Fractions and Division
4A · Chapter 6 · Lesson 6 · MATH-4A-C06-L07
Learning goal. Interpret a fraction as a quotient and connect sharing stories to numerical fractions.
Before you begin
Recall: Grade 3B: fractions of equal wholes, equivalence, number lines and simplifying; Expressing a Mixed Number as an Improper Fraction. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Write 3 1/2 as an improper fraction.
Show answer & reasoning
Each whole has 2 parts. 3 wholes and 1 more parts make 7 parts.
Write 3 9/10 as an improper fraction.
Show answer & reasoning
Each whole has 10 parts. 3 wholes and 9 more parts make 39 parts.
Write 4 5/6 as an improper fraction.
Show answer & reasoning
Each whole has 6 parts. 4 wholes and 5 more parts make 29 parts.
Key vocabulary
- equivalent fractions
- different numerators and denominators representing the same quantity
- mixed number
- whole number plus proper fraction
- improper fraction
- fraction with numerator at least its denominator
- denominator
- number of equal parts in one whole
Understand the concept
A fraction can describe a division result. Sharing three equal pies among four people gives 3/4 of a pie each. The numerator is the number of wholes being shared; the denominator is the number of equal recipients. This connects fraction notation to equal-sharing stories and helps explain improper fractions.
Model it: sharing equal wholes among recipients. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
7 identical pies are shared equally among 6 children. What fraction of one pie does each child get?
Divide 7 equal wholes into 6 shares: each gets 7/6 of a pie, equivalent to 7/6.
Check your understanding 1
4 identical pies are shared equally among 4 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 4 equal wholes into 4 shares: each gets 4/4 of a pie, equivalent to 1.
Worked example 2
5 identical pies are shared equally among 8 children. What fraction of one pie does each child get?
Divide 5 equal wholes into 8 shares: each gets 5/8 of a pie, equivalent to 5/8.
Check your understanding 2
3 identical pies are shared equally among 7 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 3 equal wholes into 7 shares: each gets 3/7 of a pie, equivalent to 3/7.
Worked example 3
3 identical pies are shared equally among 2 children. What fraction of one pie does each child get?
Divide 3 equal wholes into 2 shares: each gets 3/2 of a pie, equivalent to 3/2.
Check your understanding 3
4 identical pies are shared equally among 8 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 4 equal wholes into 8 shares: each gets 4/8 of a pie, equivalent to 1/2.
Guided practice
5 identical pies are shared equally among 9 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 5 equal wholes into 9 shares: each gets 5/9 of a pie, equivalent to 5/9.
2 identical pies are shared equally among 7 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 2 equal wholes into 7 shares: each gets 2/7 of a pie, equivalent to 2/7.
9 identical pies are shared equally among 7 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 9 equal wholes into 7 shares: each gets 9/7 of a pie, equivalent to 9/7.
5 identical pies are shared equally among 4 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 5 equal wholes into 4 shares: each gets 5/4 of a pie, equivalent to 5/4.
10 identical pies are shared equally among 4 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 10 equal wholes into 4 shares: each gets 10/4 of a pie, equivalent to 5/2.
Independent practice
8 identical pies are shared equally among 2 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 8 equal wholes into 2 shares: each gets 8/2 of a pie, equivalent to 4.
8 identical pies are shared equally among 9 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 8 equal wholes into 9 shares: each gets 8/9 of a pie, equivalent to 8/9.
6 identical pies are shared equally among 2 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 6 equal wholes into 2 shares: each gets 6/2 of a pie, equivalent to 3.
6 identical pies are shared equally among 6 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 6 equal wholes into 6 shares: each gets 6/6 of a pie, equivalent to 1.
4 identical pies are shared equally among 2 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 4 equal wholes into 2 shares: each gets 4/2 of a pie, equivalent to 2.
4 identical pies are shared equally among 3 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 4 equal wholes into 3 shares: each gets 4/3 of a pie, equivalent to 4/3.
6 identical pies are shared equally among 4 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 6 equal wholes into 4 shares: each gets 6/4 of a pie, equivalent to 3/2.
3 identical pies are shared equally among 8 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 3 equal wholes into 8 shares: each gets 3/8 of a pie, equivalent to 3/8.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Three equal pies are shared equally among four people. What fraction of a pie does each person get, and why?
Show answer & reasoning
Divide each pie into fourths: there are twelve fourths total, shared in groups of three fourths.
7 identical pies are shared equally among 9 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 7 equal wholes into 9 shares: each gets 7/9 of a pie, equivalent to 7/9.
Exit check
1 identical pies are shared equally among 5 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 1 equal wholes into 5 shares: each gets 1/5 of a pie, equivalent to 1/5.
7 identical pies are shared equally among 5 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 7 equal wholes into 5 shares: each gets 7/5 of a pie, equivalent to 7/5.
6 identical pies are shared equally among 3 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 6 equal wholes into 3 shares: each gets 6/3 of a pie, equivalent to 2.