Interpret a fraction as division of the numerator by the denominator

What you'll learn

1. Explain in their own words why a fraction a/b is equivalent to the division expression a ÷ b, using the fair-sharing interpretation: dividing a items equally among b people gives each person a/b
2. Interpret a division problem whose quotient is not a whole number and express the answer as a fraction or mixed number rather than writing a remainder
3. Verify the fraction-as-division relationship by multiplying back: if a ÷ b = a/b, then (a/b) × b = a
4. Solve word problems in which whole numbers are divided and the result is a fraction or mixed number, selecting an appropriate visual model (equal-sharing diagram, number line, or equation) to represent the situation
5. Locate a fractional or mixed-number quotient between two consecutive whole numbers on a number line, demonstrating understanding of its magnitude