Conversions
Common Core Standard: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately
when multiplying or dividing quantities.
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Converting units means to change one unit to an equivalent unit
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Most common conversions are unit rates
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12 in : 1 ft
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3 ft: 1 yd
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5,280 ft: 1 mile
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2.54 cm : 1 in
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100 cm: 1 meter
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10 mm: 1 cm
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1,000 m: 1 km
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4 cups: 1 quart
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2 cups: 1 pint
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2 pints: 1 qt
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4 qt: 1 gallon
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Using what we know about ratios, proportions, and unit rates we can easily convert from one unit to another
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There are several methods of conversion, the ones shown below are examples only, you may use an alternative
method as long as it results in the correct answer and you can explain it
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Example: Convert 4 feet to inches
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The unit rate is 12 in : 1 ft
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To get from 1 foot to 4 feet, multiply by 4
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This means multiply 12 by 4 as well
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12 ● 4 = 48 inches
Therefore, 48 inches are in 4 feet
Example: Shannon is making a large cake. It requires 8 cups of sugar, how many quarts of sugar is this?
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The unit rate is 4 cups: 1 quart
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To go from 4 cups to 8 cups, multiply by 2
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This means multiply 1 quart by 2
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1 ● 2 = 2 quarts
8 cups: 2 quarts
Example: Stephen ran 60, 543 meters at track practice this month. How many kilometers did Stephen run?
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The unit rate is 1,000 m: 1 km
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It is not easy for most people to determine what number multiplied by 1,000 equals 60,543. There is
another approach.
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When converting from a smaller unit to a bigger unit divide by the unit rate
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When converting from a bigger unit to a smaller unit multiply by the unit rate
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This works because it takes more of a small unit to take the same space as 1 big unit (12 inches
takes up the same space as just 1 foot)
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Since, we are converting from a smaller unit (meters) to a larger unit (kilometer) divide 60,543 by 1,000
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60,543 ÷ 1,000 = 60.543
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Stephen ran 60.543 kilometers this month at track practice