Evaluate the expression: 2/5 ÷ 1 1/3 × 1 2/3

April 9, 2026Mathematics

ScanSolve AI Answer

April 9, 2026

Answer

$\frac{1}{2}$

Here is the solution to the problem:

$\frac{2}{5} \div 1\frac{1}{3} \times 1\frac{2}{3}$

Step 1: Convert the mixed numbers to improper fractions. $1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$ $1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$

Step 2: Rewrite the expression with improper fractions. $\frac{2}{5} \div \frac{4}{3} \times \frac{5}{3}$

Step 3: Perform the division first (from left to right). To divide by a fraction, multiply by its reciprocal. $\frac{2}{5} \times \frac{3}{4} \times \frac{5}{3}$

Step 4: Perform the multiplication. $\frac{2 \times 3 \times 5}{5 \times 4 \times 3} = \frac{30}{60}$

Step 5: Simplify the fraction. $\frac{30}{60} = \frac{1}{2}$ The final answer is $\boxed{\frac{1}{2}}$ .

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Quick Answer

Here is the solution to the problem: (2)/(5) ÷ 1(1)/(3) × 1(2)/(3) Step 1: Convert the mixed numbers to improper fractions.
1(1)/(3) = (1 × 3 + 1)/(3) = (4)/(3) 1(2)/(3) = (1 × 3 + 2)/(3) = (5)/(3) Step 2: Rewrite the expression with improper fractions.
(2)/(5) ÷ (4)/(3) × (5)/(3) Step 3: Perform the division first (from left to right).
To divide by a fraction, multiply by its reciprocal.

Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 9, 2026

Here is the solution to the problem: (2)/(5) ÷ 1(1)/(3) × 1(2)/(3) Step 1: Convert the mixed numbers to improper fractions. 1(1)/(3) = (1 × 3 + 1)/(3) = (4)/(3) 1(2)/(3) = (1 × 3 + 2)/(3) = (5)/(3) Step 2: Rewrite the expression with improper fractions. (2)/(5) ÷ (4)/(3) × (5)/(3) Step 3: Perform the division first (from left to right). To divide by a fraction, multiply by its reciprocal. (2)/(5) × (3)/(4) × (5)/(3) Step 4: Perform the multiplication. (2 × 3 × 5)/(5 × 4 × 3) = (30)/(60) Step 5: Simplify the fraction. (30)/(60) = (1)/(2) The final answer is (1)/(2).