Find which of the following represent 3:4

General
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find which of the following represent 3:4

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Find which of the following represent 3:4

Answer:

To determine which of the given expressions or examples accurately represent the ratio (3:4), it’s important to first understand the concept of a ratio. A ratio is a way to compare two quantities by showing the relative size of one quantity with respect to another. The ratio (3:4) means for every 3 units of the first quantity, there are 4 units of the second quantity.

1. Understanding Ratios

  • Basic Definition: A ratio is written as (a:b) where (a) and (b) are numbers representing the quantities of two items.
  • Equivalent Ratios: Two ratios (a:b) and (c:d) are considered equivalent if the cross-multiplication gives the same result, i.e., (a \times d = b \times c).

2. Expressing and Simplifying Ratios

Let’s consider what (3:4) means and how to express it:

  • As a fraction: The ratio (3:4) can be expressed as the fraction (\frac{3}{4}).
  • Proportional Relationships: If (3:4) is written as (\frac{3}{4}), equivalent ratios can be found by multiplying numerator and denominator by the same non-zero number, such as (\frac{6}{8}), (\frac{9}{12}), and so on.

3. Identifying Equivalent Ratios

When given a set of ratios, we need to determine which of these are equivalent to (3:4). Here is a step-by-step process to find out:

  • Step 1: Cross Multiply: Check by cross-multiplying. For example, to compare (\frac{3}{4}) with another fraction (\frac{a}{b}), multiply to see if (3 \times b = 4 \times a).

  • Examples: Suppose we are given (\frac{15}{20}), (\frac{9}{12}), and (\frac{6}{8}) to compare to (3:4).

    • For (\frac{15}{20}):

      • Cross-multiply: (3 \times 20 = 60) and (4 \times 15 = 60). Since they are equal, (\frac{15}{20}) is equivalent to (3:4).

    • For (\frac{9}{12}):

      • Cross-multiply: (3 \times 12 = 36) and (4 \times 9 = 36). They are equal, so (\frac{9}{12}) is equivalent to (3:4).

    • For (\frac{6}{8}):

      • Cross-multiply: (3 \times 8 = 24) and (4 \times 6 = 24). They are equal, so (\frac{6}{8}) is equivalent to (3:4).

4. Visual Representation

Understanding and verifying ratios can be made easier using a visual approach:

  • Graphs and Tables: Create tables comparing different values to see if they scale equivalently.

    For example:

    Original Ratio Scaled Equivalent
    (3:4) (6:8)
    (3:4) (9:12)
    (3:4) (15:20)

Here, all scaled ratios match the (3:4) by maintaining a consistent multiplier.

5. Application in Real-Life Scenarios

Ratios like (3:4) are quite common in everyday situations. They can represent:

  • Financial Shares: If individuals invest in a business in the ratio (3:4), it implies the contributions are proportional in such a manner.
  • Recipe Adjustment: When cooking, if a recipe requires parts of ingredients in a (3:4) ratio (like oil and vinegar in a salad dressing), equal scaling maintains the intended flavor even with increased serving sizes.

Summary:

To find which expressions or representations match the ratio of (3:4), involve converting, comparing by cross-multiplication, and confirming equivalency through proportional scaling. Ratios are a fundamental tool for comparing quantities in mathematics, finance, cooking, and various other applications. By mastering how to manipulate and identify equivalent ratios, you can effectively solve many practical problems involving proportional reasoning. If you have further questions or need clarification, feel free to ask! @anonymous6