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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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22 stepsHere are the solutions to the questions:
First, we establish the conversion factors based on the given information:
From 2.a, we know that .
This means .
Also, we know that .
2. Fill in the blanks:
- a. Four cups = 1000 ml. (Given)
- b. Four cups = ____ litre.
Convert cups to milliliters.
$$ 4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml} $$Convert milliliters to litres.
$$ 1000 \text{ ml} = 1 \text{ litre} $$ So, four cups = $\boxed{\text{1}}$ litre.- c. One cup is ____ of a litre.
Convert one cup to milliliters.
$$ 1 \text{ cup} = 250 \text{ ml} $$Express this as a fraction of a litre ().
$$ \frac{250 \text{ ml}}{1000 \text{ ml}} = \frac{1}{4} $$ So, one cup is $\boxed{\frac{1}{4}}$ of a litre.- d. Two cups are ____ of a litre.
Convert two cups to milliliters.
$$ 2 \text{ cups} = 2 \times 250 \text{ ml} = 500 \text{ ml} $$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.
Convert three cups to milliliters.
$$ 3 \text{ cups} = 3 \times 250 \text{ ml} = 750 \text{ ml} $$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.
Convert four cups to milliliters.
$$ 4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml} $$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 ____ of a litre.
Convert both quantities to milliliters.
$$ 3 \text{ cups} = 3 \times 250 \text{ ml} = 750 \text{ ml} $$ $$ \frac{1}{2} \text{ of a litre} = \frac{1}{2} \times 1000 \text{ ml} = 500 \text{ ml} $$Compare the values.
$$ 750 \text{ ml} > 500 \text{ ml} $$ So, 3 cups $\boxed{>}$ $\frac{1}{2}$ of a litre.- b. of a litre ____ 4 cups.
Convert both quantities to milliliters.
$$ \frac{1}{4} \text{ of a litre} = \frac{1}{4} \times 1000 \text{ ml} = 250 \text{ ml} $$ $$ 4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml} $$Compare the values.
$$ 250 \text{ ml} < 1000 \text{ ml} $$ So, $\frac{1}{4}$ of a litre $\boxed{<}$ 4 cups.- c. 4 cups ____ 1 litre.
Convert both quantities to milliliters.
$$ 4 \text{ cups} = 4 \times 250 \text{ ml} = 1000 \text{ ml} $$ $$ 1 \text{ litre} = 1000 \text{ ml} $$Compare the values.
$$ 1000 \text{ ml} = 1000 \text{ ml} $$ So, 4 cups $\boxed{=}$ 1 litre.- d. 1 cup ____ of a litre.
Convert both quantities to milliliters.
$$ 1 \text{ cup} = 250 \text{ ml} $$ $$ \frac{1}{4} \text{ of a litre} = \frac{1}{4} \times 1000 \text{ ml} = 250 \text{ ml} $$Compare the values.
$$ 250 \text{ ml} = 250 \text{ ml} $$ So, 1 cup $\boxed{=}$ $\frac{1}{4}$ of a litre.- e. 2 cups ____ 500 ml.
Convert cups to milliliters.
$$ 2 \text{ cups} = 2 \times 250 \text{ ml} = 500 \text{ ml} $$Compare the values.
$$ 500 \text{ ml} = 500 \text{ ml} $$ So, 2 cups $\boxed{=}$ 500 ml.- f. 2 cups ____ of a litre.
Convert both quantities to milliliters.
$$ 2 \text{ cups} = 2 \times 250 \text{ ml} = 500 \text{ ml} $$ $$ \frac{1}{4} \text{ of a litre} = \frac{1}{4} \times 1000 \text{ ml} = 250 \text{ ml} $$Compare the values.
$$ 500 \text{ ml} > 250 \text{ ml} $$ So, 2 cups $\boxed{>}$ $\frac{1}{4}$ of a litre.
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