Comparing and equivalent fractions

Equivalent fractions are different names for the same amount. Look at the fraction wall: the shaded part of the half bar ends in the same place as 2 fourths, 3 sixths, 4 eighths and 6 twelfths. So 1/2 = 2/4 = 3/6 = 4/8 = 6/12. When we cut every part into 2 equal parts, the number of shaded parts doubles and the number of all parts doubles: 1/2 becomes 2/4. If we cut every part into 3 equal parts, 1/2 becomes 3/6. In other words, multiply the numerator and the denominator by the same number. We may also divide both by the same number: 6/8 = 3/4. The amount stays the same, only the size and number of the parts change.