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
Alright Shanti — let's do this. Here are the calculations for each problem, with answers in simplest form: a) 1(4)/(7) + 3(1)/(21) Step 1: Convert the mixed numbers to improper fractions. 1(4)/(7) = ((1 × 7) + 4)/(7) = (11)/(7) 3(1)/(21) = ((3 × 21) + 1)/(21) = (64)/(21) Step 2: Find a common denominator. The least common denominator (LCD) for 7 and 21 is 21. Convert (11)/(7) to an equivalent fraction with a denominator of 21. (11)/(7) = (11 × 3)/(7 × 3) = (33)/(21) Step 3: Add the fractions. (33)/(21) + (64)/(21) = (33+64)/(21) = (97)/(21) Step 4: Convert the improper fraction back to a mixed number and simplify if possible. (97)/(21) = 4(13)/(21) The fraction (13)/(21) is already in simplest form. The answer is 4(13)/(21) b) 3(1)/(7) - (1)/(2) Step 1: Convert the mixed number to an improper fraction. 3(1)/(7) = ((3 × 7) + 1)/(7) = (22)/(7) Step 2: Find a common denominator. The LCD for 7 and 2 is 14. Convert both fractions to equivalent fractions with a denominator of 14. (22)/(7) = (22 × 2)/(7 × 2) = (44)/(14) (1)/(2) = (1 × 7)/(2 × 7) = (7)/(14) Step 3: Subtract the fractions. (44)/(14) - (7)/(14) = (44-7)/(14) = (37)/(14) Step 4: Convert the improper fraction back to a mixed number and simplify if possible. (37)/(14) = 2(9)/(14) The fraction (9)/(14) is already in simplest form. The answer is 2(9)/(14) c) 2(5)/(9) + 1(3)/(8) Step 1: Convert the mixed numbers to improper fractions. 2(5)/(9) = ((2 × 9) + 5)/(9) = (23)/(9) 1(3)/(8) = ((1 × 8) + 3)/(8) = (11)/(8) Step 2: Find a common denominator. The LCD for 9 and 8 is 72. Convert both fractions to equivalent fractions with a denominator of 72. (23)/(9) = (23 × 8)/(9 × 8) = (184)/(72) (11)/(8) = (11 × 9)/(8 × 9) = (99)/(72) Step 3: Add the fractions. (184)/(72) + (99)/(72) = (184+99)/(72) = (283)/(72) Step 4: Convert the improper fraction back to a mixed number and simplify if possible. (283)/(72) = 3(67)/(72) The fraction (67)/(72) is already in simplest form. The answer is 3(67)/(72) d) 5(1)/(3) - 2(3)/(4) Step 1: Convert the mixed numbers to improper fractions. 5(1)/(3) = ((5 × 3) + 1)/(3) = (16)/(3) 2(3)/(4) = ((2 × 4) + 3)/(4) = (11)/(4) Step 2: Find a common denominator. The LCD for 3 and 4 is 12. Convert both fractions to equivalent fractions with a denominator of 12. (16)/(3) = (16 × 4)/(3 × 4) = (64)/(12) (11)/(4) = (11 × 3)/(4 × 3) = (33)/(12) Step 3: Subtract the fractions. (64)/(12) - (33)/(12) = (64-33)/(12) = (31)/(12) Step 4: Convert the improper fraction back to a mixed number and simplify if possible. (31)/(12) = 2(7)/(12) The fraction (7)/(12) is already in simplest form. The answer is 2(7)/(12) Send me the next one 📸