Before performing addition with fractions, an equation needs to have common denominators. Practice finding multiples of numbers and factors. Teach students to list all factors of both denominators until they find a factor that is common to both. They can repeat this process with multiples. Change fractions to equivalent fractions with a common denominator by multiplying or dividing both the numerator and denominator by a factor or divisor that results in the denominator being the same number. Practice finding equivalent fractions by playing a match-up game. Write representations of equivalent fractions on index cards. The students match up all of the equivalent fractions and drawings. Once the students have the equation written with common denominators, they add the numerators and write the denominator under the numerator.
Learning how to find equivalent fractions is a skill needed before performing a subtraction equation. Write at least six different equivalent fractions on the board with at least two fractions that are not equivalent. Ask the students to find the two fractions that do not belong. They will need to figure out which fractions are equivalent by converting the fractions into fractions with common denominators. Once they find the common denominators in a subtraction problem, the students subtract the numerators and place the denominator under the numerator.
The multiplication operation for fractions requires the students to multiply the numerators and the denominators to find the product. To help children understand the concept, ask them to divide a rectangle horizontally into the same number of sections as the denominator of the first factor. If the first factor in the problem is 1/3, divide the rectangle with horizontal lines into thirds. The students color in one of the third sections to represent 1/3. They divide the same rectangle into the same number of sections as the second factor's denominator. They divide it vertically for the second factor. Fill in with a different color the number of sections that is the same as the numerator. If the second factor is 1/6, they will have six equal sections with one section colored in. Now the rectangle is sectioned off into 18 sections -- three horizontally and six vertically. One of those sections is colored in by both crayons. This represents the product -- 1/3 x 1/6 = 1/18.
In order to divide fractions, teach students to do the opposite operation of division, which is multiplication. The first step is to rewrite the problem as a multiplication problem. The students write the first factor as it is. The second factor is written as its reciprocal. Flip the second factor around: The numerator becomes the denominator and the denominator becomes the numerator. Multiply the two factors.