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.
ScanSolve AI Answer
Here are the solutions to the problems: h) (-48) × (-7) Step 1: Multiply the absolute values of the numbers. 48 × 7 = 336 Step 2: Determine the sign of the product. A negative number multiplied by a negative number results in a positive number. (-48) × (-7) = 336 The product is 336. i) 11(1)/(5) - 8(4)/(5) Step 1: Convert the mixed numbers to improper fractions. 11(1)/(5) = ((11 × 5) + 1)/(5) = (55 + 1)/(5) = (56)/(5) 8(4)/(5) = ((8 × 5) + 4)/(5) = (40 + 4)/(5) = (44)/(5) Step 2: Subtract the improper fractions. (56)/(5) - (44)/(5) = (56 - 44)/(5) = (12)/(5) Step 3: Convert the improper fraction back to a mixed number. (12)/(5) = 2(2)/(5) The difference is 2(2)/(5). j) 16.12 × 3.9 Step 1: Multiply the numbers as if they were whole numbers, ignoring the decimal points for now. 1612 × 39 Step 2: Perform the multiplication. 1612 \\ × 39 \\ 14508 & (1612 × 9) \\ 48360 & (1612 × 30) \\ 62868 Step 3: Count the total number of decimal places in the original numbers. 16.12 has 2 decimal places. 3.9 has 1 decimal place. Total decimal places = 2 + 1 = 3. Step 4: Place the decimal point in the product so that it has 3 decimal places. 62.868 The product is 62.868. SECTION B: a) Round off 90.361 to the nearest tenths. Step 1: Identify the digit in the tenths place, which is 3. Step 2: Look at the digit immediately to its right, which is 6. Step 3: Since 6 is 5 or greater, round up the tenths digit. The 3 in the tenths place becomes 4. 90.361 ≈ 90.4 The rounded number is 90.4. b) Write 10.014 in words. The number 10.014 is written as Ten and fourteen thousandths. c) Which number is expanded to get 30 + 8 + 900 + 7000 + 90000? Step 1: Arrange the terms in descending order of place value. 90000 + 7000 + 900 + 30 + 8 Step 2: Add the terms together. 90000 + 7000 = 97000 97000 + 900 = 97900 97900 + 30 = 97930 97930 + 8 = 97938 The number is 97938. d) How many prime numbers are there between 101 and 110? Step 1: List the integers between 101 and 110: 102, 103, 104, 105, 106, 107, 108, 109. Step 2: Identify prime numbers (numbers greater than 1 that have no positive divisors other than 1 and themselves). • 102 is even, so it's not prime. • 103: Not divisible by 2, 3, 5, 7, 11. It is a prime number. • 104 is even, so it's not prime. • 105 ends in 5, so it's not prime. • 106 is even, so it's not prime. • 107: Not divisible by 2, 3, 5, 7, 11. It is a prime number. • 108 is even, so it's not prime. • 109: Not divisible by 2, 3, 5, 7, 11. It is a prime number. The prime numbers between 101 and 110 are 103, 107, 109. There are 3 prime numbers. e) Write the place value of 6 in the number 96784. Step 1: Identify the position of the digit 6 in the number 96784. The digit 6 is in the thousands place. Step 2: Determine its value based on its position. The place value of 6 is 6 × 1000 = 6000. The place value of 6 is 6000. f) Which fraction is bigger between (2)/(3) and (3)/(4)? Step 1: Find a common denominator for the two fractions. The least common multiple of 3 and 4 is 12. Step 2: Convert each fraction to an equivalent fraction with the common denominator. (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) Step 3: Compare the numerators of the equivalent fractions. Since 9 > 8, it means (9)/(12) > (8)/(12). Therefore, (3)/(4) is bigger than (2)/(3). The bigger fraction is (3)/(4).