Understanding Fractions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
If you shade 4 out of 7 squares, the fraction shaded is 74.
Corrected: If you shade 4 out of 7 squares, the fraction shaded is 47.
The corrected sentence is: "If you shade 4 out of 7 squares, the fraction shaded is 47." The error was fraction reversed: the original sentence "If you shade 4 out of 7 squares, the fraction shaded is 74." needed to be fixed.
2. Fix the sentence:
22 of a pie means no pie is left.
Corrected: 22 of a pie means the whole pie.
The corrected sentence is: "22 of a pie means the whole pie." The error was wrong meaning: the original sentence "22 of a pie means no pie is left." needed to be fixed.
3. Fix the sentence:
16 is larger than 12 because 6 is more than 2.
Corrected: 16 is smaller than 12 because sixths are smaller parts than halves.
The corrected sentence is: "16 is smaller than 12 because sixths are smaller parts than halves." The error was comparison error: the original sentence "16 is larger than 12 because 6 is more than 2." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In the fraction 912, the numerator is 9.
The numerator is 9 because it is the top number in the fraction 912, telling us that 9 parts out of 12 are being counted.
2. A sandwich cut into 4 equal pieces with 1 piece eaten means 14 is gone.
The answer is 14 because 1 piece was eaten out of 4 equal pieces, so the fraction gone is 1 over 4.
3. The denominator tells how many equal parts make up the whole.
The word is "equal" because fractions only work when the whole is split into parts that are all the same size.
4. 55 of a bar means the whole bar is shaded.
55 means all 5 parts out of 5 are shaded, so the whole bar is completely filled in.
Part C: True or False?
Read each statement. Circle True or False.
1. 12 and 24 represent the same amount.
True False
True. 12 and 24 are equivalent fractions because if you split 24 in half, you get 12 -- both cover the same amount of a whole.
2. A fraction must always have a denominator of 10.
True False
False. A fraction can have any number as its denominator, such as 2, 3, 5, or 100 -- it just tells how many equal parts the whole is divided into.
3. 88 equals one whole.
True False
True. 88 equals one whole because when the numerator and denominator are the same, all parts are included, making a complete whole.