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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2.3 Step 1: Calculate the total fraction of salary spent on rent and petrol. Total spent = (1)/(2) + (2)/(5) To add these fractions, find a common denominator, which is 10. (1)/(2) + (2)/(5) = (1 × 5)/(2 × 5) + (2 × 2)/(5 × 2) = (5)/(10) + (4)/(10) = (5+4)/(10) = (9)/(10) Step 2: Calculate the fraction of salary left. The total salary is represented by 1. Fraction left = 1 - (9)/(10) = (10)/(10) - (9)/(10) = (1)/(10) The fraction left for food and other necessities is (1)/(10). 3.1.1 To arrange the decimal numbers 1,008; 1,8; 1,08; 1,75; 1,88 in descending order, compare them from largest to smallest. Comparing the numbers: 1,88 (largest) 1,8 1,75 1,08 1,008 (smallest) The numbers in descending order are: 1,88; 1,8; 1,75; 1,08; 1,008. 3.1.2 Compare 0,9 and 0,900. Adding zeros to the end of a decimal number does not change its value. 0,9 = 0,90 = 0,900 Therefore, 0,9 = 0,900. 3.2 Convert (2)/(5) to a decimal fraction. To convert a fraction to a decimal, divide the numerator by the denominator. (2)/(5) = 2 ÷ 5 = 0,4 The decimal fraction is 0,4. 3.3 Round off 74,153 to two decimal places. The first two decimal places are 15. The digit in the third decimal place is 3. Since 3 is less than 5, we round down (keep the second decimal place as it is). 74,153 ≈ 74,15 Rounded to two decimal places, the number is 74,15. 3.4 a) Calculate 2,5 + 16,23. Align the decimal points and add. 2,50 + 16,23 18,73 The sum is 18,73. 3.4 b) Calculate 9,51 - (2,1 + 1,05). Step 1: Perform the addition inside the parentheses first. 2,1 + 1,05 = 3,15 Step 2: Perform the subtraction. 9,51 - 3,15 9,51 3,15 6,36 The result is 6,36.