Find the LCD (or LCM).
Multiples of 4: 4, 8, 12, 16
Multiples of 6: 6, 12, 18
LCD of 4 and 6 is 12.
Create equivalent fractions.
\(\mathsf{7 \frac{1 \times 3}{4 \times 3} = 7\frac{3}{12}
}\)
\(\mathsf{4 \frac{2 \times 2}{6 \times 2} = 4\frac{4}{12}
}\)
Add the fractions.
\(\mathsf{ \frac{3}{12} + \frac{4}{12} = \frac{7}{12} }\)
Add the whole numbers.
\(\mathsf{ 7\frac{3}{12} + 4\frac{4}{12} = 11\frac{7}{12}
}\)
Your final answer is:
\(\mathsf{ 11\frac{7}{12} }\)
Find the LCD.
Multiples of 9: 9, 18, 27
Multiples of 6: 6, 12, 18
LCD of 9 and 6 is 18.
Create equivalent fractions.
\(\mathsf{6 \frac{4 \times 2}{9 \times 2} = 6\frac{8}{18}
}\)
\(\mathsf{5 \frac{3 \times 3}{6 \times 3} = 5\frac{9}{18}
}\)
Add the fractions.
\(\mathsf{ \frac{8}{18} + \frac{9}{18} = \frac{17}{18} }\)
Add the whole numbers.
\(\mathsf{ 6\frac{8}{18} + 5\frac{9}{18} = 11\frac{17}{18}
}\)
Your final answer is:
\(\mathsf{ 11\frac{17}{18} }\)
Find the LCD.
Multiples of 4: 4, 8, 12, 16, 20,
24
Multiples of 5: 5, 10, 15, 20, 25
LCD of 4 and 5 is 20.
Create equivalent fractions.
\(\mathsf{9 \frac{3 \times 5}{4 \times 5} = 9\frac{15}{20}
}\)
\(\mathsf{10 \frac{4 \times 4}{5 \times 4} = 10\frac{16}{20}
}\)
Add the fractions.
\(\mathsf{ \frac{15}{20} + \frac{16}{20} = \frac{31}{20}
}\)
Add the whole numbers.
\(\mathsf{ 9\frac{15}{20} + 10\frac{16}{20} =
19\frac{31}{20} }\)
Simplify.
\(\mathsf{ \frac{31}{20} }\) is an improper fraction. You
can simplify \(\mathsf{ \frac{31}{20} }\) to a mixed number.
Subtract: 31 - 20 = 11
This means you can make 1 whole group of 20 with \(\mathsf{
\frac{11}{20} }\) left over.
Your new mixed number is:
\(\mathsf{ 1\frac{11}{20} }\)
So, \(\mathsf{ \frac{31}{20} = 1\frac{11}{20} }\).
Now, add the new mixed number to the whole number that was
already part of your answer.
\(\mathsf{ 19 + 1\frac{11}{20} = 20\frac{11}{20} }\)
Your final answer is:
\(\mathsf{ 20\frac{11}{20} }\)
