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Add 2 1/5

+ 3 2/3
(1 point)
Responses

5 3/8
53 eighths

5 13/15
513 over 15

5 3/15
53 over 15
Question 2
Subtract 8 5/10
- 4 2/5
(1 point)
Responses

4 1/10
41 tenth

4 3/5
4 3/5

4 3/10

1 answer

Let's solve both problems step by step.

Question 1: Add \( 2 \frac{1}{5} + 3 \frac{2}{3} \)

  1. Convert the mixed numbers to improper fractions:

    \[ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \] \[ 3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \]

  2. Find a common denominator. The least common denominator (LCD) for 5 and 3 is 15.

  3. Convert both fractions to have the common denominator:

    \[ \frac{11}{5} = \frac{11 \times 3}{5 \times 3} = \frac{33}{15} \] \[ \frac{11}{3} = \frac{11 \times 5}{3 \times 5} = \frac{55}{15} \]

  4. Add the two fractions:

    \[ \frac{33}{15} + \frac{55}{15} = \frac{33 + 55}{15} = \frac{88}{15} \]

  5. Convert the improper fraction back to a mixed number:

    \[ \frac{88}{15} = 5 \frac{13}{15} \]

So the answer to Question 1 is 5 13/15 (or "513 over 15").

Question 2: Subtract \( 8 \frac{5}{10} - 4 \frac{2}{5} \)

  1. Convert the mixed numbers to improper fractions:

    \[ 8 \frac{5}{10} = \frac{8 \times 10 + 5}{10} = \frac{80 + 5}{10} = \frac{85}{10} \] \[ 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} \]

  2. Find a common denominator. The least common denominator (LCD) for 10 and 5 is 10.

  3. Convert the second fraction:

    \[ \frac{22}{5} = \frac{22 \times 2}{5 \times 2} = \frac{44}{10} \]

  4. Subtract the two fractions:

    \[ \frac{85}{10} - \frac{44}{10} = \frac{85 - 44}{10} = \frac{41}{10} \]

  5. Convert to a mixed number:

    \[ \frac{41}{10} = 4 \frac{1}{10} \]

So the answer to Question 2 is 4 1/10 (or "41 tenth").

Final Answers:

  1. Question 1: 5 13/15
  2. Question 2: 4 1/10