Question

a rock climber is using a pulley to lower supplies 20\frac{3}{4} meters to the bottom of a cliff. the supplies reach the ground in 3\frac{1}{2} minutes. if the supplies are lowered at a constant rate, what is the change in elevation per minute?

1. circle the words in the problem that describe the value you must find.
2. would you represent the change in elevation with a positive or negative number? explain how you know.
3. explain why you can use the expression (-20\frac{3}{4})\div3\frac{1}{2} to find the answer.
4. circle the terms below that describe the two numbers in the problem.

mixed fraction improper fraction rational number

1. order the steps to find the quotient in item 3.

□ multiply numerators and multiply denominators.
□ rewrite the mixed numbers as improper fractions.
□ simplify and give the correct sign.
□ rewrite division as multiplication by the reciprocal.

Explanation:

1. The words to circle are "change in elevation per minute".
2. The change in elevation should be represented with a negative number. Since the supplies are being lowered (going downwards in elevation), the elevation is decreasing. A decrease in a quantity is typically represented by a negative number.
3. The total change in elevation is - 20\frac{3}{4} meters (negative because it is a decrease in elevation) and the time taken is 3\frac{1}{2} minutes. To find the rate of change (change in elevation per minute), we use the formula for rate which is \(\text{rate}=\frac{\text{change in quantity}}{\text{time}}\). So, we use the expression \((- 20\frac{3}{4})\div3\frac{1}{2}\).
4. The numbers \(20\frac{3}{4}\) and \(3\frac{1}{2}\) are both mixed - fractions and rational numbers.
5. The correct order of steps to find the quotient of \((-20\frac{3}{4})\div3\frac{1}{2}\) is:

• Rewrite the mixed numbers as improper fractions.
• Rewrite division as multiplication by the reciprocal.
• Multiply numerators and multiply denominators.
• Simplify and give the correct sign.

Answer:

1. The words to circle are "change in elevation per minute".
2. The change in elevation should be represented with a negative number. Since the supplies are being lowered (going downwards in elevation), the elevation is decreasing. A decrease in a quantity is typically represented by a negative number.
3. The total change in elevation is - 20\frac{3}{4} meters (negative because it is a decrease in elevation) and the time taken is 3\frac{1}{2} minutes. To find the rate of change (change in elevation per minute), we use the formula for rate which is \(\text{rate}=\frac{\text{change in quantity}}{\text{time}}\). So, we use the expression \((- 20\frac{3}{4})\div3\frac{1}{2}\).
4. The numbers \(20\frac{3}{4}\) and \(3\frac{1}{2}\) are both mixed - fractions and rational numbers.
5. The correct order of steps to find the quotient of \((-20\frac{3}{4})\div3\frac{1}{2}\) is:

• Rewrite the mixed numbers as improper fractions.
• Rewrite division as multiplication by the reciprocal.
• Multiply numerators and multiply denominators.
• Simplify and give the correct sign.