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Chapter 4: Problem 695

In the following exercises, simplify. $$ -\frac{3}{4} \div \frac{x}{3} $$

Short Answer

Expert verified
-\frac{9}{4x}

Step by step solution

01

Write the Division as Multiplication

Rewrite the division of fractions as multiplication by the reciprocal. The expression \(-\frac{3}{4} \div \frac{x}{3}\) can be rewritten as \(-\frac{3}{4} \times \frac{3}{x}\).
02

Multiply the Fractions

Multiply the numerators together and the denominators together. This gives \((-\frac{3}{4} \times \frac{3}{x} = -\frac{3 \times 3}{4 \times x} = -\frac{9}{4x}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

division of fractions
is \( \frac{3}{x} \). This flipped version is called the reciprocal.
  • Step 2: Change the division sign to multiplication. So, what was \(-\frac{3}{4} \div \frac{x}{3} \) now becomes \( -\frac{3}{4} \times \frac{3}{x} \).

  • Step 3: Perform the usual fraction multiplication, which we鈥檒l dive into in the next sections.
    • reciprocal
    is \( \frac{b}{a}\).

    This concept is particularly useful when we need to convert a division problem into a multiplication one with fractions. Let鈥檚 take our previous fraction for example, \( \frac{x}{3} \). When we take its reciprocal, it becomes \( \frac{3}{x} \).

    • Remember: The reciprocal flips the fraction upside down.

    • It鈥檚 a key step to simplify complex fraction problems.
    multiplication of fractions
    \to \( -\frac{3}{4} \times \(\frac{3}{x}\)\).

    Here are the steps to multiply fractions:
    • Multiply the numerators. In our problem, we multiply \( -3 \times 3\), resulting in -9.

    • Multiply the denominators. In the same problem, we multiply the two denominators \( 4 \times x\), resulting in \( 4x \).


      • The result of the multiplication is \( -\frac{9}{4x} \).
    • Always double-check your fractions. Simplify if possible, but in this case, \( -\frac{9}{4x} \) is already in its simplest form.


    • Multiplying fractions follows a simple and consistent rule: numerators multiply with numerators, and denominators multiply with denominators.

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    Most popular questions from this chapter

    In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x-\frac{2}{5}\) when (a) \(x=\frac{3}{5} \quad\) (b) \(x=-\frac{3}{5}\)

    In the following exercises, solve the equation. $$ y+\frac{3}{5}=\frac{7}{5} $$

    In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\left(-\frac{11}{12}\right)\) when (a) \(x=\frac{11}{12} \quad\) (b) \(x=\frac{3}{4}\)

    In the following exercises, simplify. $$ \frac{3}{5} \cdot 15 $$

    In the following exercises, perform the indicated operations and simplify. $$\frac{y}{10}-\frac{1}{3}$$
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