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 problem 3: a) 3(7)/(10) - 1(8)/(9) Step 1: Convert mixed numbers to improper fractions. 3(7)/(10) = (3 × 10 + 7)/(10) = (37)/(10) 1(8)/(9) = (1 × 9 + 8)/(9) = (17)/(9) Step 2: Find the Least Common Multiple (LCM) of the denominators 10 and 9. The LCM of 10 and 9 is 90. Step 3: Convert fractions to equivalent fractions with a denominator of 90. (37)/(10) = (37 × 9)/(10 × 9) = (333)/(90) (17)/(9) = (17 × 10)/(9 × 10) = (170)/(90) Step 4: Perform the subtraction. (333)/(90) - (170)/(90) = (333 - 170)/(90) = (163)/(90) Step 5: Convert the improper fraction to a mixed number. (163)/(90) = 1(73)/(90) The simplified answer is 1(73)/(90). b) 2(2)/(10) + 1(6)/(7) Step 1: Convert mixed numbers to improper fractions. 2(2)/(10) = (2 × 10 + 2)/(10) = (22)/(10) 1(6)/(7) = (1 × 7 + 6)/(7) = (13)/(7) Step 2: Find the LCM of the denominators 10 and 7. The LCM of 10 and 7 is 70. Step 3: Convert fractions to equivalent fractions with a denominator of 70. (22)/(10) = (22 × 7)/(10 × 7) = (154)/(70) (13)/(7) = (13 × 10)/(7 × 10) = (130)/(70) Step 4: Perform the addition. (154)/(70) + (130)/(70) = (154 + 130)/(70) = (284)/(70) Step 5: Simplify the improper fraction. Divide both numerator and denominator by their HCF, which is 2. (284 ÷ 2)/(70 ÷ 2) = (142)/(35) Convert to a mixed number: (142)/(35) = 4(2)/(35) The simplified answer is 4(2)/(35). c) 8(3)/(4) - 6(5)/(6) + (1)/(2) Step 1: Convert mixed numbers to improper fractions.