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: 3. Write a sum for the number lines below and calculate the answers. b) Step 1: Identify the fraction represented by each segment on the number line. The line from 0 to 1 is divided into 4 equal parts, so each part is (1)/(4). Step 2: Identify the first jump. It covers 2 parts, so it represents (2)/(4). Step 3: Identify the second jump. It covers 1 part, so it represents (1)/(4). Step 4: Write the sum and calculate the answer. (2)/(4) + (1)/(4) = (3)/(4) The sum is (2)/(4) + (1)/(4) = (3)/(4). c) Step 1: Identify the fraction represented by each segment on the number line. The line from 0 to 1 is divided into 3 equal parts, so each part is (1)/(3). Step 2: Identify the first jump. It covers 1 part, so it represents (1)/(3). Step 3: Identify the second jump. It covers 1 part, so it represents (1)/(3). Step 4: Write the sum and calculate the answer. (1)/(3) + (1)/(3) = (2)/(3) The sum is (1)/(3) + (1)/(3) = (2)/(3). d) Step 1: Identify the fraction represented by each segment on the number line. The line from 0 to 1 is divided into 5 equal parts, so each part is (1)/(5). Step 2: Identify the first jump. It covers 2 parts, so it represents (2)/(5). Step 3: Identify the second jump. It covers 2 parts, so it represents (2)/(5). Step 4: Write the sum and calculate the answer. (2)/(5) + (2)/(5) = (4)/(5) The sum is (2)/(5) + (2)/(5) = (4)/(5). e) Step 1: Identify the fraction represented by each segment on the number line. The line from 0 to 1 is divided into 6 equal parts, so each part is (1)/(6). Step 2: Identify the first jump. It covers 3 parts, so it represents (3)/(6). Step 3: Identify the second jump. It covers 2 parts, so it represents (2)/(6). Step 4: Write the sum and calculate the answer. (3)/(6) + (2)/(6) = (5)/(6) The sum is (3)/(6) + (2)/(6) = (5)/(6). 4. Draw number lines for the following sums. a) (1)/(4) + (2)/(4) = Step 1: Calculate the sum. (1)/(4) + (2)/(4) = (3)/(4) Step 2: Draw a number line from 0 to 1, divided into 4 equal segments. Mark the points (1)/(4), (2)/(4), (3)/(4), and 1 (or (4)/(4)). Step 3: Draw an arrow starting from 0 and ending at (1)/(4). Step 4: Draw a second arrow starting from (1)/(4) and extending (2)/(4) more, ending at (3)/(4). The number line should look like this: ` 0 ---|---|---|---|--- 1 1/4 2/4 3/4 <-----> (1/4) <-----> (2/4) ` The answer is (3)/(4). b) (1)/(2) + (1)/(4) = Step 1: Find a common denominator and calculate the sum. The common denominator for 2 and 4 is 4. (1)/(2) = (2)/(4) (2)/(4) + (1)/(4) = (3)/(4) Step 2: Draw a number line from 0 to 1, divided into 4 equal segments. Mark the points (1)/(4), (2)/(4) (or (1)/(2)), (3)/(4), and 1 (or (4)/(4)). Step 3: Draw an arrow starting from 0 and ending at (2)/(4) (which is (1)/(2)). Step 4: Draw a second arrow starting from (2)/(4) and extending (1)/(4) more, ending at (3)/(4). The number line should look like this: ` 0 ---|---|---|---|--- 1 1/4 2/4 3/4 <---------> (1/2 or 2/4) <---> (1/4) ` The answer is (3)/(4). Problem solving: A chocolate cake is cut into 30 pieces. If a fifth has been eaten, how many pieces are left? Step 1: Calculate the number of pieces eaten. Pieces eaten = (1)/(5) × 30 Pieces eaten = (30)/(5) = 6 Step 2: Calculate the number of pieces left. Pieces left = Total pieces - Pieces eaten Pieces left = 30 - 6 = 24 There are 24 pieces left. That's 2 down. 3 left today — send the next one.