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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Step 1: Round the amount of money to the nearest ten. Ksh. 995 rounded to the nearest ten is Ksh. 1000. Step 2: Round the number of grandchildren to the nearest ten. 8 grandchildren rounded to the nearest ten is 10 grandchildren. Step 3: Divide the rounded money by the rounded number of grandchildren. (1000)/(10) = 100 Each grandchild would get Ksh. 100. The amount each grandchild got is Ksh. 100. Step 1: Perform multiplication first according to DMAS (Division, Multiplication, Addition, Subtraction). 20 + 5 × 8 - 20 + 30 20 + 40 - 20 + 30 Step 2: Perform addition and subtraction from left to right. (20 + 40) - 20 + 30 60 - 20 + 30 (60 - 20) + 30 40 + 30 70 The result is 70. 1. To find an equivalent fraction for (1)/(2), multiply the numerator and denominator by the same non-zero number. Let's multiply by 2. (1 × 2)/(2 × 2) = (2)/(4) An equivalent fraction is (2)/(4). 2. To find an equivalent fraction for (2)/(3), multiply the numerator and denominator by the same non-zero number. Let's multiply by 2. (2 × 2)/(3 × 2) = (4)/(6) An equivalent fraction is (4)/(6). 3. To find the simplest form of (8)/(16), divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 8 and 16 is 8. (8 ÷ 8)/(16 ÷ 8) = (1)/(2) The simplest form is (1)/(2). Step 1: Find the fraction of girls. The total fraction of students is 1. Fraction of boys = (24)/(50). Fraction of girls = 1 - (24)/(50) = (50)/(50) - (24)/(50) = (26)/(50). Step 2: Simplify the fraction of girls. To simplify (26)/(50), divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 26 and 50 is 2. (26 ÷ 2)/(50 ÷ 2) = (13)/(25) The fraction of girls in its simplest form is (13)/(25). Step 1: Compare the fractions for avocados and mangoes. Avocados: (2)/(5) Mangoes: (1)/(7) Step 2: Find a common denominator to compare the fractions. The least common multiple (LCM) of 5 and 7 is 35. Convert (2)/(5): (2)/(5) = (2 × 7)/(5 × 7) = (14)/(35) Convert (1)/(7): (1)/(7) = (1 × 5)/(7 × 5) = (5)/(35) Step 3: Compare the equivalent fractions. Since (14)/(35) > (5)/(35), avocados are more than mangoes. The fruits that are more are avocados. Step 1: List the fractions: (2)/(3), (1)/(6), (1)/(2), (1)/(8). Step 2: Find a common denominator for all fractions. The least common multiple (LCM) of 3, 6, 2, and 8 is 24. Step 3: Convert each fraction to an equivalent fraction with a denominator of 24. (2)/(3) = (2 × 8)/(3 × 8) = (16)/(24) (1)/(6) = (1 × 4)/(6 × 4) = (4)/(24) (1)/(2) = (1 × 12)/(2 × 12) = (12)/(24) (1)/(8) = (1 × 3)/(8 × 3) = (3)/(24) Step 4: Arrange the fractions from largest to smallest based on their numerators. The numerators are 16, 4, 12, 3. In descending order: 16, 12, 4, 3. Step 5: Write the original fractions in order from largest to smallest. (2)/(3), (1)/(2), (1)/(6), (1)/(8) Step 1: List the portions of work done by each learner: John: (3)/(8) Agnes: (7)/(12) Patel: (4)/(6) Otieno: (5)/(12) Step 2: Simplify any fractions if possible. Patel: (4)/(6) = (4 ÷ 2)/(6 ÷ 2) = (2)/(3). Step 3: Find a common denominator for the fractions: (3)/(8), (7)/(12), (2)/(3), (5)/(12). The least common multiple (LCM) of 8, 12, and 3 is 24. Step 4: Convert each fraction to an equivalent fraction with a denominator of 24. John: (3)/(8) = (3 × 3)/(8 × 3) = (9)/(24) Agnes: (7)/(12) = (7 × 2)/(12 × 2) = (14)/(24) Patel: (2)/(3) = (2 × 8)/(3 × 8) = (16)/(24) Otieno: (5)/(12) = (5 × 2)/(12 × 2) = (10)/(24) Step 5: Arrange the fractions from smallest to largest based on their numerators. The numerators are 9, 14, 16, 10. In ascending order: 9, 10, 14, 16. Step 6: Write the learners' names with their original fractions in order from smallest to largest. John ((3)/(8)), Otieno ((5)/(12)), Agnes ((7)/(12)), Patel ((4)/(6)) Send me the next one 📸