Answer :
To solve the problem of subtracting mixed numbers with fractions, let's start by converting these mixed numbers into improper fractions. We're looking at the subtraction: [tex]\(4 \frac{2}{12} - 2 \frac{8}{12}\)[/tex].
1. Convert each mixed number to an improper fraction:
- For [tex]\(4 \frac{2}{12}\)[/tex]:
- Multiply the whole number 4 by the denominator 12: [tex]\(4 \times 12 = 48\)[/tex].
- Add the numerator 2: [tex]\(48 + 2 = 50\)[/tex].
- So, [tex]\(4 \frac{2}{12}\)[/tex] is the same as [tex]\(\frac{50}{12}\)[/tex].
- For [tex]\(2 \frac{8}{12}\)[/tex]:
- Multiply the whole number 2 by the denominator 12: [tex]\(2 \times 12 = 24\)[/tex].
- Add the numerator 8: [tex]\(24 + 8 = 32\)[/tex].
- So, [tex]\(2 \frac{8}{12}\)[/tex] is the same as [tex]\(\frac{32}{12}\)[/tex].
2. Set up the subtraction of the two improper fractions:
[tex]\[
\frac{50}{12} - \frac{32}{12}
\][/tex]
This subtraction shows that both fractions have the same denominator, which is 12. Therefore, when we subtract the fractions, we only need to subtract their numerators.
3. Perform the subtraction:
[tex]\[
50 - 32 = 18
\][/tex]
4. Write the result as a fraction:
The result of the subtraction is [tex]\(\frac{18}{12}\)[/tex].
This shows that the equation of subtraction using equivalent fractions is:
[tex]\[
\frac{50}{12} - \frac{32}{12}
\][/tex]
Therefore, the correct option from the given choices is:
C. [tex]\(\frac{50}{12} - \frac{32}{12}\)[/tex]
1. Convert each mixed number to an improper fraction:
- For [tex]\(4 \frac{2}{12}\)[/tex]:
- Multiply the whole number 4 by the denominator 12: [tex]\(4 \times 12 = 48\)[/tex].
- Add the numerator 2: [tex]\(48 + 2 = 50\)[/tex].
- So, [tex]\(4 \frac{2}{12}\)[/tex] is the same as [tex]\(\frac{50}{12}\)[/tex].
- For [tex]\(2 \frac{8}{12}\)[/tex]:
- Multiply the whole number 2 by the denominator 12: [tex]\(2 \times 12 = 24\)[/tex].
- Add the numerator 8: [tex]\(24 + 8 = 32\)[/tex].
- So, [tex]\(2 \frac{8}{12}\)[/tex] is the same as [tex]\(\frac{32}{12}\)[/tex].
2. Set up the subtraction of the two improper fractions:
[tex]\[
\frac{50}{12} - \frac{32}{12}
\][/tex]
This subtraction shows that both fractions have the same denominator, which is 12. Therefore, when we subtract the fractions, we only need to subtract their numerators.
3. Perform the subtraction:
[tex]\[
50 - 32 = 18
\][/tex]
4. Write the result as a fraction:
The result of the subtraction is [tex]\(\frac{18}{12}\)[/tex].
This shows that the equation of subtraction using equivalent fractions is:
[tex]\[
\frac{50}{12} - \frac{32}{12}
\][/tex]
Therefore, the correct option from the given choices is:
C. [tex]\(\frac{50}{12} - \frac{32}{12}\)[/tex]
