Question

3 2/3 + 1 2/3= 3/4+1 1/4=1/4+3 1/6=2 4/9+1/6=4 3/5+10 1/4=8 3/5+1 9/10=3 4/5+1 1/3=12 5/6+4/15=

Answer 1

$1) \: 3 \frac{2}{3} + 1 \frac{2}{3} = 5 \frac{1}{3} \\ 2) \: \frac{3}{4} + 1 \frac{1}{4} = 2 \\ 3) \: \frac{1}{4} + 3 \frac{1}{6} = 3 \frac{3 + 2}{12} = 3 \frac{5}{12}$

$4) \: 2 \frac{4}{9} + \frac{1}{6} = 2 \frac{8 + 3}{18} = 2 \frac{11}{18} \\ 5) \: 4 \frac{3}{5} + 10 \frac{1}{4} = 14 \frac{12 + 5}{20} = 14 \frac{17}{20}$

$6) \: 8 \frac{3}{5} + 1 \frac{9}{10} = 9 \frac{6 + 9}{10} = 10 \frac{1}{2} \\ 7) \: 3 \frac{4}{5} + 1 \frac{1}{3} = 4 \frac{12 + 5}{15} = 5 \frac{2}{15} \\ 8) \: 12 \frac{5}{6} + \frac{4}{15} = 12 \frac{25 + 8}{30} = 13 \frac{1}{10}$

Answer 2

Let's solve these addition problems step by step:

1. 3 2/3 + 1 2/3: Both fractions have the same denominator, so we can add them directly: (3 + 1) + (2/3 + 2/3) = 4 + 4/3 = 4 + 1 1/3 = 5 1/3

2. 3/4 + 1 1/4: The whole numbers have the same denominator as the fractions, so we can add them directly: (3 + 1) + (1/4) = 4 + 1/4 = 4 1/4

3. 1/4 + 3 1/6: Convert the whole number to a fraction with the same denominator as 1/4: (3 * 6 + 1) / 6 + 1/4 = 19/6 + 1/4 Find a common denominator (24) for 6 and 4: (19/6 * 4/4) + (1/4 * 6/6) = 76/24 + 6/24 = 82/24 Reduce the fraction if possible: 82/24 = 3 10/24 Simplify the fraction: 3 10/24 = 3 5/12

4. 2 4/9 + 1/6: Convert the whole number to a fraction with the same denominator as 1/6: (2 * 9 + 4) / 9 + 1/6 = 22/9 + 1/6 Find a common denominator (54) for 9 and 6: (22/9 * 6/6) + (1/6 * 9/9) = 132/54 + 9/54 = 141/54 Reduce the fraction if possible: 141/54 = 2 33/54 Simplify the fraction: 2 33/54 = 2 11/18

5. 4 3/5 + 10 1/4: Both fractions have different denominators, so we need to find a common denominator (20): (4 * 4 + 3) / 5 + (10 * 5 + 1) / 20 = 19/5 + 51/20 Find a common denominator (20) for both fractions: (19/5 * 4/4) + (51/20 * 1/1) = 76/20 + 51/20 = 127/20 Reduce the fraction if possible: 127/20 = 6 7/20

6. 3 4/5 + 1 1/3: Both fractions have different denominators, so we need to find a common denominator (15): (3 * 5 + 4) / 5 + (1 * 3 + 1) / 3 = 19/5 + 4/3 Find a common denominator (15) for both fractions: (19/5 * 3/3) + (4/3 * 5/5) = 57/15 + 20/15 = 77/15 Reduce the fraction if possible: 77/15 = 5 2/15

7. 12 5/6 + 4/15: Both fractions have different denominators, so we need to find a common denominator (30): (12 * 6 + 5) / 6 + (4 * 2 + 1) / 15 = 77/6 + 9/15 Find a common denominator (30) for both fractions: (77/6 * 5/5) + (9/15 * 2/2) = 385/30 + 18/30 = 403/30 Reduce the fraction if possible: 403/30 = 13 13/30

So, the results of the addition problems are:

1. 3 2/3 + 1 2/3 = 5 1/3
2. 3/4 + 1 1/4 = 4 1/4
3. 1/4 + 3 1/6 = 3 5/12
4. 2 4/9 + 1/6 = 2 11/18
5. 4 3/5 + 10 1/4 = 6 7/20
6. 3 4/5 + 1 1/3 = 5 2/15
7. 12 5/6 + 4/15 = 13 13/30