Fraction Quiz



Laurie Nielsen

Fraction Quiz

This quiz is to illustrate some troubles we have with fractions and manipulating them. See if you can answer the questions and then see if you can clarify the errors and provide some ideas to help someone understand the problem.

1. If multiplication is repeated addition, how come [pic] is less than either one of those amounts?

Multiplication is sets or groups of another set/group. You read a multiplication sentence with the word “of” as the multiplication sign. So 2X3 would be read “ I want 2 sets of 3.” If you read a fraction multiplication problem the same way, it says “I want 3/5 sets of 2/3.” Therefore, you are asking for a smaller set within the fraction that you have.

2. Mr. Smith brings his students into your room for a joint project. His class comes in girls first and then boys, you decide to demonstrate where rational numbers might be used. 15 of his 24 students are girls and 12 of your 21 students are girls. You begin to write the equation below on the board thinking you will check your solution because now 27 of the 45 students are girls. But something does not seem right. What do you do now?

[pic]

The problem is that you’re trying to add without having a common denominator. You cannot add fractions with unlike denominators.

3. The following question was on your latest homework assignment: [pic]

One student turns in the solution below. What do you say to that student?

[pic]

Though 5/4 is the correct answer, your process is not quite right. In dividing fractions, we don’t find how many numerators go into the other numerator and how many denominators go into the other denominator. We are finding how many ¾ can be pulled out of 15/16?

4. A student asserts that [pic] because of her picture:

How do you respond? When comparing fractions, you have to compare them to the same size whole unit- You are comparing two WHOLE objects of different sizes in your drawing.

5. When asked to reduce the fraction [pic] to lowest terms a student gives you this answer.

Is the student right? What do you say to him?

Yes. “Great job- next time please show your work.” Since he rewrote the 16/64 and crossed it off I’m guessing I need to reteach turning a fraction into its simplest form.

6. A student answers the following problem in the manner below.

Two children want to split [pic] of a pizza so that each gets the same amount. How much will each receive?

Solution: [pic]

What does the answer [pic] mean?

The number of halves in ¾ of a pizza. She found out how many halves were in ¾. So there are 1-1/2 halves of pizza.

7. When dividing fractions, why don’t we need to get a common denominator? What happens if we do? Example: [pic]

There is no need to find the common denominator because you are trying to find how many of the one fraction “sits in” or “how many sets of a fraction are in the other fraction”. When you find the GCD then you are having to do the math with bigger numbers and that gets pretty challenging.

8. When asked which he would rather have, [pic] or [pic] of a cake, a young student says [pic] because there are more pieces. What should be your response?

But the pieces are smaller! How do you know that you are getting more of the cake than the person who picks the 2/5?

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[pic]

3

2

5

2

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