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: 1. Fill in >, <, or =. a) Compare (1)/(3) and (1)/(4). Step 1: Find a common denominator for 3 and 4, which is 12. (1)/(3) = (1 × 4)/(3 × 4) = (4)/(12) (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) Step 2: Compare the new fractions. Since 4 > 3, then (4)/(12) > (3)/(12). Therefore, (1)/(3) > (1)/(4). The answer is >. b) Compare (2)/(5) and (3)/(6). Step 1: Simplify (3)/(6) to (1)/(2). Step 2: Find a common denominator for 5 and 2, which is 10. (2)/(5) = (2 × 2)/(5 × 2) = (4)/(10) (1)/(2) = (1 × 5)/(2 × 5) = (5)/(10) Step 3: Compare the new fractions. Since 4 < 5, then (4)/(10) < (5)/(10). Therefore, (2)/(5) < (3)/(6). The answer is <. c) Compare (4)/(7) and (2)/(5). Step 1: Find a common denominator for 7 and 5, which is 35. (4)/(7) = (4 × 5)/(7 × 5) = (20)/(35) (2)/(5) = (2 × 7)/(5 × 7) = (14)/(35) Step 2: Compare the new fractions. Since 20 > 14, then (20)/(35) > (14)/(35). Therefore, (4)/(7) > (2)/(5). The answer is >. d) Compare (3)/(6) and (2)/(4). Step 1: Simplify both fractions. (3)/(6) = (1)/(2) (2)/(4) = (1)/(2) Step 2: Compare the simplified fractions. Since both are equal to (1)/(2). Therefore, (3)/(6) = (2)/(4). The answer is =. e) Compare (2)/(8) and (1)/(4). Step 1: Simplify (2)/(8). (2)/(8) = (1)/(4) Step 2: Compare the simplified fraction with (1)/(4). Since both are equal to (1)/(4). Therefore, (2)/(8) = (1)/(4). The answer is =. f) Compare (1)/(3) and (3)/(5). Step 1: Find a common denominator for 3 and 5, which is 15. (1)/(3) = (1 × 5)/(3 × 5) = (5)/(15) (3)/(5) = (3 × 3)/(5 × 3) = (9)/(15) Step 2: Compare the new fractions. Since 5 < 9, then (5)/(15) < (9)/(15). Therefore, (1)/(3) < (3)/(5). The answer is <. 2. What fractions are shown by the arrow? a) The number line is divided into 4 equal parts between 0 and 1. Each part represents (1)/(4). The arrow points to the second mark. (2)/(4) = (1)/(2) The fraction is (1)/(2). b) The number line is divided into 4 equal parts between 1 and 2. Each part represents (1)/(4). The arrow points to the second mark after 1. 1 + (2)/(4) = 1 + (1)/(2) = (3)/(2) The fraction is (3)/(2). c) The number line is divided into 4 equal parts between 4 and 5. Each part represents (1)/(4). The arrow points to the third mark after 4. 4 + (3)/(4) = (16)/(4) + (3)/(4) = (19)/(4) The fraction is (19)/(4). d) The number line is divided into 4 equal parts between 5 and 6. Each part represents (1)/(4). The arrow points to the second mark after 5. 5 + (2)/(4) = 5 + (1)/(2) = (11)/(2) The fraction is (11)/(2). Send me the next one 📸