Fractions addition worksheet with four problems.

Here are the step-by-step solutions for the problems on the worksheet.

1 a. $5 \frac{3}{8} + 1 \frac{4}{7}$

* Step 1: Add the whole numbers together.
$5 + 1 = 6$
* Step 2: Find a common denominator for the fractions $\frac{3}{8}$ and $\frac{4}{7}$. Since 8 and 7 don't share any factors, multiply them: $8 \times 7 = 56$.
* Step 3: Convert the fractions.
$\frac{3}{8} = \frac{3 \times 7}{8 \times 7} = \frac{21}{56}$
$\frac{4}{7} = \frac{4 \times 8}{7 \times 8} = \frac{32}{56}$
* Step 4: Add the new fractions.
$\frac{21}{56} + \frac{32}{56} = \frac{53}{56}$
* Step 5: Combine the whole number and the fraction.
$6 \frac{53}{56}$

1 b. $5 \frac{4}{20} + 10 \frac{4}{6}$

* Step 1: Simplify the fractions first to make it easier.
$\frac{4}{20}$ simplifies to $\frac{1}{5}$ (divide top and bottom by 4).
$\frac{4}{6}$ simplifies to $\frac{2}{3}$ (divide top and bottom by 2).
The problem is now: $5 \frac{1}{5} + 10 \frac{2}{3}$
* Step 2: Add the whole numbers.
$5 + 10 = 15$
* Step 3: Find a common denominator for $\frac{1}{5}$ and $\frac{2}{3}$. Multiply $5 \times 3 = 15$.
* Step 4: Convert the fractions.
$\frac{1}{5} = \frac{3}{15}$
$\frac{2}{3} = \frac{10}{15}$
* Step 5: Add the fractions.
$\frac{3}{15} + \frac{10}{15} = \frac{13}{15}$
* Step 6: Combine them.
$15 \frac{13}{15}$

2 a. $9 \frac{1}{9} + 10 \frac{2}{4}$

* Step 1: Simplify the second fraction.
$\frac{2}{4}$ simplifies to $\frac{1}{2}$.
The problem is now: $9 \frac{1}{9} + 10 \frac{1}{2}$
* Step 2: Add the whole numbers.
$9 + 10 = 19$
* Step 3: Find a common denominator for $\frac{1}{9}$ and $\frac{1}{2}$. Multiply $9 \times 2 = 18$.
* Step 4: Convert the fractions.
$\frac{1}{9} = \frac{2}{18}$
$\frac{1}{2} = \frac{9}{18}$
* Step 5: Add the fractions.
$\frac{2}{18} + \frac{9}{18} = \frac{11}{18}$
* Step 6: Combine them.
$19 \frac{11}{18}$

2 b. $5 \frac{1}{6} + 4 \frac{5}{24}$

* Step 1: Add the whole numbers.
$5 + 4 = 9$
* Step 2: Look at the denominators 6 and 24. Since 24 is a multiple of 6 ($6 \times 4 = 24$), the common denominator is 24. You only need to change the first fraction.
* Step 3: Convert $\frac{1}{6}$.
$\frac{1 \times 4}{6 \times 4} = \frac{4}{24}$
* Step 4: Add the fractions.
$\frac{4}{24} + \frac{5}{24} = \frac{9}{24}$
* Step 5: Simplify the resulting fraction. Both 9 and 24 can be divided by 3.
$9 \div 3 = 3$
$24 \div 3 = 8$
So, $\frac{9}{24}$ becomes $\frac{3}{8}$.
* Step 6: Combine the whole number and simplified fraction.
$9 \frac{3}{8}$

Final Answer:
1 a. $6 \frac{53}{56}$
1 b. $15 \frac{13}{15}$
2 a. $19 \frac{11}{18}$
2 b. $9 \frac{3}{8}$