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[tex] \frac{2}{10} = \frac{4}{a-3}[/tex]

Solve the proportion, then leave the fraction in a fraction as simplest form. Thanks! :)

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Space

Answer:

[tex]\displaystyle a = 23[/tex]

General Formulas and Concepts:

Math

  • Simplifying

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{2}{10} = \frac{4}{a - 3}[/tex]

Step 2: Solve for a

  1. [Proportion] Simplify fraction:                                                                         [tex]\displaystyle \frac{1}{5} = \frac{4}{a - 3}[/tex]
  2. [Multiplication Property of Equality] Cross-multiply:                                     [tex]\displaystyle a - 3 = 20[/tex]
  3. [Addition Property of Equality] Add 3 on both sides:                                   [tex]\displaystyle a = 23[/tex]

Here we see that in order for the proportion to be equal, a must equal 23. Plugging in a back into the proportion should yield us a fraction equivalent to the original fraction.

Solution:

Step-1: Use cross multiplication

  • [tex]\frac{2}{10} = \frac{4}{a - 3}[/tex]
  • [tex]2(a - 3) = 4(10)[/tex]

Step-2: Simplify both sides

  • [tex]2(a - 3) = 4(10)[/tex]
  • [tex]2a - 6 = 40[/tex]

Step-3: Add 6 both sides

  • [tex]2a - 6 + 6 = 40 + 6[/tex]
  • [tex]2a = 46[/tex]

Step-4: Divide 2 both sides

  • [tex]2a = 46[/tex]
  • => [tex]\frac{2a}{2} = \frac{46}{2}[/tex]
  • => [tex]a = 23[/tex]

Double-check:

Step-1: Substitute the value of a into the proportion

  • [tex]\frac{2}{10} = \frac{4}{a - 3}[/tex]
  • => [tex]\frac{2}{10} = \frac{4}{23 - 3}[/tex]
  • => [tex]\frac{2}{10} = \frac{4}{20}[/tex]

Step-2: Simplify both sides.

  • [tex]\frac{2}{10} = \frac{4}{20}[/tex]
  • => [tex]\frac{1}{5} = \frac{1}{5} (Correct)[/tex]

The value of a must be 23 to make the proportion true.

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