Mixed Numbers and Improper Fractions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The number 3/8 is an improper fraction because eight is bigger than three.
Corrected: The number 3/8 is a proper fraction because the numerator three is smaller than the denominator eight.
Since 3 is less than 8, the fraction 3/8 is proper, not improper.
2. Fix the sentence:
A fraction bar showing 4 out of 3 equal parts shaded is impossible.
Corrected: A fraction bar showing 4 out of 3 equal parts shaded means more than one whole bar, which is the improper fraction 4/3.
We can shade 4 thirds by using one full bar of 3 thirds plus one extra third, which models 4/3 = 1 1/3.
3. Fix the sentence:
The mixed number 2 0/5 is the same as 2/5.
Corrected: The mixed number 2 0/5 is the same as the whole number 2.
Since 0/5 = 0, the value 2 0/5 = 2 + 0 = 2, not 2/5.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A fraction is called improper when its numerator is greater than or equal to its denominator.
By definition, an improper fraction has numerator at least as large as the denominator.
2. Two pies cut into 4 equal slices each have a total of 8 slices, written as 8/4.
Two whole pies of 4 slices each give 8 fourths, so 8/4 = 2 wholes.
3. The mixed number 4 2/3 written as an improper fraction is 14/3.
4 multiplied by 3 is 12, plus 2 equals 14, so 4 2/3 = 14/3.
4. 13/5 written as a mixed number is 2 3/5 because 13 divided by 5 leaves remainder 3.
13 ÷ 5 = 2 remainder 3, so 13/5 = 2 3/5.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Maria sees the fraction 8/8 on a fraction bar fully shaded. How would you describe its value to a Grade 4 friend?
Sample answer: I would say 8/8 means every one of the 8 equal parts is shaded, so it makes one full bar. That is exactly 1 whole, even though it looks like a fraction.
Recognizing that any b/b equals 1 whole is a key Grade 4 standard (4.NF.3b).
2. How can you tell, just by looking, whether a fraction is greater than 1?
Sample answer: I look at the numerator and denominator. If the numerator is bigger than the denominator, the fraction is greater than 1. For example, 9/4 has 9 on top and 4 on bottom, so it is more than one whole.
Any improper fraction with numerator greater than denominator is more than 1 whole, which Grade 4 students must recognize.