Conversion Factor

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Conversion Factor: meaning, method and solved example (6th Grade) – Maths PDF

In short: Conversion factor names the fraction, worth exactly 1, that you multiply by to restate a measurement in a new unit, for example 12 inches over 1 foot.

6th GradeRatios and Percents6.RP.A.3d

What is Conversion Factor?

Every conversion factor starts from a fact like 1 yard = 3 feet. Top and bottom describe one and the same length, so the fraction is worth 1, and multiplying by it only rewrites the length in other units.

Precisely, if \(a\) of unit A equals \(b\) of unit B, then \(\frac{b \text{ B}}{a \text{ A}}\) and \(\frac{a \text{ A}}{b \text{ B}}\) both equal 1. Choose the one that cancels the unit you want to remove.

How to spot it

  • A problem gives a length, weight or volume in one unit and asks for the answer in another.
  • Two units appear with a known link, such as 5,280 feet in a mile or 16 ounces in a pound.
  • The word “per” connects two units in the statement of the fact you are given.
  • A speed or price is quoted in one set of units but you need a different set.

The method

  1. Write the starting measurement with its unit as a fraction over 1.
  2. Write the conversion factor so the unit you want to remove sits on the opposite side of the fraction bar.
  3. Multiply, cancel the matching units, and multiply the remaining numbers.
  4. Check that only the target unit remains and that the size of the number makes sense.
9 galx4 qt1 gal=36 qtgallons cancel, quarts remain: 9 x 4 = 36
Multiplying 9 gallons by 4 quarts per gallon gives 36 quarts.

Conversion Factor: solved example

Problem

A canoe outfitter in Minnesota rents a cooler that holds 3.5 gallons of water. How many cups is that, given that 1 gallon = 16 cups?

Solution

Choose the factor with gallons on the bottom so they cancel: \(\frac{16 \text{ cups}}{1 \text{ gallon}}\).

Multiply: \(3.5 \text{ gallons} \times \frac{16 \text{ cups}}{1 \text{ gallon}} = 56 \text{ cups}\). The cooler holds 56 cups.

Try it

Question 1

Convert 7.5 feet to inches using 1 foot = 12 inches.

Show the answer

\(7.5 \times \frac{12 \text{ in}}{1 \text{ ft}} = 90\) inches.

Question 2

A pot of chili calls for 48 fluid ounces of stock. Express that in pints if 16 fluid ounces = 1 pint.

Show the answer

Put fluid ounces on the bottom: \(48 \times \frac{1 \text{ pt}}{16 \text{ fl oz}} = 3\) pints.

Conversion Factor vs. Unit Rate

A unit rate compares two different quantities, such as miles and hours, and changes the size of the story. A fraction used to convert units compares two names for the same amount, so it equals 1 and leaves the size untouched.

Unit Rate

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