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
Okay, Sheela, let's simplify these expressions. a) Simplify 3(1)/(4) - 2(2)/(5) + 1(1)/(10). Step 1: Convert mixed numbers to improper fractions. 3(1)/(4) = ((3 × 4) + 1)/(4) = (13)/(4) 2(2)/(5) = ((2 × 5) + 2)/(5) = (12)/(5) 1(1)/(10) = ((1 × 10) + 1)/(10) = (11)/(10) Step 2: Rewrite the expression. (13)/(4) - (12)/(5) + (11)/(10) Step 3: Find the least common multiple (LCM) of the denominators 4, 5, and 10. The LCM is 20. Step 4: Convert each fraction to an equivalent fraction with a denominator of 20. (13)/(4) = (13 × 5)/(4 × 5) = (65)/(20) (12)/(5) = (12 × 4)/(5 × 4) = (48)/(20) (11)/(10) = (11 × 2)/(10 × 2) = (22)/(20) Step 5: Perform the addition and subtraction. (65)/(20) - (48)/(20) + (22)/(20) = (65 - 48 + 22)/(20) = (17 + 22)/(20) = (39)/(20) Step 6: Convert the improper fraction back to a mixed number. (39)/(20) = 1(19)/(20) The simplified expression is 1(19)/(20). d) Simplify 5 - 3(1)/(7) + 2(3)/(14). Step 1: Convert mixed numbers to improper fractions. 5 = (5)/(1) 3(1)/(7) = ((3 × 7) + 1)/(7) = (22)/(7) 2(3)/(14) = ((2 × 14) + 3)/(14) = (31)/(14) Step 2: Rewrite the expression. (5)/(1) - (22)/(7) + (31)/(14) Step 3: Find the least common multiple (LCM) of the denominators 1, 7, and 14. The LCM is 14. Step 4: Convert each term to an equivalent fraction with a denominator of 14. (5)/(1) = (5 × 14)/(1 × 14) = (70)/(14) (22)/(7) = (22 × 2)/(7 × 2) = (44)/(14) Step 5: Perform the addition and subtraction. (70)/(14) - (44)/(14) + (31)/(14) = (70 - 44 + 31)/(14) = (26 + 31)/(14) = (57)/(14) Step 6: Convert the improper fraction back to a mixed number. (57)/(14) = 4(1)/(14) The simplified expression is 4(1)/(14). That's 2 down. 3 left today — send the next one.