Answer :
Certainly! Let's go through each of the numbered problems step by step:
12) Conversion: 6 kg to 600 g to 3000 g
1. Convert kilograms to grams:
- We know that 1 kilogram (kg) is equivalent to 1000 grams (g).
- Therefore, 6 kg is equal to [tex]\(6 \times 1000 = 6000\)[/tex] grams.
2. Add the weights:
- You are given additional weights of 600 g and 3000 g to add to the original 6000 g.
- Sum up these weights:
[tex]\[
6000 \text{ g} + 600 \text{ g} + 3000 \text{ g} = 9600 \text{ g}
\][/tex]
13) Conversion: 47 seconds to 1 minute
1. Understanding time conversion:
- 1 minute is equal to 60 seconds.
2. Add the time in seconds:
- You have 47 seconds, and you add 1 minute (60 seconds) to it.
- Sum up these seconds:
[tex]\[
47 \text{ s} + 60 \text{ s} = 107 \text{ s}
\][/tex]
14) Adding mixed numbers and fractions: [tex]\(3 \frac{1}{7} + 0 \frac{4}{14}\)[/tex]
1. Convert to improper fractions:
- The mixed number [tex]\(3 \frac{1}{7}\)[/tex] can be converted:
- Multiply 3 by 7 and add 1:
[tex]\[
3 \times 7 + 1 = 22
\][/tex]
- So, it becomes [tex]\(\frac{22}{7}\)[/tex].
- The mixed number [tex]\(0 \frac{4}{14}\)[/tex] is:
- Since the whole number is 0, it's simply [tex]\(\frac{4}{14}\)[/tex].
2. Simplify the second fraction (optional but helpful):
- Simplify [tex]\(\frac{4}{14}\)[/tex] to [tex]\(\frac{2}{7}\)[/tex] by dividing both the numerator and the denominator by 2.
3. Add the fractions:
- Since both fractions [tex]\(\frac{22}{7}\)[/tex] and [tex]\(\frac{2}{7}\)[/tex] have the same denominator, simply add the numerators:
[tex]\[
\frac{22 + 2}{7} = \frac{24}{7}
\][/tex]
4. Convert back to a mixed number (if needed):
- Divide 24 by 7 to get 3 with a remainder of 3. Therefore, the mixed number is:
[tex]\[
3 \frac{3}{7}
\][/tex]
- In decimal form, this is approximately 3.4285714285714284.
These are the step-by-step solutions for each part of the problem.
12) Conversion: 6 kg to 600 g to 3000 g
1. Convert kilograms to grams:
- We know that 1 kilogram (kg) is equivalent to 1000 grams (g).
- Therefore, 6 kg is equal to [tex]\(6 \times 1000 = 6000\)[/tex] grams.
2. Add the weights:
- You are given additional weights of 600 g and 3000 g to add to the original 6000 g.
- Sum up these weights:
[tex]\[
6000 \text{ g} + 600 \text{ g} + 3000 \text{ g} = 9600 \text{ g}
\][/tex]
13) Conversion: 47 seconds to 1 minute
1. Understanding time conversion:
- 1 minute is equal to 60 seconds.
2. Add the time in seconds:
- You have 47 seconds, and you add 1 minute (60 seconds) to it.
- Sum up these seconds:
[tex]\[
47 \text{ s} + 60 \text{ s} = 107 \text{ s}
\][/tex]
14) Adding mixed numbers and fractions: [tex]\(3 \frac{1}{7} + 0 \frac{4}{14}\)[/tex]
1. Convert to improper fractions:
- The mixed number [tex]\(3 \frac{1}{7}\)[/tex] can be converted:
- Multiply 3 by 7 and add 1:
[tex]\[
3 \times 7 + 1 = 22
\][/tex]
- So, it becomes [tex]\(\frac{22}{7}\)[/tex].
- The mixed number [tex]\(0 \frac{4}{14}\)[/tex] is:
- Since the whole number is 0, it's simply [tex]\(\frac{4}{14}\)[/tex].
2. Simplify the second fraction (optional but helpful):
- Simplify [tex]\(\frac{4}{14}\)[/tex] to [tex]\(\frac{2}{7}\)[/tex] by dividing both the numerator and the denominator by 2.
3. Add the fractions:
- Since both fractions [tex]\(\frac{22}{7}\)[/tex] and [tex]\(\frac{2}{7}\)[/tex] have the same denominator, simply add the numerators:
[tex]\[
\frac{22 + 2}{7} = \frac{24}{7}
\][/tex]
4. Convert back to a mixed number (if needed):
- Divide 24 by 7 to get 3 with a remainder of 3. Therefore, the mixed number is:
[tex]\[
3 \frac{3}{7}
\][/tex]
- In decimal form, this is approximately 3.4285714285714284.
These are the step-by-step solutions for each part of the problem.
