Simplify 4 1/4z+3 1/28z

$4 \frac{1}{4} \cdot z + 3 \frac{1}{28} \cdot z$

Step 1

Convert $4 \frac{1}{4}$ to an improper fraction.

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

$(4 + \frac{1}{4}) \cdot z + 3 \frac{1}{28} \cdot z$

Add $4$ and $\frac{1}{4}$ .

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

$(4 \cdot \frac{4}{4} + \frac{1}{4}) \cdot z + 3 \frac{1}{28} \cdot z$

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

$(\frac{4 \cdot 4}{4} + \frac{1}{4}) \cdot z + 3 \frac{1}{28} \cdot z$

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 1}{4} \cdot z + 3 \frac{1}{28} \cdot z$

Simplify the numerator.

Multiply $4$ by $4$ .

$\frac{16 + 1}{4} \cdot z + 3 \frac{1}{28} \cdot z$

Add $16$ and $1$ .

$\frac{17}{4} \cdot z + 3 \frac{1}{28} \cdot z$

Step 2

Convert $3 \frac{1}{28}$ to an improper fraction.

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

$\frac{17}{4} \cdot z + (3 + \frac{1}{28}) \cdot z$

Add $3$ and $\frac{1}{28}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$\frac{17}{4} \cdot z + (3 \cdot \frac{28}{28} + \frac{1}{28}) \cdot z$

Combine $3$ and $\frac{28}{28}$ .

$\frac{17}{4} \cdot z + (\frac{3 \cdot 28}{28} + \frac{1}{28}) \cdot z$

Combine the numerators over the common denominator.

$\frac{17}{4} \cdot z + \frac{3 \cdot 28 + 1}{28} \cdot z$

Simplify the numerator.

Multiply $3$ by $28$ .

$\frac{17}{4} \cdot z + \frac{84 + 1}{28} \cdot z$

Add $84$ and $1$ .

$\frac{17}{4} \cdot z + \frac{85}{28} \cdot z$

Step 3

Simplify each term.

Combine $\frac{17}{4}$ and $z$ .

$\frac{17 z}{4} + \frac{85}{28} \cdot z$

Combine $\frac{85}{28}$ and $z$ .

$\frac{17 z}{4} + \frac{85 z}{28}$

Step 4

To write $\frac{17 z}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{17 z}{4} \cdot \frac{7}{7} + \frac{85 z}{28}$

Step 5

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{17 z}{4}$ by $\frac{7}{7}$ .

$\frac{17 z \cdot 7}{4 \cdot 7} + \frac{85 z}{28}$

Multiply $4$ by $7$ .

$\frac{17 z \cdot 7}{28} + \frac{85 z}{28}$

Step 6

Combine the numerators over the common denominator.

$\frac{17 z \cdot 7 + 85 z}{28}$

Step 7

Simplify the numerator.

Factor $17 z$ out of $17 z \cdot 7 + 85 z$ .

Factor $17 z$ out of $17 z \cdot 7$ .

$\frac{17 z (7) + 85 z}{28}$

Factor $17 z$ out of $85 z$ .

$\frac{17 z (7) + 17 z (5)}{28}$

Factor $17 z$ out of $17 z (7) + 17 z (5)$ .

$\frac{17 z (7 + 5)}{28}$

Add $7$ and $5$ .

$\frac{17 z \cdot 12}{28}$

Multiply $12$ by $17$ .

$\frac{204 z}{28}$

Step 8

Cancel the common factor of $204$ and $28$ .

Factor $4$ out of $204 z$ .

$\frac{4 (51 z)}{28}$

Cancel the common factors.

Factor $4$ out of $28$ .

$\frac{4 (51 z)}{4 (7)}$

Cancel the common factor.

$\frac{4 (51 z)}{4 \cdot 7}$

Rewrite the expression.

$\frac{51 z}{7}$

Simplify 4 1/4*z+3 1/28*z

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Simplify 4 1/4z+3 1/28z