Math worksheet for reducing fractions to their lowest terms.

To reduce a fraction to its lowest terms, we need to find the largest number that divides evenly into both the top number (numerator) and the bottom number (denominator). This is called the Greatest Common Divisor (GCD). Once we find it, we divide both numbers by it.

Here is the step-by-step reduction for each problem on the sheet:

Row 1:
* 2/4: Both are divisible by 2. $2 \div 2 = 1$, $4 \div 2 = 2$. Answer: 1/2
* 35/40: Both end in 5 or 0, so they are divisible by 5. $35 \div 5 = 7$, $40 \div 5 = 8$. Answer: 7/8
* 10/16: Both are even, so divide by 2. $10 \div 2 = 5$, $16 \div 2 = 8$. Answer: 5/8
* 8/36: Both are divisible by 4. $8 \div 4 = 2$, $36 \div 4 = 9$. Answer: 2/9

Row 2:
* 18/20: Both are even, divide by 2. $18 \div 2 = 9$, $20 \div 2 = 10$. Answer: 9/10
* 4/36: Both are divisible by 4. $4 \div 4 = 1$, $36 \div 4 = 9$. Answer: 1/9
* 6/9: Both are divisible by 3. $6 \div 3 = 2$, $9 \div 3 = 3$. Answer: 2/3
* 2/10: Both are even, divide by 2. $2 \div 2 = 1$, $10 \div 2 = 5$. Answer: 1/5

Row 3:
* 3/30: Both are divisible by 3. $3 \div 3 = 1$, $30 \div 3 = 10$. Answer: 1/10
* 44/48: Both are divisible by 4. $44 \div 4 = 11$, $48 \div 4 = 12$. Answer: 11/12
* 5/15: Both are divisible by 5. $5 \div 5 = 1$, $15 \div 5 = 3$. Answer: 1/3
* 10/35: Both are divisible by 5. $10 \div 5 = 2$, $35 \div 5 = 7$. Answer: 2/7

Row 4:
* 10/45: Both are divisible by 5. $10 \div 5 = 2$, $45 \div 5 = 9$. Answer: 2/9
* 6/14: Both are even, divide by 2. $6 \div 2 = 3$, $14 \div 2 = 7$. Answer: 3/7
* 28/32: Both are divisible by 4. $28 \div 4 = 7$, $32 \div 4 = 8$. Answer: 7/8
* 20/24: Both are divisible by 4. $20 \div 4 = 5$, $24 \div 4 = 6$. Answer: 5/6

Row 5:
* 5/15: Both are divisible by 5. $5 \div 5 = 1$, $15 \div 5 = 3$. Answer: 1/3
* 4/32: Both are divisible by 4. $4 \div 4 = 1$, $32 \div 4 = 8$. Answer: 1/8
* 30/35: Both are divisible by 5. $30 \div 5 = 6$, $35 \div 5 = 7$. Answer: 6/7
* 3/6: Both are divisible by 3. $3 \div 3 = 1$, $6 \div 3 = 2$. Answer: 1/2

Row 6:
* 14/24: Both are even, divide by 2. $14 \div 2 = 7$, $24 \div 2 = 12$. Answer: 7/12
* 18/20: Both are even, divide by 2. $18 \div 2 = 9$, $20 \div 2 = 10$. Answer: 9/10
* 14/18: Both are even, divide by 2. $14 \div 2 = 7$, $18 \div 2 = 9$. Answer: 7/9
* 5/35: Both are divisible by 5. $5 \div 5 = 1$, $35 \div 5 = 7$. Answer: 1/7

Row 7:
* 4/40: Both are divisible by 4. $4 \div 4 = 1$, $40 \div 4 = 10$. Answer: 1/10
* 35/50: Both are divisible by 5. $35 \div 5 = 7$, $50 \div 5 = 10$. Answer: 7/10
* 2/18: Both are even, divide by 2. $2 \div 2 = 1$, $18 \div 2 = 9$. Answer: 1/9
* 2/4: Both are divisible by 2. $2 \div 2 = 1$, $4 \div 2 = 2$. Answer: 1/2

Row 8:
* 2/6: Both are divisible by 2. $2 \div 2 = 1$, $6 \div 2 = 3$. Answer: 1/3
* 2/14: Both are even, divide by 2. $2 \div 2 = 1$, $14 \div 2 = 7$. Answer: 1/7
* 28/40: Both are divisible by 4. $28 \div 4 = 7$, $40 \div 4 = 10$. Answer: 7/10
* 4/28: Both are divisible by 4. $4 \div 4 = 1$, $28 \div 4 = 7$. Answer: 1/7

Row 9:
* 45/50: Both are divisible by 5. $45 \div 5 = 9$, $50 \div 5 = 10$. Answer: 9/10
* 12/28: Both are divisible by 4. $12 \div 4 = 3$, $28 \div 4 = 7$. Answer: 3/7
* 12/40: Both are divisible by 4. $12 \div 4 = 3$, $40 \div 4 = 10$. Answer: 3/10
* 25/60: Both are divisible by 5. $25 \div 5 = 5$, $60 \div 5 = 12$. Answer: 5/12

Final Answer:
Row 1: 1/2, 7/8, 5/8, 2/9
Row 2: 9/10, 1/9, 2/3, 1/5
Row 3: 1/10, 11/12, 1/3, 2/7
Row 4: 2/9, 3/7, 7/8, 5/6
Row 5: 1/3, 1/8, 6/7, 1/2
Row 6: 7/12, 9/10, 7/9, 1/7
Row 7: 1/10, 7/10, 1/9, 1/2
Row 8: 1/3, 1/7, 7/10, 1/7
Row 9: 9/10, 3/7, 3/10, 5/12