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Which jug holds more: A or B?

Mathematics

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2. d) An Olympic size swimming pool holds about

  1. Convert all options to a common unit, such as litres (ℓ\ell).

    • i) 20000 ml=20000×11000ℓ=20ℓ20000 \text{ ml} = 20000 \times \frac{1}{1000} \ell = 20 \ell
    • ii) 20000ℓ20000 \ell
    • iii) 2000 kl=2000×1000ℓ=2000000ℓ2000 \text{ kl} = 2000 \times 1000 \ell = 2000000 \ell
  2. Compare with the typical volume of an Olympic swimming pool, which is approximately 2.5 millionℓ2.5 \text{ million} \ell (2500 m32500 \text{ m}^3).

  3. The closest option is 2000000ℓ2000000 \ell.

    The correct option is iii).

    2000 kl\boxed{2000 \text{ kl}}

    2. e) How can you check each of your answers?
    You can check by researching the standard capacities of these items (teaspoon, bucket, bath, Olympic pool) and converting units to ensure consistency.

    3. Jug A

    a) Does jug A hold more or less than 1 litre?

  4. The top mark of Jug A is 500.

    Assuming the units are millilitres (ml), as is common for measuring jugs.

  5. Convert 1 litre to millilitres

    1 litre=1000 ml1 \text{ litre} = 1000 \text{ ml}.

  6. Compare 500 ml500 \text{ ml} with 1000 ml1000 \text{ ml}.

    Jug A holds less than 1 litre.

    Less than 1 litre\boxed{\text{Less than 1 litre}}

    b) How much can jug A hold, if you fill it to the top mark?
    The top mark on Jug A is 500.

    500 ml\boxed{500 \text{ ml}}

    c) What does each mark in between the numbers show?

  7. Observe the numbered marks, e.g., 100 and 200.

    The difference is 200−100=100 ml200 - 100 = 100 \text{ ml}.

  8. Count the number of intervals between these two numbered marks.

    There are 5 intervals.

  9. Divide the difference by the number of intervals

    100 ml5=20 ml\frac{100 \text{ ml}}{5} = 20 \text{ ml}.
    Each mark shows 20 ml.

    20 ml\boxed{20 \text{ ml}}

    d) About how much milk is in the jug?

  10. The milk level is above 200 ml200 \text{ ml}.

  11. Count the number of small marks above 200 ml200 \text{ ml}.

    The milk level is at the second mark above 200 ml200 \text{ ml}.

  12. Multiply the number of marks by the value of each mark

    2×20 ml=40 ml2 \times 20 \text{ ml} = 40 \text{ ml}.

  13. Add this to the 200 ml200 \text{ ml} mark

    200 ml+40 ml=240 ml200 \text{ ml} + 40 \text{ ml} = 240 \text{ ml}.
    There is about 240 ml of milk in Jug A.

    240 ml\boxed{240 \text{ ml}}

    3. Jug B

    a) Does jug B hold more or less than 1 litre?

  14. The top mark of Jug B is 1000.

    Assuming the units are millilitres (ml).

  15. Convert 1 litre to millilitres

    1 litre=1000 ml1 \text{ litre} = 1000 \text{ ml}.

  16. Compare 1000 ml1000 \text{ ml} with 1000 ml1000 \text{ ml}.

    Jug B holds exactly 1 litre.

    Exactly 1 litre\boxed{\text{Exactly 1 litre}}

    b) How much can this jug hold, if you fill it to the top mark?
    The top mark on Jug B is 1000.

    1000 ml\boxed{1000 \text{ ml}}

    c) What does each mark in between the numbers show?

  17. Observe the numbered marks, e.g., 200 and 400.

    The difference is 400−200=200 ml400 - 200 = 200 \text{ ml}.

  18. Count the number of intervals between these two numbered marks.

    There are 5 intervals.

  19. Divide the difference by the number of intervals

    200 ml5=40 ml\frac{200 \text{ ml}}{5} = 40 \text{ ml}.
    Each mark shows 40 ml.

    40 ml\boxed{40 \text{ ml}}

    d) About how much milk is in the jug?

  20. The milk level is above 200 ml200 \text{ ml}.

  21. Count the number of small marks above 200 ml200 \text{ ml}.

    The milk level is at the first mark above 200 ml200 \text{ ml}.

  22. Multiply the number of marks by the value of each mark

    1×40 ml=40 ml1 \times 40 \text{ ml} = 40 \text{ ml}.

  23. Add this to the 200 ml200 \text{ ml} mark

    200 ml+40 ml=240 ml200 \text{ ml} + 40 \text{ ml} = 240 \text{ ml}.
    There is about 240 ml of milk in Jug B.

    240 ml\boxed{240 \text{ ml}}

    Which jug holds more: A or B?

  24. Jug A holds 500 ml500 \text{ ml} to its top mark.

  25. Jug B holds 1000 ml1000 \text{ ml} to its top mark.

  26. Compare the maximum capacities

    1000 ml>500 ml1000 \text{ ml} > 500 \text{ ml}.
    Jug B holds more.

    Jug B\boxed{\text{Jug B}}
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