Applying Partitive Division: Fraction ÷ Whole Number
Applying Partitive Division: Fraction divided by Whole Number teaches Grade 6 students to solve problems where a fractional amount is split into a whole number of equal groups, giving a fraction as the group size. Covered in Illustrative Mathematics Grade 6, Unit 4: Dividing Fractions, the procedure divides the numerator by the whole number (when possible) or multiplies by its reciprocal: (a/b) divided by c = a/(bc). Visual models like fraction bars make the fair-sharing process concrete before the formula is applied.
Key Concepts
Partitive division with a fraction dividend and whole number divisor , $\frac{a}{b} \div c$, answers the question: "If an amount $\frac{a}{b}$ is split into $c$ equal groups , what is the size of one group ?".
Common Questions
How do you divide a fraction by a whole number?
To divide a/b by whole number c, multiply the denominator by c: (a/b) divided by c = a/(b times c). Equivalently, multiply by the reciprocal 1/c.
What is 3/4 divided by 3?
3/4 divided by 3 = 3/(4 times 3) = 3/12 = 1/4. Split 3/4 into 3 equal groups; each group is 1/4.
How do you visualize fraction divided by whole number?
Draw the fraction divided into equal sections. Regroup those sections into the given number of groups. Each group represents the quotient.
Where is applying partitive division fraction divided by whole number in Illustrative Mathematics Grade 6?
This is in Unit 4: Dividing Fractions of Illustrative Mathematics Grade 6.
Why does the denominator get larger when dividing a fraction by a whole number?
Dividing into more equal groups makes each group smaller. A larger denominator means a smaller fraction, which makes sense since you are sharing less per group.