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 for the fractions questions: 1. Write an equivalent fraction for each of the following: a) To find an equivalent fraction for (1)/(2), we can multiply the numerator and denominator by 2. (1)/(2) = (1 × 2)/(2 × 2) = (2)/(4) b) To find an equivalent fraction for (2)/(6), we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 2. (2)/(6) = (2 ÷ 2)/(6 ÷ 2) = (1)/(3) c) To find an equivalent fraction for (4)/(6), we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 2. (4)/(6) = (4 ÷ 2)/(6 ÷ 2) = (2)/(3) d) To find an equivalent fraction for (1)/(3), we can multiply the numerator and denominator by 2. (1)/(3) = (1 × 2)/(3 × 2) = (2)/(6) e) The fraction (2)/(2) represents a whole. (2)/(2) = 1 f) To find an equivalent fraction for (3)/(6), we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 3. (3)/(6) = (3 ÷ 3)/(6 ÷ 3) = (1)/(2) g) To find an equivalent fraction for (2)/(3), we can multiply the numerator and denominator by 2. (2)/(3) = (2 × 2)/(3 × 2) = (4)/(6) h) The fraction (6)/(6) represents a whole. (6)/(6) = 1 i) To find an equivalent fraction for (1)/(3), we can multiply the numerator and denominator by 2. (1)/(3) = (1 × 2)/(3 × 2) = (2)/(6) j) To find an equivalent fraction for (2)/(3), we can multiply the numerator and denominator by 2. (2)/(3) = (2 × 2)/(3 × 2) = (4)/(6) k) To find an equivalent fraction for (1)/(2), we can multiply the numerator and denominator by 2. (1)/(2) = (1 × 2)/(2 × 2) = (2)/(4) l) To find an equivalent fraction for (5)/(6), we can multiply the numerator and denominator by 2. (5)/(6) = (5 × 2)/(6 × 2) = (10)/(12) 2. Fill in <, > or =: a) Compare (1)/(2) and (1)/(3). To compare, convert to a common denominator of 6: (1)/(2) = (3)/(6) and (1)/(3) = (2)/(6). (3)/(6) > (2)/(6) (1)/(2) > (1)/(3) b) Compare (1)/(2) and (1)/(6). To compare, convert to a common denominator of 6: (1)/(2) = (3)/(6). (3)/(6) > (1)/(6) (1)/(2) > (1)/(6) c) Compare (1)/(3) and (3)/(6). To compare, convert to a common denominator of 6: (1)/(3) = (2)/(6). (2)/(6) < (3)/(6) (1)/(3) < (3)/(6) d) Compare (1)/(2) and (2)/(3). To compare, convert to a common denominator of 6: (1)/(2) = (3)/(6) and (2)/(3) = (4)/(6). (3)/(6) < (4)/(6) (1)/(2) < (2)/(3) e) Compare (2)/(3) and (1)/(6). To compare, convert to a common denominator of 6: (2)/(3) = (4)/(6). (4)/(6) > (1)/(6) (2)/(3) > (1)/(6) f) Compare (5)/(6) and (2)/(3). To compare, convert to a common denominator of 6: (2)/(3) = (4)/(6). (5)/(6) > (4)/(6) (5)/(6) > (2)/(3) g) Compare (2)/(3) and (6)/(6). Simplify (6)/(6) = 1. (2)/(3) < 1 (2)/(3) < (6)/(6) h) Compare (1)/(3) and (4)/(6). To compare, convert to a common denominator of 6: (1)/(3) = (2)/(6). (2)/(6) < (4)/(6) (1)/(3) < (4)/(6) i) Compare (1)/(6) and (2)/(6). The denominators are already the same. (1)/(6) < (2)/(6) (1)/(6) < (2)/(6) j) Compare (1)/(2) and (3)/(3). Simplify (3)/(3) = 1. (1)/(2) < 1 (1)/(2) < (3)/(3) k) Compare (1)/(2) and (1)/(6). To compare, convert to a common denominator of 6: (1)/(2) = (3)/(6). (3)/(6) > (1)/(6) (1)/(2) > (1)/(6) What's next?