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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Welcome back — missed you this week. Here are the solutions to the problems: Question 8: a) Step 1: Perform the subtraction. 26 - 42 = -16 Step 2: Perform the addition. -16 + 19 = 3 The answer is 3. b) Step 1: Perform the multiplication. 34 × 12 = 408 Step 2: Perform the additions from left to right. 408 + 3 = 411 411 + 8 = 419 The answer is 419. c) Step 1: Perform the multiplication. 70 × 40 = 2800 Step 2: Perform the division. 2800 ÷ 8 = 350 Step 3: Perform the subtraction. 350 - 186 = 164 The answer is 164. Question 9: Estimate the answer by rounding off each number to the nearest ten. Step 1: Round 9476 to the nearest ten. The last digit is 6, so round up. 9476 ≈ 9480 Step 2: Round 29 to the nearest ten. The last digit is 9, so round up. 29 ≈ 30 Step 3: Perform the division with the rounded numbers. 9480 ÷ 30 = 316 The estimated answer is 316. Question 10: Estimate the amount of water used in one day by rounding off the numbers to the nearest ten. Step 1: Round the total litres of water (7643) to the nearest ten. The last digit is 3, so round down. 7643 ≈ 7640 Step 2: Round the number of days (147) to the nearest ten. The last digit is 7, so round up. 147 ≈ 150 Step 3: Divide the estimated total water by the estimated number of days. (7640)/(150) = (764)/(15) 764 ÷ 15 ≈ 50.93 Rounding to the nearest whole number for an estimate: 50.93 ≈ 51 The estimated amount of water used in one day is 51 litres. Question 1 (Fractions section): Find the least number of books that can be shared equally among 4 or 5 learners. This requires finding the Least Common Multiple (LCM) of 4 and 5. Step 1: List multiples of 4. 4, 8, 12, 16, 20, 24, Step 2: List multiples of 5. 5, 10, 15, 20, 25, Step 3: The least common multiple is 20. The least number of books is 20. Question 2: a) (4)/(9) + (3)/(9) Step 1: Add the numerators since the denominators are the same. (4+3)/(9) = (7)/(9) The answer is (7)/(9). b) (2)/(5) + (3)/(10) Step 1: Find a common denominator. The LCM of 5 and 10 is 10. Step 2: Convert (2)/(5) to an equivalent fraction with a denominator of 10. (2)/(5) = (2 × 2)/(5 × 2) = (4)/(10) Step 3: Add the fractions. (4)/(10) + (3)/(10) = (4+3)/(10) = (7)/(10) The answer is (7)/(10). c) (15)/(16) - (7)/(8) Step 1: Find a common denominator. The LCM of 16 and 8 is 16. Step 2: Convert (7)/(8) to an equivalent fraction with a denominator of 16. (7)/(8) = (7 × 2)/(8 × 2) = (14)/(16) Step 3: Subtract the fractions. (15)/(16) - (14)/(16) = (15-14)/(16) = (1)/(16) The answer is (1)/(16). d) (11)/(14) - (3)/(7) Step 1: Find a common denominator. The LCM of 14 and 7 is 14. Step 2: Convert (3)/(7) to an equivalent fraction with a denominator of 14. (3)/(7) = (3 × 2)/(7 × 2) = (6)/(14) Step 3: Subtract the fractions. (11)/(14) - (6)/(14) = (11-6)/(14) = (5)/(14) The answer is (5)/(14). Question 3: A traffic camera takes a photo every 4 minutes. Another camera takes a photo every 6 minutes. After how long will the two cameras take a photo together? This requires finding the Least Common Multiple (LCM) of 4 and 6. Step 1: List multiples of 4. 4, 8, 12, 16, 20, Step 2: List multiples of 6. 6, 12, 18, 24, Step 3: The least common multiple is 12. The two cameras will take a photo together after 12 minutes. Question 4: Khadija carried (7)/(8) litres of water to school. She took (1)/(2) litres of the water. How much water did she remain with? Step 1: Set up the subtraction problem. (7)/(8) - (1)/(2) Step 2: Find a common denominator. The LCM of 8 and 2 is 8. Step 3: Convert (1)/(2) to an equivalent fraction with a denominator of 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 4: Subtract the fractions. (7)/(8) - (4)/(8) = (7-4)/(8) = (3)/(8) Khadija remained with (3)/(8) litres of water. Send me the next one 📸