Fractions represent part to whole relationships. The numerator tells how many parts are represented. The denominator shows the number of equal parts the whole is divided into. The fraction 2/3 shows that the whole was cut into three equal shares. The numerator represents two of the three pieces of the whole. Show children examples of sharing a whole. Use arrays, number lines, linking cubes, squares and circles to give them different representations of the whole.
Fractions define how to share items equally. The whole may not be one when sharing equally. If four kids shared three pizzas equally, the whole is not one pizza, but three pizzas. The denominator still shows how many pieces the whole is cut into equally. If each pizza is cut into four pieces, the denominator will show that there are 12 equal shares. To share the pizza equally, each child receives three pieces, or 3 of the 12 pieces -- 3/12.
Ratios are written as fractions. Ratios explain the quantity of one item compared to the quantity of another item. The ratio of boys to girls in the classroom is an example to show ratio. The numerator is the number of boys in the classroom. The denominator is the number of girls in the classroom. Ratios are helpful to look at when comparing values. The ratio could also be a part to whole ratio. The ratio of boys to the total number of students in the class looks different than the ratio of boys to girls. The numerator stays the same because the same number of boys is represented. The denominator changes when the value changes to the number of kids in the class.
Like fractions, decimals and percents represent the part to whole relationship. Percents show how many out of 100 are represented. The denominator is always 100 in a percentage number. If the child answered 85 percent correctly on a math test, it means out of 100 problems he answered 85 of them correctly -- 85/100. Decimals show the part to whole relationship, also. The numbers before the decimal point are whole numbers. The numbers after the decimal point represent the fraction of the whole. The place value of the number determines how many parts of the whole was equally shared. Every denominator in a decimal number is a multiple of 10 -- tenths, hundredths, thousandths, ten-thousandths.