ction: (2) $$ \frac{y}{8}+\frac{1}{2} y $$ (3) $$ \frac{1}{4} x-1 \frac{1}{2} $$ (5) $$ 2-\frac{1}{4} p-\frac{3}{5} $$ (6) $$ a+\frac{1}{4} a-1 \frac{1}{6} $$ (8) $$ \frac{2}{3} k-2 \div \frac{14}{k} $$ (9) $$ -1 \frac{1}{3} x-\frac{2}{7} \div \frac{20}{21 x} $$ (2) $$ \frac{2 x-1}{4}+\frac{x+2}{2} $$ (3) $$ 2+\frac{2 x+3}{2} $$ (5) $$ \frac{1}{6} a-\frac{a-1}{8} $$ (6) $$ \frac{2 x}{3}-\frac{3 x}{2}-\frac{x+1}{6} $$ (8) $$ 2-\frac{x-4}{4}-\frac{1}{8}(x+1) $$ (9) $$ \frac{x-3}{3}+x-3 $$

Question

UpStudy AI · Accepted Answer

Let's solve each expression step by step.

### Expression (2)
$$
\frac{y}{8} + \frac{1}{2} y
$$
To combine these fractions, we need a common denominator. The common denominator for 8 and 2 is 8.

1. Rewrite $$\frac{1}{2} y$$ with a denominator of 8:
   $$
   \frac{1}{2} y = \frac{4}{8} y
   $$
2. Now combine:
   $$
   \frac{y}{8} + \frac{4y}{8} = \frac{y + 4y}{8} = \frac{5y}{8}
   $$

### Expression (3)
$$
\frac{1}{4} x - 1 \frac{1}{2}
$$
First, convert $$1 \frac{1}{2}$$ to an improper fraction:
$$
1 \frac{1}{2} = \frac{3}{2}
$$
Now, we can rewrite the expression:
$$
\frac{1}{4} x - \frac{3}{2}
$$
To combine these, we need a common denominator, which is 4:
1. Rewrite $$\frac{3}{2}$$ with a denominator of 4:
   $$
   \frac{3}{2} = \frac{6}{4}
   $$
2. Now combine:
   $$
   \frac{1}{4} x - \frac{6}{4} = \frac{x - 6}{4}
   $$

### Expression (5)
$$
2 - \frac{1}{4} p - \frac{3}{5}
$$
Convert 2 to a fraction with a common denominator of 20:
$$
2 = \frac{40}{20}
$$
Now rewrite $$\frac{1}{4} p$$ and $$\frac{3}{5}$$:
1. $$\frac{1}{4} p = \frac{5}{20} p$$
2. $$\frac{3}{5} = \frac{12}{20}$$

Now combine:
$$
\frac{40}{20} - \frac{5}{20} p - \frac{12}{20} = \frac{40 - 12 - 5p}{20} = \frac{28 - 5p}{20}
$$

### Expression (6)
$$
a + \frac{1}{4} a - 1 \frac{1}{6}
$$
Convert $$1 \frac{1}{6}$$ to an improper fraction:
$$
1 \frac{1}{6} = \frac{7}{6}
$$
Now rewrite the expression:
$$
a + \frac{1}{4} a - \frac{7}{6}
$$
Combine $$a$$ and $$\frac{1}{4} a$$:
1. Rewrite $$a$$ as $$\frac{4}{4} a$$:
   $$
   \frac{4}{4} a + \frac{1}{4} a = \frac{5}{4} a
   $$
2. Now we need a common denominator of 12 to combine:
   $$
   \frac{5}{4} a = \frac{15}{12} a \quad \text{and} \quad \frac{7}{6} = \frac{14}{12}
   $$
3. Combine:
   $$
   \frac{15}{12} a - \frac{14}{12} = \frac{15a - 14}{12}
   $$

### Expression (8)
$$
\frac{2}{3} k - 2 \div \frac{14}{k}
$$
First, rewrite the division:
$$
2 \div \frac{14}{k} = 2 \cdot \frac{k}{14} = \frac{2k}{14} = \frac{k}{7}
$$
Now combine:
$$
\frac{2}{3} k - \frac{k}{7}
$$
Find a common denominator of 21:
1. Rewrite $$\frac{2}{3} k$$ as $$\frac{14}{21} k$$ and $$\frac{k}{7}$$ as $$\frac{3}{21} k$$:
   $$
   \frac{14}{21} k - \frac{3}{21} k = \frac{11}{21} k
   $$

### Expression (9)
$$
-1 \frac{1}{3} x - \frac{2}{7} \div \frac{20}{21 x}
$$
Convert $$1 \frac{1}{3}$$ to an improper fraction:
$$
-1 \frac{1}{3} = -\frac{4}{3}
$$
Now rewrite the division:
$$
-\frac{2}{7} \div \frac{20}{21 x} = -\frac{2}{7} \cdot \frac{21 x}{20} = -\frac{42 x}{140} = -\frac{3 x}{10}
$$
Combine:
$$
-\frac{4}{3} x - \left(-\frac{3}{10} x\right)
$$
Find a common denominator of 30:
1. Rewrite $$-\frac{4}{3} x$$ as $$-\frac{40}{30} x$$ and $$-\frac{3}{10} x$$ as $$-\frac{9}{30} x$$:
   $$
   -\frac{40}{30} x + \frac{9}{30} x = -\frac{31}{30} x
   $$

### Summary of Results
1. $$ \frac{5y}{8} $$
2. $$ \frac{x - 6}{4} $$
3. $$ \frac{28 - 5p}{20} $$
4. $$ \frac{15a - 14}{12} $$
5. $$ \frac{11k}{21} $$
6. $$ -\frac{31x}{30} $$

Now, let's solve the remaining expressions:

### Expression (2)
$$
\frac{2x - 1}{4} + \frac{x + 2}{2}
$$
Find a common denominator of 4:
1. Rewrite $$\frac{x + 2}{2}$$ as $$\frac{2(x + 2)}{4} = \frac{2x + 4}{4}$$
2. Combine:
   $$
   \frac{2x - 1 + 2x + 4}{4} = \frac{4x + 3}{4}
   $$

### Expression (3)
$$
2 + \frac{2x + 3}{2}
$$
Convert 2 to a fraction:
$$
2 = \frac{4}{2}
$$
Combine:

Here are the simplified results for each expression: 1. $$ \frac{5y}{8} $$ 2. $$ \frac{x - 6}{4} $$ 3. $$ \frac{28 - 5p}{20} $$ 4. $$ \frac{15a - 14}{12} $$ 5. $$ \frac{11k}{21} $$ 6. $$ -\frac{31x}{30} $$ 7. $$ \frac{4x + 3}{4} $$ 8. $$ 2 + \frac{2x + 3}{2} $$ 9. $$ \frac{x - 3}{3} + x - 3 $$ These are the simplified forms of the given expressions.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions