Simplify 5 4/7i+4 3/5i

$5 \frac{4}{7} i + 4 \frac{3}{5} i$

Step 1

Convert $5 \frac{4}{7}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(5 + \frac{4}{7}) i + 4 \frac{3}{5} i$

Add $5$ and $\frac{4}{7}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(5 \cdot \frac{7}{7} + \frac{4}{7}) i + 4 \frac{3}{5} i$

Combine $5$ and $\frac{7}{7}$ .

$(\frac{5 \cdot 7}{7} + \frac{4}{7}) i + 4 \frac{3}{5} i$

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 + 4}{7} i + 4 \frac{3}{5} i$

Simplify the numerator.

Multiply $5$ by $7$ .

$\frac{35 + 4}{7} i + 4 \frac{3}{5} i$

Add $35$ and $4$ .

$\frac{39}{7} i + 4 \frac{3}{5} i$

Step 2

Convert $4 \frac{3}{5}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{7} i + (4 + \frac{3}{5}) i$

Add $4$ and $\frac{3}{5}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{39}{7} i + (4 \cdot \frac{5}{5} + \frac{3}{5}) i$

Combine $4$ and $\frac{5}{5}$ .

$\frac{39}{7} i + (\frac{4 \cdot 5}{5} + \frac{3}{5}) i$

Combine the numerators over the common denominator.

$\frac{39}{7} i + \frac{4 \cdot 5 + 3}{5} i$

Simplify the numerator.

Multiply $4$ by $5$ .

$\frac{39}{7} i + \frac{20 + 3}{5} i$

Add $20$ and $3$ .

$\frac{39}{7} i + \frac{23}{5} i$

Step 3

Simplify each term.

Combine $\frac{39}{7}$ and $i$ .

$\frac{39 i}{7} + \frac{23}{5} i$

Combine $\frac{23}{5}$ and $i$ .

$\frac{39 i}{7} + \frac{23 i}{5}$

Step 4

To write $\frac{39 i}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{39 i}{7} \cdot \frac{5}{5} + \frac{23 i}{5}$

Step 5

To write $\frac{23 i}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{39 i}{7} \cdot \frac{5}{5} + \frac{23 i}{5} \cdot \frac{7}{7}$

Step 6

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{39 i}{7}$ by $\frac{5}{5}$ .

$\frac{39 i \cdot 5}{7 \cdot 5} + \frac{23 i}{5} \cdot \frac{7}{7}$

Multiply $7$ by $5$ .

$\frac{39 i \cdot 5}{35} + \frac{23 i}{5} \cdot \frac{7}{7}$

Multiply $\frac{23 i}{5}$ by $\frac{7}{7}$ .

$\frac{39 i \cdot 5}{35} + \frac{23 i \cdot 7}{5 \cdot 7}$

Multiply $5$ by $7$ .

$\frac{39 i \cdot 5}{35} + \frac{23 i \cdot 7}{35}$

Step 7

Combine the numerators over the common denominator.

$\frac{356 i}{35}$

Simplify 5 4/7i+4 3/5i

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