To fully understand what it means to multiply a whole number by a fraction, students can represent an example problem with drawings. If they need to multiply 4 by 5/8, they can draw four cakes and "cut" each cake into eight pieces by drawing asterisks on them. Then, they shade in five of the pieces on each cake. Students can then see that they have taken four wholes and multiplied each of them by 5/8.
When students have shaded their four cakes, they can count the number of shaded slices, getting 20. They know that there are eight slices in each cake, so they can figure out the total number of whole cakes they have by drawing new cakes, dividing them into eighths, and shading the eighths until they have shaded 20 of them. They should finish with two cakes completely shaded and 4/8 of a third. They can then see that multiplying four cakes by 5/8 gives them two and a half cakes.
Now that students have seen what multiplying a whole number by a fraction means in concrete terms, they can learn the quicker, purely numerical way to solve the problem. The teacher can remind students that a whole number can also be written as a fraction, by writing the whole number as the numerator and the number 1 as the denominator. Students can then solve the problem by multiplying the numerators and the denominators, getting 20/8. They can then reduce the fraction to 5/2, and then to 2 1/2.
For extra practice, students can write out the multiplication problem as an addition problem. 4 x 5/8 is the same problem as 5/8 + 5/8 + 5/8 + 5/8. Students should know that they add fractions with the same denominator by adding the numerators together and not changing the denominator. By doing this, students will again get 20/8, which they can again reduce down to 2 1/2. Teachers can explain to students that this is a good system to use if they ever get confused.