Math Problem Statement

-2 - 3/4 * x * 1/5 - (-3/5 * x * 4/6)

Solution

The expression given in the image is:

234x15(35x46)-2 - \frac{3}{4} x \cdot \frac{1}{5} - \left( -\frac{3}{5} x \cdot \frac{4}{6} \right)

Now let's simplify this step by step.

Step 1: Simplify the products

  • For the term 34x15\frac{3}{4} x \cdot \frac{1}{5}, multiply the fractions:

3415=3×14×5=320\frac{3}{4} \cdot \frac{1}{5} = \frac{3 \times 1}{4 \times 5} = \frac{3}{20}

So the second term becomes: 320x- \frac{3}{20} x

  • For the term 35x46\frac{3}{5} x \cdot \frac{4}{6}, multiply the fractions:

3546=3×45×6=1230=25\frac{3}{5} \cdot \frac{4}{6} = \frac{3 \times 4}{5 \times 6} = \frac{12}{30} = \frac{2}{5}

The term inside the parentheses becomes: (25x)-\left( -\frac{2}{5} x \right) Which simplifies to: +25x+\frac{2}{5} x

Step 2: Combine the terms

Now, the expression becomes: 2320x+25x-2 - \frac{3}{20} x + \frac{2}{5} x

Step 3: Combine like terms

To combine 320x-\frac{3}{20}x and 25x\frac{2}{5}x, we need a common denominator. The common denominator between 20 and 5 is 20.

Convert 25\frac{2}{5} to have a denominator of 20: 25=820\frac{2}{5} = \frac{8}{20}

Now the expression is: 2320x+820x-2 - \frac{3}{20}x + \frac{8}{20}x

Combine the fractions: 3+820x=520x=14x\frac{-3 + 8}{20}x = \frac{5}{20}x = \frac{1}{4}x

Final Answer:

2+14x-2 + \frac{1}{4}x

This is the simplified form of the expression.

Would you like further details or any clarifications?


Here are five related questions:

  1. How do you combine fractions with different denominators?
  2. What are the steps to simplify expressions with parentheses?
  3. What happens when you multiply two fractions?
  4. How can you handle negative signs when simplifying algebraic expressions?
  5. What is the significance of common denominators when adding or subtracting fractions?

Tip: Always make sure to distribute negative signs carefully when simplifying terms inside parentheses.

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Math Problem Analysis

Mathematical Concepts

Algebra
Fraction Multiplication
Simplifying Expressions

Formulas

a/b * c/d = (a * c) / (b * d)
Combining like terms
Common denominator in fraction addition

Theorems

Distributive property
Addition of fractions with common denominators

Suitable Grade Level

Grades 6-8