Math Problem Statement

Solve the following fraction problems: 1. (3/8) + (1/12) 2. (2/3) + (7/12) 3. (6/10) + (7/15) 4. (5/8) + (5/12) 5. (5/12) + (3/15)

Solution

Let's go through each of the problems and solve them.

  1. 38+112\frac{3}{8} + \frac{1}{12}:

    • The least common denominator (LCD) of 8 and 12 is 24.
    • Convert both fractions to have a denominator of 24: 38=924,112=224\frac{3}{8} = \frac{9}{24}, \quad \frac{1}{12} = \frac{2}{24}
    • Now add the fractions: 924+224=1124\frac{9}{24} + \frac{2}{24} = \frac{11}{24}
    • Answer: 1124\frac{11}{24}.
  2. 23+712\frac{2}{3} + \frac{7}{12}:

    • The LCD of 3 and 12 is 12.
    • Convert both fractions: 23=812,712=712\frac{2}{3} = \frac{8}{12}, \quad \frac{7}{12} = \frac{7}{12}
    • Now add the fractions: 812+712=1512\frac{8}{12} + \frac{7}{12} = \frac{15}{12}
    • Simplify: 1512=54=114\frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}
    • Answer: 1141 \frac{1}{4} or 54\frac{5}{4}.
  3. 610+715\frac{6}{10} + \frac{7}{15}:

    • The LCD of 10 and 15 is 30.
    • Convert both fractions: 610=1830,715=1430\frac{6}{10} = \frac{18}{30}, \quad \frac{7}{15} = \frac{14}{30}
    • Now add the fractions: 1830+1430=3230\frac{18}{30} + \frac{14}{30} = \frac{32}{30}
    • Simplify: 3230=1615\frac{32}{30} = \frac{16}{15}
    • Answer: 1615\frac{16}{15} or 11151 \frac{1}{15}.
  4. 58+512\frac{5}{8} + \frac{5}{12}:

    • The LCD of 8 and 12 is 24.
    • Convert both fractions: 58=1524,512=1024\frac{5}{8} = \frac{15}{24}, \quad \frac{5}{12} = \frac{10}{24}
    • Now add the fractions: 1524+1024=2524\frac{15}{24} + \frac{10}{24} = \frac{25}{24}
    • Simplify: 2524=1124\frac{25}{24} = 1 \frac{1}{24}
    • Answer: 11241 \frac{1}{24} or 2524\frac{25}{24}.
  5. 512+315\frac{5}{12} + \frac{3}{15}:

    • The LCD of 12 and 15 is 60.
    • Convert both fractions: 512=2560,315=1260\frac{5}{12} = \frac{25}{60}, \quad \frac{3}{15} = \frac{12}{60}
    • Now add the fractions: 2560+1260=3760\frac{25}{60} + \frac{12}{60} = \frac{37}{60}
    • Answer: 3760\frac{37}{60}.

Would you like further details on any of these steps? Here are 5 related questions for practice:

  1. What is the least common denominator of 6 and 9?
  2. Simplify the sum 720+1130\frac{7}{20} + \frac{11}{30}.
  3. What is 12+13\frac{1}{2} + \frac{1}{3} in its simplest form?
  4. Add 49+56\frac{4}{9} + \frac{5}{6} and simplify.
  5. If you have 78+25\frac{7}{8} + \frac{2}{5}, what is the result?

Tip: When adding fractions, always find the least common denominator to make the addition easier.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Fractions
Addition of Fractions
Least Common Denominator

Formulas

LCD of two numbers
Addition of fractions with different denominators

Theorems

Concept of Least Common Denominator (LCD)

Suitable Grade Level

Grades 5-7