Distinguishing Dividend and Divisor in Word Problems
To correctly model a division word problem, the total amount being shared is always the dividend (first number) and the number of shares is always the divisor (second number), written as Total Being Shared / Number of Shares, as covered in Illustrative Mathematics Grade 5, Chapter 2: Fractions as Quotients and Fraction Multiplication. For example, 3 pizzas shared among 8 friends is 3 / 8, not 8 / 3.
Key Concepts
To correctly model an equal sharing situation, the division expression must be set up as: $$ \text{Total Amount Being Shared} \div \text{Number of Shares} $$.
Common Questions
What is the dividend in a division problem?
The dividend is the total quantity being divided or shared; it is always the first number in a division expression, written as: Total Being Shared / Number of Groups.
What is the divisor in a division problem?
The divisor is the number of equal groups or shares you are dividing into; it is always the second number in a division expression.
How do you set up a division word problem correctly?
Ask yourself: what is the total amount being shared? That is the dividend. How many groups or people is it shared among? That is the divisor. Write dividend / divisor.
What is the difference between 3/8 and 8/3?
3/8 means 3 objects shared among 8 people (each gets 3/8 of an object); 8/3 means 8 objects shared among 3 people (each gets 8/3 objects); the order completely changes the meaning.
Why do students often reverse dividend and divisor?
Students sometimes confuse which number comes first because they focus on the people or groups rather than the total being divided; remembering that the total always comes first prevents this common error.