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 fraction word problems: Problem 1: Mother bought (4)/(5) kg of fish and (7)/(10) kg of prawns. What is the total mass of seafood bought by mother in kg? Step 1: Identify the given masses. Mass of fish = (4)/(5) kg Mass of prawns = (7)/(10) kg Step 2: To find the total mass, add the two fractions. Total mass = (4)/(5) + (7)/(10) Step 3: Find the least common multiple (LCM) of the denominators 5 and 10, which is 10. Step 4: Convert (4)/(5) to an equivalent fraction with a denominator of 10. (4)/(5) = (4 × 2)/(5 × 2) = (8)/(10) Step 5: Add the fractions. (8)/(10) + (7)/(10) = (8+7)/(10) = (15)/(10) Step 6: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5. (15 ÷ 5)/(10 ÷ 5) = (3)/(2) The total mass of seafood bought is (3)/(2) kg. (3)/(2) kg Problem 2: Priscilla uses (3)/(8) kg of sugar to make biscuits and (1)/(2) kg of sugar to make cakes. Calculate the total mass of sugar used in kg. Step 1: Identify the given masses of sugar. Mass of sugar for biscuits = (3)/(8) kg Mass of sugar for cakes = (1)/(2) kg Step 2: To find the total mass, add the two fractions. Total mass = (3)/(8) + (1)/(2) Step 3: Find the LCM of the denominators 8 and 2, which is 8. Step 4: Convert (1)/(2) to an equivalent fraction with a denominator of 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 5: Add the fractions. (3)/(8) + (4)/(8) = (3+4)/(8) = (7)/(8) The total mass of sugar used is (7)/(8) kg. (7)/(8) kg That's 2 down. 3 left today — send the next one.