Quotient The fraction 5may also be considered as a quotient. 3 divided by 5. This meaning alsoHuman Computer Interaction indicates partitioning. For example. suppose you had 20 big biscuits to share equally among five people. If you gave each person one biscuit. then another, and so on until you had distributed all the biscuits. you could represent this process mathematically by the quotient 20 + 5. Each person would get four biscuits. However, what if you had just three big biscuits and you still wanted to share them equally among five people? Now the quotient would be 3 ÷ 5. How much would each person get? Would anyone get a whole biscuit? One Way to solve this problem would be to use pictures of the biscuits. as shown in figure 12.1. This interpretation of fractions is used when a remainder in a division problem is expressed as a fraction. It is also the interpretation that is needed to change any fraction to a decimal (i.e. ais equivalent to 0.625).
FIGURE 12.1
The quotient Interpretation of a fraction

Begin with 3 biscuits. Cut each Into 5 parts.
• 4■ 4I■ ■■ 1,10, ik 10 • 4,, 114
Each person gels iot each =cult Thus, each person gets 1 5 + 5+ 5 or s or 3 – 5 – 5.
Ratio The fraction notation S may also represent a ratio — for example. in a class of 6 boys and 10 girls. the ratio of boys to girls is 6 to 10. which is equivalent to 3:5. That is. for every 3 boys there are 5 girls or there are as many boys as girls.

The ratio interpretation of fractions is conceptually different from the pan-whole and quotient inter-pretations. since it doesn’t involve the idea of partitioning. In this chapter. we focus on the pail-whole interpretation and bring in the quotient interpretation as relevant (see the next chapter for discussion of the ratio interpretation). You may read about the measurement meaning (Flores. Samson. & Yanik. 2007). but we have not made a special section on this meaning since it is closely aligned with the measurable attributes discussed here.