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
Fresh day Sharmadee, let's solve. Here are the solutions for adding the unlike fractions: 1. (1)/(2) + (2)/(3) Step 1: Find the least common multiple (LCM) of the denominators 2 and 3, which is 6. Step 2: Convert the fractions to equivalent fractions with the common denominator. (1)/(2) = (1 × 3)/(2 × 3) = (3)/(6) (2)/(3) = (2 × 2)/(3 × 2) = (4)/(6) Step 3: Add the new fractions. (3)/(6) + (4)/(6) = (3+4)/(6) = (7)/(6) (7)/(6) 2. (8)/(12) + (8)/(11) Step 1: Find the LCM of the denominators 12 and 11, which is 12 × 11 = 132. Step 2: Convert the fractions to equivalent fractions with the common denominator. (8)/(12) = (8 × 11)/(12 × 11) = (88)/(132) (8)/(11) = (8 × 12)/(11 × 12) = (96)/(132) Step 3: Add the new fractions. (88)/(132) + (96)/(132) = (88+96)/(132) = (184)/(132) Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. (184 ÷ 4)/(132 ÷ 4) = (46)/(33) (46)/(33) 3. (2)/(7) + (6)/(10) Step 1: Simplify (6)/(10) to (3)/(5). The problem becomes (2)/(7) + (3)/(5). Step 2: Find the LCM of the denominators 7 and 5, which is 7 × 5 = 35. Step 3: Convert the fractions to equivalent fractions with the common denominator. (2)/(7) = (2 × 5)/(7 × 5) = (10)/(35) (3)/(5) = (3 × 7)/(5 × 7) = (21)/(35) Step 4: Add the new fractions. (10)/(35) + (21)/(35) = (10+21)/(35) = (31)/(35) (31)/(35) 4. (1)/(6) + (6)/(11) Step 1: Find the LCM of the denominators 6 and 11, which is 6 × 11 = 66. Step 2: Convert the fractions to equivalent fractions with the common denominator. (1)/(6) = (1 × 11)/(6 × 11) = (11)/(66) (6)/(11) = (6 × 6)/(11 × 6) = (36)/(66) Step 3: Add the new fractions. (11)/(66) + (36)/(66) = (11+36)/(66) = (47)/(66) (47)/(66) 5. (5)/(9) + (1)/(2) Step 1: Find the LCM of the denominators 9 and 2, which is 9 × 2 = 18. Step 2: Convert the fractions to equivalent fractions with the common denominator. (5)/(9) = (5 × 2)/(9 × 2) = (10)/(18) (1)/(2) = (1 × 9)/(2 × 9) = (9)/(18) Step 3: Add the new fractions. (10)/(18) + (9)/(18) = (10+9)/(18) = (19)/(18) (19)/(18) 6. (9)/(12) + (2)/(12) Step 1: The fractions already have a common denominator. Step 2: Add the numerators. (9)/(12) + (2)/(12) = (9+2)/(12) = (11)/(12) (11)/(12) 7. (2)/(7) + (1)/(4) Step 1: Find the LCM of the denominators 7 and 4, which is 7 × 4 = 28. Step 2: Convert the fractions to equivalent fractions with the common denominator. (2)/(7) = (2 × 4)/(7 × 4) = (8)/(28) (1)/(4) = (1 × 7)/(4 × 7) = (7)/(28) Step 3: Add the new fractions. (8)/(28) + (7)/(28) = (8+7)/(28) = (15)/(28) (15)/(28) 8. (1)/(4) + (6)/(8) Step 1: Simplify (6)/(8) to (3)/(4). The problem becomes (1)/(4) + (3)/(4). Step 2: The fractions already have a common denominator. Step 3: Add the numerators. (1)/(4) + (3)/(4) = (1+3)/(4) = (4)/(4) Step 4: Simplify the fraction. (4)/(4) = 1 1 9. (4)/(10) + (4)/(5) Step 1: Simplify (4)/(10) to (2)/(5). The problem becomes (2)/(5) + (4)/(5). Step 2: The fractions already have a common denominator. Step 3: Add the numerators. (2)/(5) + (4)/(5) = (2+4)/(5) = (6)/(5) (6)/(5) 10. (1)/(2) + (8)/(11) Step 1: Find the LCM of the denominators 2 and 11, which is 2 × 11 = 22. Step 2: Convert the fractions to equivalent fractions with the common denominator. (1)/(2) = (1 × 11)/(2 × 11) = (11)/(22) (8)/(11) = (8 × 2)/(11 × 2) = (16)/(22) Step 3: Add the new fractions. (11)/(22) + (16)/(22) = (11+16)/(22) = (27)/(22) (27)/(22) Got more? Send 'em!