 (c) -9 x +4 (d) +72 +9

Mathematics

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8 parts
i

27,360,045\text{27,360,045}

ii

1, 2, 4, 5, 10, 20\text{1, 2, 4, 5, 10, 20}

iii

1418\frac{14}{18}

iv

31\text{31}

a
6
b
-2
c
-36
d
-8

Step-by-step solution

12 steps

Here are the solutions to the problems:

8 (a) Write down

Part i· 2 steps

the number twenty-seven million, three hundred sixty thousand, forty-five in figures.

  1. Identify the place values for each part of the number.

    Twenty-seven million is 27,000,000.
    Three hundred sixty thousand is 360,000.
    Forty-five is 45.

  2. Combine these values.

    27,000,000+360,000+45=27,360,04527,000,000 + 360,000 + 45 = 27,360,045

    The number is 27,360,045\boxed{\text{27,360,045}}.

Part ii

1, 2, 4, 5, 10, 20\text{1, 2, 4, 5, 10, 20}

the six factors of 20.

  1. Find all numbers that divide 20 evenly.

    • 1×20=201 \times 20 = 20
    • 2×10=202 \times 10 = 20
    • 4×5=204 \times 5 = 20 The factors are 1, 2, 4, 5, 10, 20. The six factors of 20 are 1, 2, 4, 5, 10, 20\boxed{\text{1, 2, 4, 5, 10, 20}}.

Part iii

1418\frac{14}{18}

a fraction that is equivalent to 79\frac{7}{9}.

  1. Multiply the numerator and the denominator by the same non-zero integer.

    Let's use 2.

    7×29×2=1418\frac{7 \times 2}{9 \times 2} = \frac{14}{18}

    An equivalent fraction is 1418\boxed{\frac{14}{18}}.

Part iv

31\text{31}

a prime number between 30 and 40.

  1. List numbers between 30 and 40

    31, 32, 33, 34, 35, 36, 37, 38, 39.

  2. Identify which of these are prime (only divisible by 1 and themselves).

    • 31 is prime.
    • 32 is divisible by 2.
    • 33 is divisible by 3.
    • 34 is divisible by 2.
    • 35 is divisible by 5.
    • 36 is divisible by 2.
    • 37 is prime.
    • 38 is divisible by 2.
    • 39 is divisible by 3. A prime number between 30 and 40 is 31\boxed{\text{31}} (or 37).

    9 Work out

Part a6

−6+12-6 + 12

  1. Add the numbers.

    Since the signs are different, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.

    12−6=612 - 6 = 6

    The result is 6\boxed{6}.

Part b-2

+5−7+5 - 7

  1. Subtract 7 from 5.

    5−7=−25 - 7 = -2

    The result is −2\boxed{-2}.

Part c-36

−9×+4-9 \times +4

  1. Multiply the absolute values of the numbers.

    9×4=369 \times 4 = 36
  2. Determine the sign of the product.

    A negative number multiplied by a positive number results in a negative number.

    −9×4=−36-9 \times 4 = -36

    The result is −36\boxed{-36}.

Part d-8

−72÷+9-72 \div +9

  1. Divide the absolute values of the numbers.

    72÷9=872 \div 9 = 8
  2. Determine the sign of the quotient.

    A negative number divided by a positive number results in a negative number.

    −72÷9=−8-72 \div 9 = -8

    The result is −8\boxed{-8}.

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