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Fill in the blanks: a. Four cups = 1000 ml. b. Four cups = _ litre. c. One cup is of a litre. d. Two cups are of a litre. e. Three cups are _ of a litre.

Mathematics

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Here are the solutions to the questions:

First, we establish the conversion factors based on the given information:
From 2.a, we know that 4 cups=1000 ml4 \text{ cups} = 1000 \text{ ml}.
This means 1 cup=1000 ml4=250 ml1 \text{ cup} = \frac{1000 \text{ ml}}{4} = 250 \text{ ml}.
Also, we know that 1 litre=1000 ml1 \text{ litre} = 1000 \text{ ml}.

2. Fill in the blanks:

  • a. Four cups = 1000 ml. (Given)
  • b. Four cups = ____ litre.
  1. Convert cups to milliliters.

    $$
    4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml}
    $$
    
  2. Convert milliliters to litres.

    $$
    1000 \text{ ml} = 1 \text{ litre}
    $$
    So, four cups = $\boxed{\text{1}}$ litre.
    
    • c. One cup is ____ of a litre.
  3. Convert one cup to milliliters.

    $$
    1 \text{ cup} = 250 \text{ ml}
    $$
    
  4. Express this as a fraction of a litre (1 litre=1000 ml1 \text{ litre} = 1000 \text{ ml}).

    $$
    \frac{250 \text{ ml}}{1000 \text{ ml}} = \frac{1}{4}
    $$
    So, one cup is $\boxed{\frac{1}{4}}$ of a litre.
    
    • d. Two cups are ____ of a litre.
  5. Convert two cups to milliliters.

    $$
    2 \text{ cups} = 2 \times 250 \text{ ml} = 500 \text{ ml}
    $$
    
  6. Express this as a fraction of a litre.

    $$
    \frac{500 \text{ ml}}{1000 \text{ ml}} = \frac{1}{2}
    $$
    So, two cups are $\boxed{\frac{1}{2}}$ of a litre.
    
    • e. Three cups are ____ of a litre.
  7. Convert three cups to milliliters.

    $$
    3 \text{ cups} = 3 \times 250 \text{ ml} = 750 \text{ ml}
    $$
    
  8. Express this as a fraction of a litre.

    $$
    \frac{750 \text{ ml}}{1000 \text{ ml}} = \frac{3}{4}
    $$
    So, three cups are $\boxed{\frac{3}{4}}$ of a litre.
    
    • f. Four cups are ____ of a litre.
  9. Convert four cups to milliliters.

    $$
    4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml}
    $$
    
  10. Express this as a fraction of a litre.

    $$
    \frac{1000 \text{ ml}}{1000 \text{ ml}} = 1
    $$
    So, four cups are $\boxed{\text{1}}$ of a litre.
    

    3. Fill in <, > or =:

    • a. 3 cups ____ 12\frac{1}{2} of a litre.
  11. Convert both quantities to milliliters.

    $$
    3 \text{ cups} = 3 \times 250 \text{ ml} = 750 \text{ ml}
    $$
    $$
    \frac{1}{2} \text{ of a litre} = \frac{1}{2} \times 1000 \text{ ml} = 500 \text{ ml}
    $$
    
  12. Compare the values.

    $$
    750 \text{ ml} > 500 \text{ ml}
    $$
    So, 3 cups $\boxed{>}$ $\frac{1}{2}$ of a litre.
    
    • b. 14\frac{1}{4} of a litre ____ 4 cups.
  13. Convert both quantities to milliliters.

    $$
    \frac{1}{4} \text{ of a litre} = \frac{1}{4} \times 1000 \text{ ml} = 250 \text{ ml}
    $$
    $$
    4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml}
    $$
    
  14. Compare the values.

    $$
    250 \text{ ml} < 1000 \text{ ml}
    $$
    So, $\frac{1}{4}$ of a litre $\boxed{<}$ 4 cups.
    
    • c. 4 cups ____ 1 litre.
  15. Convert both quantities to milliliters.

    $$
    4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml}
    $$
    $$
    1 \text{ litre} = 1000 \text{ ml}
    $$
    
  16. Compare the values.

    $$
    1000 \text{ ml} = 1000 \text{ ml}
    $$
    So, 4 cups $\boxed{=}$ 1 litre.
    
    • d. 1 cup ____ 14\frac{1}{4} of a litre.
  17. Convert both quantities to milliliters.

    $$
    1 \text{ cup} = 250 \text{ ml}
    $$
    $$
    \frac{1}{4} \text{ of a litre} = \frac{1}{4} \times 1000 \text{ ml} = 250 \text{ ml}
    $$
    
  18. Compare the values.

    $$
    250 \text{ ml} = 250 \text{ ml}
    $$
    So, 1 cup $\boxed{=}$ $\frac{1}{4}$ of a litre.
    
    • e. 2 cups ____ 500 ml.
  19. Convert cups to milliliters.

    $$
    2 \text{ cups} = 2 \times 250 \text{ ml} = 500 \text{ ml}
    $$
    
  20. Compare the values.

    $$
    500 \text{ ml} = 500 \text{ ml}
    $$
    So, 2 cups $\boxed{=}$ 500 ml.
    
    • f. 2 cups ____ 14\frac{1}{4} of a litre.
  21. Convert both quantities to milliliters.

    $$
    2 \text{ cups} = 2 \times 250 \text{ ml} = 500 \text{ ml}
    $$
    $$
    \frac{1}{4} \text{ of a litre} = \frac{1}{4} \times 1000 \text{ ml} = 250 \text{ ml}
    $$
    
  22. Compare the values.

    $$
    500 \text{ ml} > 250 \text{ ml}
    $$
    So, 2 cups $\boxed{>}$ $\frac{1}{4}$ of a litre.
    
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