Fractions can only be added if their denominators are the same, since that means that the fraction pieces are identical in size.
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Fraction understanding is slow to develop for most children; making the transition from handling whole numbers to parts of wholes requires a shift in thinking that should be supported carefully and patiently by the teacher.
Once students are familiar with the way common fractions are written, and the meanings of the “top number” (numerator) and the “bottom number” (denominator), they can start to tackle questions involving addition of fractions in which the denominators are the same.
Use pictures or objects to support students’ thinking about these questions, so that they can see for themselves that the denominators are merely a sort of “label” that indicates the size of the pieces, and so adding two fractions such as three fourths and two fourths requires that we add the three and the two, but not the fours.
Once a child is familiar with adding fractions with like denominators, move on to questions in which denominators are “linked”, but not the same.
A good place to start is with halves and fourths / quarters, as children are most likely familiar with these fractions. Ask the child to draw a diagram or represent the fractions using physical materials, and then ask the child how it would be possible to add the two fractions, to lead the child to see that one denominator will need to be changed to make the pieces being added the same size.
