Understanding Fractions — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which fraction is equivalent to 36?
A) 13
B) 24
C) 12
D) 34
36 equals 12 because dividing the numerator and denominator by 3 simplifies the fraction to 12.
2. Which is greater: 45 or 49?
A) 49
B) They are equal
C) 45
D) Cannot compare
45 is greater because fifths are larger pieces than ninths, so 4 fifths covers more than 4 ninths.
3. On a number line from 0 to 1 split into 8 parts, which fraction is at the sixth mark?
A) 66
B) 68
C) 86
D) 34
The sixth mark on a number line split into 8 equal parts is 68 because you count 6 jumps from 0 out of 8 total.
4. Which pair of fractions is equivalent?
A) 13 and 25
B) 24 and 36
C) 12 and 34
D) 23 and 34
24 and 36 are equivalent because both simplify to 12 when you divide the numerator and denominator by their common factor.
Part B: Fill in the Blank
Write the correct answer on each line.
1. 410 is equivalent to 2 5 .
Dividing both 4 and 10 by 2 gives 25, so the missing numerator is 2.
2. Comparing 13 and 16, the fraction 13 is greater.
13 is greater than 16 because thirds are bigger pieces than sixths -- the fewer parts a whole is split into, the larger each piece.
3. A ribbon is cut into 10 equal pieces. Taking 5 pieces is the same as taking 12 of the ribbon.
5 out of 10 pieces is 510, which simplifies to 12 because 5 is exactly half of 10.
4. On a number line, 23 comes after 13.
23 comes after 13 on a number line because 2 thirds is a larger amount than 1 third, placing it farther to the right.
5. 812 is equivalent to 2 3 .
Dividing both 8 and 12 by 4 gives 23, so the missing numerator is 2.