Math Problem Statement

-1\dfrac{1}{3} \div 2\dfrac{2}{5} =

Solution

To solve the expression 113÷225-1 \frac{1}{3} \div 2 \frac{2}{5}, let's first convert the mixed numbers into improper fractions and then perform the division.

Step 1: Convert mixed numbers to improper fractions.

  1. For 113-1 \frac{1}{3}: 113=1×3+13=3+13=23-1 \frac{1}{3} = \frac{-1 \times 3 + 1}{3} = \frac{-3 + 1}{3} = \frac{-2}{3}

  2. For 2252 \frac{2}{5}: 225=2×5+25=10+25=1252 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}

So the expression becomes: 23÷125\frac{-2}{3} \div \frac{12}{5}

Step 2: Division of fractions.

To divide fractions, we multiply by the reciprocal of the second fraction: 23÷125=23×512\frac{-2}{3} \div \frac{12}{5} = \frac{-2}{3} \times \frac{5}{12}

Step 3: Multiply the fractions.

23×512=2×53×12=1036\frac{-2}{3} \times \frac{5}{12} = \frac{-2 \times 5}{3 \times 12} = \frac{-10}{36}

Step 4: Simplify the fraction.

1036=518\frac{-10}{36} = \frac{-5}{18}

Final Answer:

113÷225=518-1 \frac{1}{3} \div 2 \frac{2}{5} = \frac{-5}{18}

Would you like more details on any of the steps, or do you have any other questions?

Related Questions:

  1. How do you convert a mixed number to an improper fraction?
  2. How do you multiply two fractions together?
  3. Can you explain why we multiply by the reciprocal when dividing fractions?
  4. What is the process for simplifying a fraction?
  5. How do you convert an improper fraction back to a mixed number?

Tip: When dividing fractions, always remember to multiply by the reciprocal of the second fraction.

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Math Problem Analysis

Mathematical Concepts

Mixed Numbers
Improper Fractions
Fraction Division
Simplification of Fractions

Formulas

To convert a mixed number to an improper fraction: a\dfrac{b}{c} = \frac{ac + b}{c}
To divide fractions: \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Theorems

Reciprocal of a Fraction

Suitable Grade Level

Grades 5-7