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A. Calculate multiples of 5 and 6, their LCM. 11. 1.2 million goods sold/year. a) Total goods/year? b) 2/12 of total? c) 6/12 of total? d) 9/12 of total?

Mathematics

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Here are the solutions to the problems:

A. Calculate the following (continuation)

  • Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
  • Multiples of 6: 6, 12, 18, 24, 30, 36, ...
  • LCM: The least common multiple of 5 and 6 is 30\boxed{\text{30}}.

11. 1.2 million goods are sold per annum (each year).
The total amount of goods is 1.2 million, which is 1,200,000.

Part a

What is the total amount of goods sold per year?

The total amount of goods sold per year is 1,200,000\boxed{\text{1,200,000}}.

Part b· 2 steps

What is 212\frac{2}{12} of the total amount?

  1. Calculate the fraction of the total amount.

    212×1,200,000\frac{2}{12} \times 1,200,000
  2. Simplify the fraction and multiply.

    16×1,200,000=1,200,0006=200,000\frac{1}{6} \times 1,200,000 = \frac{1,200,000}{6} = 200,000

    The amount is 200,000\boxed{\text{200,000}}.

Part c· 2 steps

What is 612\frac{6}{12} of the total amount?

  1. Calculate the fraction of the total amount.

    612×1,200,000\frac{6}{12} \times 1,200,000
  2. Simplify the fraction and multiply.

    12×1,200,000=1,200,0002=600,000\frac{1}{2} \times 1,200,000 = \frac{1,200,000}{2} = 600,000

    The amount is 600,000\boxed{\text{600,000}}.

Part d· 2 steps

What is 912\frac{9}{12} of the total amount?

  1. Calculate the fraction of the total amount.

    912×1,200,000\frac{9}{12} \times 1,200,000
  2. Simplify the fraction and multiply.

    34×1,200,000=3×1,200,0004=3×300,000=900,000\frac{3}{4} \times 1,200,000 = \frac{3 \times 1,200,000}{4} = 3 \times 300,000 = 900,000

    The amount is 900,000\boxed{\text{900,000}}.

Part e· 2 steps

What is 1112\frac{11}{12} of the total amount?

  1. Calculate the fraction of the total amount.

    1112×1,200,000\frac{11}{12} \times 1,200,000
  2. Multiply.

    11×(1,200,00012)=11×100,000=1,100,00011 \times \left(\frac{1,200,000}{12}\right) = 11 \times 100,000 = 1,100,000

    The amount is 1,100,000\boxed{\text{1,100,000}}.

    12. What percentage of the circle is red?

    • Top-left circle: The circle is divided into 4 equal parts. 1 of these parts is red. Fraction red: 14\frac{1}{4} Percentage red: 14×100%=25%\frac{1}{4} \times 100\% = \boxed{\text{25\%}}

    • Top-right circle: The circle is divided into 2 equal parts. 1 of these parts is red. Fraction red: 12\frac{1}{2} Percentage red: 12×100%=50%\frac{1}{2} \times 100\% = \boxed{\text{50\%}}

    • Bottom-left circle: The circle is divided into 4 equal parts. 3 of these parts are red. Fraction red: 34\frac{3}{4} Percentage red: 34×100%=75%\frac{3}{4} \times 100\% = \boxed{\text{75\%}}

    • Bottom-right circle: The circle is divided into 4 equal parts. 0 of these parts are red (all parts are white). Fraction red: 04=0\frac{0}{4} = 0 Percentage red: 0×100%=0%0 \times 100\% = \boxed{\text{0\%}}

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