Question

there are 28.35 grams in an ounce and 2.21 pounds in a kilogram. miriam converted 7 kilograms to ounces, but her answer is not correct. what is the best explanation of her error?
7kg×(1000g/1kg)×(28.35g/1oz)≈198,450oz
○ miriam set up the problem correctly but made a multiplication error.
○ miriam multiplied correctly, but her second fraction should be (1kg/1000g).
○ miriam multiplied correctly, but her third fraction should be (1oz/28.35g).
○ miriam is missing a fraction that is needed to convert the 7 kilograms to pounds.

Explanation:

Step1: Analyze unit conversion setup

To convert kilograms to ounces, we need to convert kg to grams first (using \( \frac{1000\,\text{g}}{1\,\text{kg}} \), which Miriam did correctly), then grams to ounces. The conversion from grams to ounces should use the reciprocal of the given "grams per ounce" because we want to cancel grams and get ounces. So instead of \( \frac{28.35\,\text{g}}{1\,\text{oz}} \), we need \( \frac{1\,\text{oz}}{28.35\,\text{g}} \).

Step2: Evaluate each option

• Option 1: Multiplication error? Let's check \( 7\times1000\times28.35 = 7\times28350 = 198450 \), so multiplication is correct. Eliminate.
• Option 2: The second fraction is \( \frac{1000\,\text{g}}{1\,\text{kg}} \), which is correct for kg to g. Eliminate.
• Option 3: The third fraction should be \( \frac{1\,\text{oz}}{28.35\,\text{g}} \) (to cancel grams), which matches this option. Correct.
• Option 4: We don't need to convert to pounds. We can go from kg to g to oz directly. Eliminate.

Answer:

C. Miriam multiplied correctly, but her third fraction should be \( \frac{1\,\text{oz}}{28.35\,\text{g}} \) (the third option in the list)