MMR Theme 1 Farm Swap Helpful Vocab

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Dimensional analysis

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It leverages the principle that multiplying by a fraction equal to one (e.g., 12 inches/1 foot) doesn't change the value, but it can change the units.

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Dimensional Analysis

Step 1:

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1. 1. Identify the given and desired units:

   Determine what units you are starting with and what units you want to end up with. 

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Dimensional Analysis

Step 2:

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1. 2. Find conversion factors:

   Identify the relationships between the given and desired units. For example, 1 foot = 12 inches, or 1 kg = 2.2 pounds. 

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Dimensional Analysis

Step 3:

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1. 3. Set up conversion factors as fractions:

   Create fractions where the numerator and denominator represent equivalent quantities, but in different units. Choose the fraction that will cancel out the unwanted units. 

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Dimensional Analysis

Step 4:

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1. 4. Multiply and cancel units:

   Multiply the given value by the conversion factor(s) in a way that the unwanted units cancel out, leaving only the desired units. 

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Dimensional Analysis

Step 5:

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1. 5. Calculate the result:

   Perform the necessary multiplication and division to get the final answer with the correct units. 

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Proportion

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A mathematical comparison between two numbers

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Ratio:

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A ratio compares two quantities. For example, x:y or x/y, read as "x is to y". 

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Proportion:

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A proportion is an equation stating that two ratios are equal. The general form is a:b :: c:d, which can also be written as a/b = c/d. 

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Proportion/Ratio Example:

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If 2 pencils cost $1, then 4 pencils will cost $2. This can be expressed as the proportion 2/1 = 4/2, or 2:1 :: 4:2