Evaluate 3 2/3 – 3 1/3 ÷ 3 2/3 (4

Explanation

Follow order of operations. First, add inside parentheses: 4 one-third plus 2 one-third equals 6 two-thirds. Convert mixed numbers to improper fractions: 3 two-thirds equals eleven-thirds, 3 one-third equals ten-thirds, 3 two-thirds equals eleven-thirds, and 6 two-thirds equals twenty-thirds.

Next, handle division before subtraction: ten-thirds ÷ eleven-thirds equals ten-thirds × three-elevenths equals thirty over thirty-three equals ten-elevenths. Now multiply: ten-elevenths times twenty-thirds equals two hundred over two hundred fifty-three.

Finally subtract: eleven-thirds minus two hundred over two hundred fifty-three. Find common denominator. Convert eleven-thirds to have denominator 253, but better to calculate: 11 ÷ 3 equals 3.667, and 200 ÷ 253 equals 0.791. Wait, recalculate: 3.667 minus 0.791 × 6.667 equals approximately 3.53, which is 3 thirty-five over sixty-six.