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Simplify an expression of mixed fractions with 'of', division and brackets (BODMAS, 'of' first)

This type of question, asked 4 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 26 Oct 2023 Tier II. All 8 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    21
    The value of [47 of 245×123−(312−216)]÷(315÷412 of 513)\left[\frac{4}{7} \text{ of } 2\frac{4}{5} \times 1\frac{2}{3} - \left(3\frac{1}{2} - 2\frac{1}{6}\right)\right] \div \left(3\frac{1}{5} \div 4\frac{1}{2} \text{ of } 5\frac{1}{3}\right) is:

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  2. Question 2

    15 Nov 2020 Tier II

    1
    The value of 3÷18 of 3×6+21×6÷18−3÷2+3−3÷9 of 3×93 \div 18 \text{ of } 3 \times 6 + 21 \times 6 \div 18 - 3 \div 2 + 3 - 3 \div 9 \text{ of } 3 \times 9 is:

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  3. Question 3

    29 Jan 2022 Tier II

    85
    Let x=534−37×1534+2235÷1112534÷514+535÷3415x = \frac{5\frac{3}{4} - \frac{3}{7} \times 15\frac{3}{4} + 2\frac{2}{35} \div 1\frac{11}{25}}{\frac{3}{4} \div 5\frac{1}{4} + 5\frac{3}{5} \div 3\frac{4}{15}}. When yy is added to xx, the result is 713\frac{7}{13}. What is the value of yy?

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  4. Question 4

    29 Jan 2022 Tier II

    46
    The value of (267 of 415÷23)×519÷(34×223 of 12÷14)\left(2\frac{6}{7} \text{ of } 4\frac{1}{5} \div \frac{2}{3}\right) \times 5\frac{1}{9} \div \left(\frac{3}{4} \times 2\frac{2}{3} \text{ of } \frac{1}{2} \div \frac{1}{4}\right) is:

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  5. Question 5

    29 Jan 2022 Tier II

    17
    The value of (113÷267 of 535)×(625÷412 of 513)÷(34×223÷59 of 115)=k\left(1\frac{1}{3} \div 2\frac{6}{7} \text{ of } 5\frac{3}{5}\right) \times \left(6\frac{2}{5} \div 4\frac{1}{2} \text{ of } 5\frac{1}{3}\right) \div \left(\frac{3}{4} \times 2\frac{2}{3} \div \frac{5}{9} \text{ of } 1\frac{1}{5}\right) = k, where k lies between:

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  6. Question 6

    3 Feb 2022 Tier II

    30
    The value of 9÷{12+13+14+16÷(34−13) of 29}9 \div \left\{\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6} \div \left(\frac{3}{4} - \frac{1}{3}\right) \text{ of } \frac{2}{9}\right\} is:

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  7. Question 7

    3 Feb 2022 Tier II

    57
    The value of 15÷8−54 of (83×916)+(98×34)−(532÷57)+3815 \div 8 - \frac{5}{4} \text{ of } \left(\frac{8}{3} \times \frac{9}{16}\right) + \left(\frac{9}{8} \times \frac{3}{4}\right) - \left(\frac{5}{32} \div \frac{5}{7}\right) + \frac{3}{8} is:

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  8. Question 8

    26 Oct 2023 Tier II

    18
    What is the value of [18+{16×(3645÷2425)−(1221×1415÷2445)}+2736]\left[\frac{1}{8} + \left\{\frac{1}{6} \times \left(\frac{36}{45} \div \frac{24}{25}\right) - \left(\frac{12}{21} \times \frac{14}{15} \div \frac{24}{45}\right)\right\} + \frac{27}{36}\right]?

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