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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b) Step 1: Convert mixed numbers to improper fractions or add whole numbers and fractions separately. 3(3)/(5) + 1(2)/(5) = (3+1) + ((3)/(5) + (2)/(5)) Step 2: Add the whole numbers and the fractions. 4 + (3+2)/(5) = 4 + (5)/(5) Step 3: Simplify the fraction. 4 + 1 = 5 The answer is 5. c) Step 1: Rewrite the subtraction of a negative number as addition. 14 - (-26) = 14 + 26 Step 2: Perform the addition. 14 + 26 = 40 The answer is 40. d) Step 1: Multiply the numbers as if they were integers. 357 × 27 = 9639 Step 2: Count the total number of decimal places in the original numbers (3 in 0.357 and 1 in 2.7, for a total of 4). Step 3: Place the decimal point in the product. 0.357 × 2.7 = 0.9639 The answer is 0.9639. e) Step 1: Perform the operation inside the parentheses first. 60 - 84 = -24 Step 2: Substitute the result back into the expression. -17 - (-24) Step 3: Rewrite the subtraction of a negative number as addition. -17 + 24 Step 4: Perform the addition. -17 + 24 = 7 The answer is 7. f) Step 1: Convert the mixed number to an improper fraction. 6(2)/(3) = ((6 × 3) + 2)/(3) = (18 + 2)/(3) = (20)/(3) Step 2: Find a common denominator for the fractions (20)/(3) and (1)/(8). The least common multiple of 3 and 8 is 24. Step 3: Convert both fractions to have the common denominator. (20)/(3) = (20 × 8)/(3 × 8) = (160)/(24) (1)/(8) = (1 × 3)/(8 × 3) = (3)/(24) Step 4: Perform the subtraction. (160)/(24) - (3)/(24) = (160 - 3)/(24) = (157)/(24) Step 5: Convert the improper fraction back to a mixed number. 157 ÷ 24 = 6 with a remainder of 13 So, (157)/(24) = 6(13)/(24). The answer is 6(13)/(24). g) Step 1: Perform the division. 130.2 ÷ 62 Step 2: Divide 130 by 62. 130 ÷ 62 = 2 with a remainder of 6 Step 3: Bring down the 2 after the decimal point. 62 ÷ 62 = 1 Step 4: Place the decimal point in the quotient. 130.2 ÷ 62 = 2.1 The answer is 2.1. h) Step 1: Multiply 403 by 2. 403 × 2 = 806 Step 2: Multiply 403 by 40. 403 × 40 = 16120 Step 3: Add the results from Step 1 and Step 2. 806 + 16120 = 16926 The answer is 16926. i) Step 1: Add the whole numbers. 9 + 16 = 25 Step 2: Add the fractions. Since they have the same denominator, add the numerators. (4)/(6) + (2)/(6) = (4+2)/(6) = (6)/(6) Step 3: Simplify the fraction. (6)/(6) = 1 Step 4: Add the results from Step 1 and Step 3. 25 + 1 = 26 The answer is 26. j) Step 1: Perform the division. 3857 ÷ 19 Step 2: Divide 38 by 19. 38 ÷ 19 = 2 Step 3: Bring down 5. 5 ÷ 19 = 0 with a remainder of 5. Step 4: Bring down 7. 57 ÷ 19 = 3. 3857 ÷ 19 = 203 The answer is 203. 2. a) Step 1: Identify the range for the number: greater than 160 and smaller than 180. Step 2: List multiples of 17 until one falls within the specified range. 17 × 9 = 153 17 × 10 = 170 17 × 11 = 187 Step 3: Select the multiple that is between 160 and 180. The number is 170. 2. b) Step 1: List all integers between 20 and 45. 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 Step 2: Identify prime numbers (numbers greater than 1 that have no positive divisors other than 1 and themselves) from the list. • 23 (prime) • 29 (prime) • 31 (prime) • 37 (prime) • 41 (prime) • 43 (prime) Step 3: Count the identified prime numbers. There are 6 prime numbers between 20 and 45. The answer is 6. 3 done, 2 left today. You're making progress.