Question

(3 1/2 hours) how many minutes?

Answer 1

210 minutes

Explanation:

To convert from hours to minutes, we can multiply by a conversion ratio:

`\left(3 (1)/(2) \text{ hr}\right)\left(\frac{60 \text{ min}}{1 \text{ hr}}\right)`

↓ converting the mixed number to a fraction

`\left((7)/(2) \text{ hr}\right)\left(\frac{60 \text{ min}}{1 \text{ hr}}\right)`

↓ canceling the hours unit

`(7)/(2) \cdot 60 \text{ min}`

↓ multiplying

`\boxed{210\text{ min}}`

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Note: When we multiply something by a conversion ratio, we are not changing the value of it, but rather changing its form. In other words, a conversion ratios has a value of 1, and anything multiplied by 1 is itself. To illustrate this:

`\frac{60 \text{ min}}{1 \text{ hr}} = \frac{60 \text{ min}}{60\text{ min}} = (1)/(1) = 1`

because

`1 \text{ hr} = 60 \text{ min}`.

Answer 2

210 minutes

Explanation:

We know that 1 hour = 60 minutes.

3 hours = 3 * 60 = 180 minutes

1/2 hour = 1/2 * 60 minutes = 30 minutes

3 1/2 hours = 180+30 = 210 minutes