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Add, subtract, multiply, and divide mixed numbers with step-by-step solutions showing improper fraction conversions.
A mixed number combines a whole number and a proper fraction, like 2½. It represents a quantity greater than 1 in an easy-to-understand format.
Whole number (2) plus a proper fraction (½). Represents 2 and one-half.
Same value as 2½, but as a single fraction where numerator ≥ denominator.
Multiply whole number by denominator, add numerator, keep denominator
Divide numerator by denominator. Quotient is whole, remainder is new numerator
A mixed number is a whole number combined with a proper fraction, like 3½ or 2⅔. It's called 'mixed' because it mixes whole numbers with fractions. Mixed numbers are easier to visualize than improper fractions for values greater than 1.
Mixed numbers are better for everyday measurements and easy visualization (like 2½ cups). Improper fractions are better for calculations because they're easier to multiply, divide, add, and subtract. Convert to improper for math, then back to mixed for the final answer.
Yes, you can add whole numbers separately and fractions separately, but only if the fractions don't add up to more than 1. It's more reliable to convert to improper fractions first to avoid errors.
Convert the mixed number to an improper fraction first. For example, 2½ × 3 becomes 5/2 × 3/1 = 15/2 = 7½. Or multiply the whole number and fraction parts separately, but converting is more reliable.
Always convert improper fractions back to mixed numbers for the final answer (unless specifically asked not to). For example, if you get 17/4, convert it to 4¼. This makes the answer easier to understand.
Yes! They represent exactly the same value (2.5). The improper fraction 5/2 and the mixed number 2½ are just different ways of writing the same quantity. Both equal 2.5 as a decimal.