## “Fraction of a Fraction” Math Problems

**Anticipatory Set**: As a warm-up activity for students, put the problem “What is 1/2 of 1/4?” on the board. Ask students to solve the problem and then choose two students from each row or each table group to write their answer on the board. Have the students take their seats. Now engage in a classroom discussion by asking the class which answer is correct and circle the responses. Typical student answers might be: 1/2, 1/4. 1/6, 2/6, or 1/8 and your student responses may surprise you with most students choosing 1/6 or 1/8. So which one is correct: 1/8 of course.

**Lesson Objective**: Problem solving “Fraction of a Fraction” math problems.

There are fractions that start with basic problem solving such as 1/2 = 50% = 3/6 = 4/8 and so on. And then there are fraction of a fraction problems that require a different mathematical processing. So let’s get started by solving some of these problems.

**Directions**: Solve for the following and put a brief explanation on how you got your final answer next to each problem.

1. 2/3 of 2/3

2. 1/4 of 1/3

3. 1/3 of 3/4

4. 1/5 of 1/5

5. 1/2 of 1/5

**Answers**:

1. 2/3 of 2/3 = 4/9 because the “of” means you multiply “x” the two numerators and the denominators, so 2 x 2 = 4 and 3 x 3 =9

2. 1/4 of 1/3 = 1/12 because you multiply 1 x 1=1 and 4 x 3 = 12

3. 1/3 of 3/4 = 3/12 because you multiply 1 x 3 = 3 and 3 x 4 = 12, but you have to simplify, so you divide 3/3=1 and 3/12=4 – final answer = 1/4

4. 1/5 of 1/5 = 1/10 because you multiply 1 x 1 = 1 and 5 x 5 = 10

5. 1/2 of 1/5 = 1/10 because you multiply 1 x 1 = 1 and 2 x 5 = 10

**Additional Strategies**: You can also provide elementary students with manipulatives in different colors, so that visual and kinesthetic learners can see and touch math problem solving using groups of manipulatives to represent fractional parts. Another visual tool that is always fun and creative for students is allowing them to work collaboratively in groups of 2 and giving each group a piece of butcher paper and markers in five colors for each problem (groups can share the markers).

**Bonus Word Problem**: To challenge students even further, provide a word problem, set a timer and the first two groups that problem solve correctly will get an extra 10 minutes on their class project on Friday or some other extrinsic reward that students are motivated to work hard to achieve in your classroom.

1. One-third of students in your class are males, and 1/2 of those male students have black hair. If there are 5 males in the class with black hair, how many students total are there in the classroom?

**Answer**: 5 male students have black hair and 1/2 of these male students have black hair, so 5 x 2 = 10 males and since 1/3 are males, there are 10 X 3 = 30 students in the class which means there are 20 females in the class. The class is 1/3 males and 2/3 female. Checking the math processing might look like this: 10/30 males = 1/3 males and 20/30 females = 2/3 females in your class. A simpler method would be to count the number of males and females in the class, but then that’s too easy.

**Closure**: Fraction of Fraction problems can provide lots of fun for younger students trying to understand how to figure out parts of wholes or 50% of the $19.99 school backpack, which by the way is equal to a 1/2 of $19.99 = $9.995.