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:
5/4 equals 1 and 1/2 because 5 minus 4 is 1 over 2.
Corrected: 5/4 equals 1 and 1/4 because 5 minus 4 is 1 over the same denominator 4.
When converting an improper fraction to a mixed number, the remainder stays over the same denominator, so 5/4 = 1 1/4.
2. Fix the sentence:
The number 7/3 is a proper fraction because the top is bigger.
Corrected: The number 7/3 is an improper fraction because the numerator is greater than the denominator.
A fraction is improper when the numerator is greater than or equal to the denominator, so 7/3 is improper, not proper.
3. Fix the sentence:
Two and one half written as an improper fraction is 3/2 because 2 plus 1 is 3.
Corrected: Two and one half written as an improper fraction is 5/2 because 2 times 2 plus 1 is 5.
To turn 2 1/2 into an improper fraction, do 2 multiplied by 2 then add 1, which gives 5/2, not 3/2.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The fraction 6/6 equals exactly 1 whole(s) because the numerator and denominator are the same.
Any fraction whose numerator equals its denominator equals 1 whole, so 6/6 = 1.
2. Write 9/4 as a mixed number: 9 divided by 4 is 2 with remainder 1, so 9/4 = 2 1/4.
9 divided by 4 gives quotient 2 and remainder 1, so the mixed number is 2 1/4.
3. Write 1 3/5 as an improper fraction: 1 times 5 plus 3 = 8/5.
1 times 5 is 5, plus 3 equals 8, so 1 3/5 = 8/5.
4. On a number line, the improper fraction 11/4 sits between the whole numbers 2 and 3.
11 divided by 4 is 2 remainder 3, so 11/4 = 2 3/4, which lies between 2 and 3.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why is 4/4 equal to 1 whole? Explain in your own Grade 4 words.
Sample answer: When the numerator and denominator are the same, every part of the whole has been counted. So 4/4 means all four pieces of one whole are there, which equals exactly 1 whole.
Any fraction b/b shows the whole has been fully covered, so it equals 1 whole, a key Grade 4 idea (4.NF.3b).
2. Explain the difference between a proper fraction and an improper fraction with an example.
Sample answer: A proper fraction has a numerator smaller than its denominator, like 3/5. An improper fraction has a numerator equal to or larger than its denominator, like 7/5, which is more than one whole.
Knowing this difference helps Grade 4 students decide whether a fraction is less than 1 or at least 1 whole.