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 problems 25 and 26. Problem 25: a) Simplify: (1)/(5) + (3)/(5) + (2)/(5) Step 1: Add the numerators since the denominators are the same. (1)/(5) + (3)/(5) + (2)/(5) = (1+3+2)/(5) Step 2: Perform the addition. = (6)/(5) The simplified expression is (6)/(5). b) Arrange (2)/(3), (5)/(12) and (1)/(8) in ascending order. Step 1: Find the Least Common Multiple (LCM) of the denominators (3, 12, 8). The LCM of 3, 12, and 8 is 24. Step 2: Convert each fraction to an equivalent fraction with a denominator of 24. (2)/(3) = (2 × 8)/(3 × 8) = (16)/(24) (5)/(12) = (5 × 2)/(12 × 2) = (10)/(24) (1)/(8) = (1 × 3)/(8 × 3) = (3)/(24) Step 3: Compare the numerators and arrange the fractions in ascending order (smallest to largest). The numerators are 16, 10, and 3. In ascending order, they are 3, 10, 16. So, the fractions in ascending order are (3)/(24), (10)/(24), (16)/(24). Step 4: Write the fractions in their original form. (1)/(8), (5)/(12), (2)/(3) The fractions in ascending order are (1)/(8), (5)/(12), (2)/(3). Problem 26: Study the bill table below and complete it correctly. a) Complete the table. Step 1: Calculate the Amount for Sugar. Quantity = 3 kg Unit Cost = sh 4200 per kg Amount = Quantity × Unit Cost = 3 kg × sh 4200/kg = sh 12600. Step 2: Calculate the Quantity for Rice. Unit Cost = sh 4900 per kg Amount = sh 9800 Quantity = Amount / Unit Cost = sh 9800 / (sh 4900/kg) = 2 kg. Step 3: Calculate the Unit Cost for Salt. Quantity = 500 gm = 0.5 kg Amount = sh 800 Unit Cost = Amount / Quantity = sh 800 / 0.5 kg = sh 1600 per kg. Step 4: Calculate the Total Amount. Total Amount = Amount (Sugar) + Amount (Rice) + Amount (Salt) Total Amount = sh 12600 + sh 9800 + sh 800 = sh 23200. The completed table is: | ITEM | QUANTITY | UNIT COST | AMOUNT | | :--- | :------- | :---------- | :------- | | Sugar | 3 kg | sh 4200 per kg | sh 12600 | | Rice | 2 kg | sh 4900 per kg | sh 9800 | | Salt | 500 gm | sh 1600 per kg | sh 800 | | Total | | | sh 23200 | b) If Joseph was given a discount of sh 400, how much did he pay? Step 1: Identify the Total Amount and the Discount. Total Amount = sh 23200 Discount = sh 400 Step 2: Subtract the discount from the total amount. Amount Paid = Total Amount - Discount Amount Paid = sh 23200 - sh 400 = sh 22800. Joseph paid sh 22800. Last free one today — make it count tomorrow, or type /upgrade for unlimited.