To subtract the two expressions, we want to distribute the multiplication and then combine like terms.
Starting with the first expression, \( \frac{1}{2} (z + 4) \), distribute the \( \frac{1}{2} \):
\[
\frac{1}{2} z + \frac{1}{2} \cdot 4 = \frac{1}{2} z + 2
\]
For the second expression, \( 3 \left( \frac{1}{4} z + 1 \right) \), distribute the 3:
\[
3 \cdot \frac{1}{4} z + 3 \cdot 1 = \frac{3}{4} z + 3
\]
Now, we can write the subtraction of the two expressions:
\[
\frac{1}{2} z + 2 - \left( \frac{3}{4} z + 3 \right)
\]
To subtract the second expression, we distribute the negative sign:
\[
\frac{1}{2} z + 2 - \frac{3}{4} z - 3
\]
Now, we need to combine like terms. To do this with the variable terms, we will want to have a common denominator. The common denominator for \( \frac{1}{2} \) and \( \frac{3}{4} \) is 4. Rewrite the terms accordingly:
\[
\frac{2}{4} z - \frac{3}{4} z + 2 - 3
\]
Now, we combine the z terms:
\[
\left(\frac{2}{4} - \frac{3}{4}\right) z = -\frac{1}{4} z
\]
And the constants:
\[
2 - 3 = -1
\]
So, put it all together:
\[
-\frac{1}{4} z - 1
\]
This is the final subtracted expression with fractions.
Subtract 1/2 (z + 4) - 3 (1/4z + 1) use fractions in final form.
3 answers
Make it more simple
Certainly! Let's simplify the expression in a step-by-step manner:
You want to subtract the following two expressions:
\[ \frac{1}{2} (z + 4) \quad \text{and} \quad 3 \left( \frac{1}{4}z + 1 \right) \]
First, distribute the fractions within each expression:
\[ \frac{1}{2} (z) + \frac{1}{2} (4) = \frac{1}{2}z + 2 \]
\[ 3 \left( \frac{1}{4}z \right) + 3(1) = \frac{3}{4}z + 3 \]
Now, to subtract the second expression from the first, we'll write it out:
\[ \left( \frac{1}{2}z + 2 \right) - \left( \frac{3}{4}z + 3 \right) \]
To perform the subtraction, we distribute the negative sign to both terms in the second expression:
\[ \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \]
We find a common denominator for the variable terms: the least common multiple of 2 and 4 is 4.
Convert \( \frac{1}{2}z \) to an equivalent fraction with a denominator of 4:
\[ \frac{2}{4}z \]
Now, the subtraction of the variable terms with the common denominator:
\[ \frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z \]
For the constant terms:
\[ 2 - 3 = -1 \]
Bringing these together:
\[ -\frac{1}{4}z - 1 \]
Thus, we've arrived at the simplest form of the expression with fractions:
\[ -\frac{1}{4}z - 1 \]
You want to subtract the following two expressions:
\[ \frac{1}{2} (z + 4) \quad \text{and} \quad 3 \left( \frac{1}{4}z + 1 \right) \]
First, distribute the fractions within each expression:
\[ \frac{1}{2} (z) + \frac{1}{2} (4) = \frac{1}{2}z + 2 \]
\[ 3 \left( \frac{1}{4}z \right) + 3(1) = \frac{3}{4}z + 3 \]
Now, to subtract the second expression from the first, we'll write it out:
\[ \left( \frac{1}{2}z + 2 \right) - \left( \frac{3}{4}z + 3 \right) \]
To perform the subtraction, we distribute the negative sign to both terms in the second expression:
\[ \frac{1}{2}z + 2 - \frac{3}{4}z - 3 \]
We find a common denominator for the variable terms: the least common multiple of 2 and 4 is 4.
Convert \( \frac{1}{2}z \) to an equivalent fraction with a denominator of 4:
\[ \frac{2}{4}z \]
Now, the subtraction of the variable terms with the common denominator:
\[ \frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z \]
For the constant terms:
\[ 2 - 3 = -1 \]
Bringing these together:
\[ -\frac{1}{4}z - 1 \]
Thus, we've arrived at the simplest form of the expression with fractions:
\[ -\frac{1}{4}z - 1 \]
1 answer