Understanding Fractions — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which fraction is equivalent to 46?
A) 24
B) 48
C) 23
D) 34
Dividing both 4 and 6 by their common factor 2 gives 23, the simplest form of the same fraction. So 23 is equivalent to 46.
2. Which is greater: 56 or 510?
A) 510
B) 56
C) They are equal
D) Cannot compare
When numerators are the same, the fraction with the smaller denominator is larger because the whole is split into fewer, bigger pieces. Sixths are bigger than tenths, so 56 is greater than 510.
3. Which fraction equals 28?
A) 12
B) 13
C) 24
D) 14
Dividing both 2 and 8 by 2 simplifies 28 to 14, which is the same amount written with smaller numbers. So 14 equals 28.
4. A number line from 0 to 1 is divided into 3 equal parts. What fraction is at the second mark?
A) 13
B) 23
C) 33
D) 12
Splitting the line from 0 to 1 into 3 equal parts puts marks at 13, 23, and 33. The second mark is 23 of the way from 0 to 1.
Part B: Fill in the Blank
Write the correct answer on each line.
1. On a number line, 34 is between 12 and 1.
On a number line, 34 is past 12 but has not yet reached the whole, since 44 would be 1. So 34 sits between 12 and 1.
2. 68 is equivalent to 3 /4.
Dividing both 6 and 8 by 2 simplifies 68 to 34, which is the same amount with smaller numbers. So the missing numerator is 3.
3. A pie is cut into 8 slices. Eating 4 slices means you ate 12 of the pie.
Eating 4 of the 8 equal slices means you ate 48 of the pie, and 48 simplifies to 12 because 4 is half of 8. So you ate 12 of the pie.
4. Comparing 45 and 410, the fraction 45 is greater.
With the same numerator on both fractions, the one with the smaller denominator is larger because the pieces are bigger. Fifths are bigger than tenths, so 45 is greater than 410.
5. 22 = 33 = 44, so they all equal 1.
Whenever the numerator and denominator match, every equal part of the whole is counted, which fills it completely. So 22, 33, and 44 all equal 1.