Have students draw a picture of two matching cakes and explain that a cake represents one whole, or the number 1. Tell them to draw lines on one cake, dividing it into four equal pieces, and have them lightly shade three of those pieces. Explain that if you cut a cake into four pieces and eat three of them, you have eaten 3/4 of the cake.
Tell the students to draw lines on the second cake, dividing it into eight equal pieces, and have them lightly shade six of those pieces. Explain that if you cut the same cake into eight pieces and eat six pieces, you have eaten 6/8 of the cake.
Have students compare their cakes and note that the same amount of each one is shaded. Explain that even though they have eaten more pieces of the second cake, they have eaten the same proportion of the cake because 3/4 and 6/8 represent the same part of the whole, making them equivalent fractions.
Have students write 3/4 under their first cake and tell them that they can find equivalent fractions for 3/4 by multiplying the numerator and denominator by the same number. Have them multiply the numerator, 3, and the denominator, 4, by 2 to get 6 and 8.
Have students write the answers as a new fraction equivalent to the original fraction. The original numerator, 3, becomes 6, and the original denominator, 4, becomes 8. The new fraction is 6/8, which is equivalent to 3/4. Point out that 3/4 is in simplest form, meaning that it cannot be reduced further, but that 6/8 can be reduced.
Have students write 6/8 under their second cake and tell them that they can find equivalent fractions for 6/8 by dividing the numerator and denominator by the same number. Have them divide 6 and 8 by 2 to get 3 and 4.
Have students set up the answers as a fraction in the same relationship as in the original fraction. The original numerator, 6, becomes 3, and the original denominator, 8, become 4. The fraction becomes 3/4, which is equivalent to 6/8. Point out that they have reversed the multiplication process while reducing the fraction.