Mixed numbers and improper fractions

To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient counts wholes. Write the remainder over the same denominator. For 14/5, 2 × 5 = 10 and 3 × 5 = 15 is too much. There are 2 wholes and 4 fifths left: 2 4/5. The remainder must be smaller than the denominator.

To change a mixed number to an improper fraction, count every part in the same units. Multiply the whole number by the denominator, add the numerator, and keep the denominator. For 1 2/7, the whole contains 7 sevenths. Add 2 more: 7 + 2 = 9. So 1 2/7 = 9/7.

When denominators match, add the numerators and keep the denominator. The parts keep their size. For 4/3 + 5/3, add 4 + 5 = 9 thirds. Group them in threes: 9/3 = 3. If parts remain after making wholes, write those parts over the same denominator.

To add mixed numbers with matching denominators, add their whole numbers and then their fraction parts. For 1 1/6 + 2 3/6, the wholes make 3 and the sixths make 4/6. The total is 3 4/6. If the fraction parts fill another whole, include it in the whole-number part.