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) (1)/(3) (1)/(4) Step 1: Find a common denominator for (1)/(3) and (1)/(4), which is 12. (1)/(3) = (1 × 4)/(3 × 4) = (4)/(12) (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) Step 2: Compare the fractions. (4)/(12) > (3)/(12) So, (1)/(3) > (1)/(4). b) (3)/(5) (2)/(3) Step 1: Find a common denominator for (3)/(5) and (2)/(3), which is 15. (3)/(5) = (3 × 3)/(5 × 3) = (9)/(15) (2)/(3) = (2 × 5)/(3 × 5) = (10)/(15) Step 2: Compare the fractions. (9)/(15) < (10)/(15) So, (3)/(5) < (2)/(3). c) (4)/(7) (2)/(5) Step 1: Find a common denominator for (4)/(7) and (2)/(5), which is 35. (4)/(7) = (4 × 5)/(7 × 5) = (20)/(35) (2)/(5) = (2 × 7)/(5 × 7) = (14)/(35) Step 2: Compare the fractions. (20)/(35) > (14)/(35) So, (4)/(7) > (2)/(5). d) (1)/(6) (1)/(3) Step 1: Find a common denominator for (1)/(6) and (1)/(3), which is 6. (1)/(3) = (1 × 2)/(3 × 2) = (2)/(6) Step 2: Compare the fractions. (1)/(6) < (2)/(6) So, (1)/(6) < (1)/(3). e) (2)/(8) (1)/(4) Step 1: Simplify the fraction (2)/(8). (2)/(8) = (2 ÷ 2)/(8 ÷ 2) = (1)/(4) Step 2: Compare the fractions. (1)/(4) = (1)/(4) So, (2)/(8) = (1)/(4). f) (2)/(5) (3)/(10) Step 1: Find a common denominator for (2)/(5) and (3)/(10), which is 10. (2)/(5) = (2 × 2)/(5 × 2) = (4)/(10) Step 2: Compare the fractions. (4)/(10) > (3)/(10) So, (2)/(5) > (3)/(10). 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 third mark. The fraction is (3)/(4). 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. The fraction is 1 + (2)/(4) = 1 + (1)/(2) = (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. The fraction is 4 + (3)/(4) = (16)/(4) + (3)/(4) = (19)/(4). d) This part of the question is not visible in the image. 3 done, 2 left today. You're making progress.