Answer :
To find out how much salt Mabel added altogether, let's break down the problem step-by-step.
1. Convert mixed numbers to improper fractions:
- Mabel first added [tex]\(1 \frac{2}{3}\)[/tex] tablespoons of salt. We can express this as an improper fraction:
[tex]\[
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
\][/tex]
- Later, she added [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of salt:
[tex]\[
1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}
\][/tex]
2. Add the improper fractions:
- To add [tex]\(\frac{5}{3}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex], we first find a common denominator, which is 6.
- Convert [tex]\(\frac{5}{3}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
\][/tex]
- Convert [tex]\(\frac{3}{2}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\][/tex]
- Now add the fractions:
[tex]\[
\frac{10}{6} + \frac{9}{6} = \frac{19}{6}
\][/tex]
3. Convert the improper fraction to a mixed number:
- Divide 19 by 6. The quotient is 3 and the remainder is 1.
- So, [tex]\(\frac{19}{6} = 3 \frac{1}{6}\)[/tex]
Therefore, Mabel added a total of [tex]\(3 \frac{1}{6}\)[/tex] tablespoons of salt. The correct answer is:
C. [tex]\(3 \frac{1}{6}\)[/tex] tablespoon
1. Convert mixed numbers to improper fractions:
- Mabel first added [tex]\(1 \frac{2}{3}\)[/tex] tablespoons of salt. We can express this as an improper fraction:
[tex]\[
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
\][/tex]
- Later, she added [tex]\(1 \frac{1}{2}\)[/tex] tablespoons of salt:
[tex]\[
1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}
\][/tex]
2. Add the improper fractions:
- To add [tex]\(\frac{5}{3}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex], we first find a common denominator, which is 6.
- Convert [tex]\(\frac{5}{3}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
\][/tex]
- Convert [tex]\(\frac{3}{2}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\][/tex]
- Now add the fractions:
[tex]\[
\frac{10}{6} + \frac{9}{6} = \frac{19}{6}
\][/tex]
3. Convert the improper fraction to a mixed number:
- Divide 19 by 6. The quotient is 3 and the remainder is 1.
- So, [tex]\(\frac{19}{6} = 3 \frac{1}{6}\)[/tex]
Therefore, Mabel added a total of [tex]\(3 \frac{1}{6}\)[/tex] tablespoons of salt. The correct answer is:
C. [tex]\(3 \frac{1}{6}\)[/tex] tablespoon
