Math / Algebra

QuestionFill in the boxes to add the expressions. $\begin{aligned} \left(\frac{8}{17} z-15\right)+\left(\frac{3}{17} z+16\right) & =\left({ }^{+}+\right)+(-15+\ldots) \\ & =\ldots{ }^{+}+ \end{aligned}$ $\begin{aligned} \left(\frac{8}{17} z-15\right)+\left(\frac{3}{17} z+16\right) & =\left(\square+\frac{3}{17} z\right)+(-15+\square) \\ & =\square z+\square \end{aligned}$ (Simplify your answers. Use integers or fractions for any numbers in the expressions.)

Studdy Solution

STEP 1

1. We are asked to add two algebraic expressions.
2. The expressions involve like terms that can be combined.
3. The goal is to fill in the boxes with the correct simplified terms.

STEP 2

1. Identify and combine like terms in the expression.
2. Fill in the boxes with the simplified terms.

STEP 3

Identify the like terms in the expression $\left(\frac{8}{17} z-15\right)+\left(\frac{3}{17} z+16\right)$ .
- The like terms involving $z$ are $\frac{8}{17} z$ and $\frac{3}{17} z$ . - The constant terms are $-15$ and $16$ .

STEP 4

Combine the like terms involving $z$ :
$\frac{8}{17} z + \frac{3}{17} z = \frac{8 + 3}{17} z = \frac{11}{17} z$
Fill in the first box with $\frac{8}{17} z$ and the second box with $\frac{3}{17} z$ .

STEP 5

Combine the constant terms:
$-15 + 16 = 1$
Fill in the third box with $-15$ and the fourth box with $16$ .

STEP 6

Write the simplified expression:
$\frac{11}{17} z + 1$
Fill in the final boxes with $\frac{11}{17}$ and $1$ .

Was this helpful?

Studdy Solution

STEP 1

1. We are asked to add two algebraic expressions.
2. The expressions involve like terms that can be combined.
3. The goal is to fill in the boxes with the correct simplified terms.

STEP 2

1. Identify and combine like terms in the expression.
2. Fill in the boxes with the simplified terms.

STEP 3

Identify the like terms in the expression $\left(\frac{8}{17} z-15\right)+\left(\frac{3}{17} z+16\right)$ .
- The like terms involving $z$ are $\frac{8}{17} z$ and $\frac{3}{17} z$ . - The constant terms are $-15$ and $16$ .

STEP 4

Combine the like terms involving $z$ :
$\frac{8}{17} z + \frac{3}{17} z = \frac{8 + 3}{17} z = \frac{11}{17} z$
Fill in the first box with $\frac{8}{17} z$ and the second box with $\frac{3}{17} z$ .

STEP 5

Combine the constant terms:
$-15 + 16 = 1$
Fill in the third box with $-15$ and the fourth box with $16$ .

STEP 6

Write the simplified expression:
$\frac{11}{17} z + 1$
Fill in the final boxes with $\frac{11}{17}$ and $1$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. We are asked to add two algebraic expressions.2. The expressions involve like terms that can be combined.3. The goal is to fill in the boxes with the correct simplified terms.

STEP 2

1. Identify and combine like terms in the expression.2. Fill in the boxes with the simplified terms.

STEP 3

Identify the like terms in the expression (817z−15)+(317z+16)\left(\frac{8}{17} z-15\right)+\left(\frac{3}{17} z+16\right)(178​z−15)+(173​z+16).- The like terms involving zzz are 817z\frac{8}{17} z178​z and 317z\frac{3}{17} z173​z. - The constant terms are −15-15−15 and 161616.

STEP 4

Combine the like terms involving zzz:817z+317z=8+317z=1117z\frac{8}{17} z + \frac{3}{17} z = \frac{8 + 3}{17} z = \frac{11}{17} z178​z+173​z=178+3​z=1711​zFill in the first box with 817z\frac{8}{17} z178​z and the second box with 317z\frac{3}{17} z173​z.

STEP 5

Combine the constant terms:−15+16=1-15 + 16 = 1−15+16=1Fill in the third box with −15-15−15 and the fourth box with 161616.

STEP 6

Write the simplified expression:1117z+1\frac{11}{17} z + 11711​z+1Fill in the final boxes with 1117\frac{11}{17}1711​ and 111.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We are asked to add two algebraic expressions.
2. The expressions involve like terms that can be combined.
3. The goal is to fill in the boxes with the correct simplified terms.

1. Identify and combine like terms in the expression.
2. Fill in the boxes with the simplified terms.

Identify the like terms in the expression $\left(\frac{8}{17} z-15\right)+\left(\frac{3}{17} z+16\right)$ .
- The like terms involving $z$ are $\frac{8}{17} z$ and $\frac{3}{17} z$ . - The constant terms are $-15$ and $16$ .

Combine the like terms involving $z$ :
$\frac{8}{17} z + \frac{3}{17} z = \frac{8 + 3}{17} z = \frac{11}{17} z$
Fill in the first box with $\frac{8}{17} z$ and the second box with $\frac{3}{17} z$ .

Combine the constant terms:
$-15 + 16 = 1$
Fill in the third box with $-15$ and the fourth box with $16$ .

Write the simplified expression:
$\frac{11}{17} z + 1$
Fill in the final boxes with $\frac{11}{17}$ and $1$ .