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: 4. Step 1: Identify the initial amount of cake. The initial amount of cake in the fridge was (5)/(12). Step 2: Determine the fraction of the cake Alexis ate. Alexis ate (4)/(7) of the leftover cake, which is (5)/(12). To find out how much she ate, we multiply these fractions. Amount Alexis ate = (4)/(7) × (5)/(12) Step 3: Calculate the amount Alexis ate. (4)/(7) × (5)/(12) = (4 × 5)/(7 × 12) = (20)/(84) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. (20 ÷ 4)/(84 ÷ 4) = (5)/(21) Alexis had (5)/(21) of the original cake. The amount of cake Alexis had was (5)/(21). 5. This question asks about "donuts" but the context is about "meat pies". Assuming "donuts" is a typo and it should be "meat pies", we will calculate the number of meat pies Bookyeuwaa is left with. Step 1: Identify the total number of meat pies. Bookyeuwaa baked 542 meat pies. Step 2: Determine how many friends will be served. She planned to serve 7 friends equally. Step 3: Calculate the number of pies each friend receives and the remainder for Bookyeuwaa. We divide the total pies by the number of friends: 542 ÷ 7 542 = 7 × 77 + 3 This means each of the 7 friends will receive 77 meat pies, and there will be a remainder of 3 meat pies. Bookyeuwaa will be left with the remainder. Bookyeuwaa will be left with 3 meat pies. 6. Step 1: Find the quotient of 88,668 and 9. To find the quotient, we divide 88,668 by 9. 88,668 ÷ 9 = 9,852 The quotient of 88,668 and 9 is 9,852. 7a. Step 1: Simplify the fractions. The given expression is (4)/(5) + (3)/(9). The fraction (3)/(9) can be simplified by dividing both the numerator and the denominator by 3: (3)/(9) = (3 ÷ 3)/(9 ÷ 3) = (1)/(3) So the expression becomes: (4)/(5) + (1)/(3) Step 2: Find a common denominator. The least common multiple of 5 and 3 is 15. Convert each fraction to an equivalent fraction with a denominator of 15. For (4)/(5): (4)/(5) = (4 × 3)/(5 × 3) = (12)/(15) For (1)/(3): (1)/(3) = (1 × 5)/(3 × 5) = (5)/(15) Step 3: Add the fractions. Now add the fractions with the common denominator: (12)/(15) + (5)/(15) = (12 + 5)/(15) = (17)/(15) The fraction (17)/(15) can also be written as a mixed number: 1 (2)/(15) The simplified sum is (17)/(15) or 1 (2)/(15).