Question

6. Use a one unit multiplier to convert 20 inches to centimeters.

7. Use two unit multipliers to convert 25 feet to centimeters.

Answer 1

6. Multiply the given equation by 20

... 20×1 in. = 20×2.54 cm

... 20 in = 50.8 cm

7. Multiply the equation (1 foot = 12 inches) by 25.

... 25×1 ft = 25×12 in

... 25 ft = 300 in

Now, multiply the equation for conversion to cm by 300

... 300×1 in = 300×2.54 cm

... 300 in = 762 cm

Using the transitive property of equality,

... 25 ft = 300 in = 762 cm

... 25 ft = 762 cm

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A "unit multiplier" is no doubt explained in your lesson. We assume it is a fraction whose value is 1, but that has different units in numerator and denominator. The equation 1 in = 2.54 cm gives rise to two unit multipliers, depending on which conversion you need or want:

`1=\frac{1\,\text{in}}{2.54\,\text{cm}}=\frac{2.54\,\text{cm}}{1\,\text{in}}`

Since you're converting to centimeters, you want the one with cm in the numerator.

`(20\,\text{in})*\frac{2.54\,\text{cm}}{1\,\text{in}}=50.8\,\text{cm}`

`(25\,\text{ft})*\frac{12\,\text{in}}{1\,\text{ft}}*\frac{2.54\,\text{cm}}{1\,\text{in}}=762\,\text{cm}`