This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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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 ml. This means 1 cup = 1000 ml4 = 250 ml. Also, we know that 1 litre = 1000 ml. 2. Fill in the blanks: a. Four cups = 1000 ml. (Given) b. Four cups = ____ litre. Step 1: Convert cups to milliliters. 4 cups = 4 × 250 ml = 1000 ml Step 2: Convert milliliters to litres. 1000 ml = 1 litre So, four cups = 1 litre. c. One cup is ____ of a litre. Step 1: Convert one cup to milliliters. 1 cup = 250 ml Step 2: Express this as a fraction of a litre (1 litre = 1000 ml). 250 ml1000 ml = (1)/(4) So, one cup is (1)/(4) of a litre. d. Two cups are ____ of a litre. Step 1: Convert two cups to milliliters. 2 cups = 2 × 250 ml = 500 ml Step 2: Express this as a fraction of a litre. 500 ml1000 ml = (1)/(2) So, two cups are (1)/(2) of a litre. e. Three cups are ____ of a litre. Step 1: Convert three cups to milliliters. 3 cups = 3 × 250 ml = 750 ml Step 2: Express this as a fraction of a litre. 750 ml1000 ml = (3)/(4) So, three cups are (3)/(4) of a litre. f. Four cups are ____ of a litre. Step 1: Convert four cups to milliliters. 4 cups = 4 × 250 ml = 1000 ml Step 2: Express this as a fraction of a litre. 1000 ml1000 ml = 1 So, four cups are 1 of a litre. 3. Fill in <, > or =: a. 3 cups ____ (1)/(2) of a litre. Step 1: Convert both quantities to milliliters. 3 cups = 3 × 250 ml = 750 ml (1)/(2) of a litre = (1)/(2) × 1000 ml = 500 ml Step 2: Compare the values. 750 ml > 500 ml So, 3 cups > (1)/(2) of a litre. b. (1)/(4) of a litre ____ 4 cups. Step 1: Convert both quantities to milliliters. (1)/(4) of a litre = (1)/(4) × 1000 ml = 250 ml 4 cups = 4 × 250 ml = 1000 ml Step 2: Compare the values. 250 ml < 1000 ml So, (1)/(4) of a litre < 4 cups. c. 4 cups ____ 1 litre. Step 1: Convert both quantities to milliliters. 4 cups = 4 × 250 ml = 1000 ml 1 litre = 1000 ml Step 2: Compare the values. 1000 ml = 1000 ml So, 4 cups = 1 litre. d. 1 cup ____ (1)/(4) of a litre. Step 1: Convert both quantities to milliliters. 1 cup = 250 ml (1)/(4) of a litre = (1)/(4) × 1000 ml = 250 ml Step 2: Compare the values. 250 ml = 250 ml So, 1 cup = (1)/(4) of a litre. e. 2 cups ____ 500 ml. Step 1: Convert cups to milliliters. 2 cups = 2 × 250 ml = 500 ml Step 2: Compare the values. 500 ml = 500 ml So, 2 cups = 500 ml. f. 2 cups ____ (1)/(4) of a litre. Step 1: Convert both quantities to milliliters. 2 cups = 2 × 250 ml = 500 ml (1)/(4) of a litre = (1)/(4) × 1000 ml = 250 ml Step 2: Compare the values. 500 ml > 250 ml So, 2 cups > (1)/(4) of a litre. What's next? Send 'em! 📸