Understanding Fractions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. 12 is equivalent to 2 4 .
Equivalent fractions name the same amount even when the numbers look different. Multiplying both 1 and 2 by 2 gives 24, so 12 = 24.
2. 23 is equivalent to 4 6 .
If you double both the numerator and the denominator of 23, you get 46, which still names the same amount. So the missing denominator is 6.
3. 13 is equivalent to 2 6 .
Sixths are made by cutting each third in half, so one third becomes two of those smaller pieces. That is why 13 = 26.
4. 34 is equivalent to 6 8 .
Doubling both numbers in 34 keeps the fraction the same size, and 3 doubled is 6 while 4 doubled is 8. So 34 is equivalent to 68.
5. Two fractions are equivalent if they name the same amount.
Two fractions are equivalent when they cover the same portion of a whole, even if the pieces are cut differently. They name the same amount.
6. 12 = 3 6 .
Multiplying the numerator and denominator of 12 by 3 gives 36, which still represents one half. So the missing denominator is 6.
7. 28 is equivalent to 1 4 .
Dividing both 2 and 8 by 2 simplifies 28 to 14, which is the same amount written with smaller numbers. So 28 is equivalent to 14.
8. 46 is equivalent to 2 3 .
When you divide both 4 and 6 by 2, you get 23, a simpler form of the same fraction. So 46 is equivalent to 23.
9. 14 is equivalent to 2 8 .
Doubling both numbers in 14 gives 28, and doubling does not change how much of the whole is covered. So 14 is equivalent to 28.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
12
→ 36
26
23
→ 46
68
34
→ 68
36
13
→ 26
46
Each pair on the right is the same amount as the fraction on the left, just with the numerator and denominator multiplied by the same number. 12 doubles to 36, 23 doubles to 46, 34 doubles to 68, and 13 doubles to 26.