To multiply mixed numbers, convert them to improper fractions first, then multiply numerators and denominators. 2 1/3 x 1 1/2 = 7/3 x 3/2 = 21/6 = 3 1/2. While it is possible to use the distributive property (2 1/3 x 1 1/2 = 2 x 1 + 2 x 1/2 + 1/3 x 1 + 1/3 x 1/2), this is error-prone with four partial products. Converting to improper fractions is more reliable. Students should estimate first (2 1/3 x 1 1/2 is about 2 x 1.5 = 3) to check the reasonableness of their answer.
Practice converting mixed numbers to improper fractions until fluent (prerequisite skill). Then apply the fraction multiplication algorithm. Emphasize estimation before computing. Use area models for simple cases (1 1/2 x 2 1/3) to build intuition. Always convert the answer back to a mixed number and simplify.
You already know two key skills: how to multiply fractions (multiply the numerators, multiply the denominators) and how to convert a mixed number into an improper fraction (multiply the whole number by the denominator, add the numerator, keep the denominator). Multiplying mixed numbers is simply a combination of these two skills — and the reason you convert first is to make the fraction multiplication step clean and reliable.
Consider 2⅓ × 1½. Converting: 2⅓ = 7/3 (since 2 × 3 + 1 = 7) and 1½ = 3/2. Now multiply: 7/3 × 3/2 = 21/6. Simplify: 21/6 = 3½. The convert-then-multiply method works because improper fractions behave exactly like ordinary fractions — there is no special rule needed. The most common mistake is to try to multiply the whole-number parts and the fraction parts separately: 2⅓ × 1½ ≠ (2 × 1) + (⅓ × ½). That approach misses two cross terms: 2 × ½ and 1 × ⅓. The distributive property actually requires four partial products, not two, so the separate-parts method almost always gives the wrong answer.
Before you compute, always estimate. Round each mixed number to the nearest whole number: 2⅓ is close to 2, and 1½ is close to 2, so the answer should be around 4. Your computed answer of 3½ is in that ballpark — reasonable. If your calculation had come out as 21 or 0.35, the estimate would immediately flag the error. After multiplying, convert the improper fraction back to a mixed number and simplify if possible (cancel common factors before multiplying when you can, to keep the numbers small). The full sequence — estimate, convert, multiply, simplify, check — is the reliable routine for every mixed-number multiplication problem.