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Divide mixed numbers and fractions with step-by-step solutions using the Keep, Change, Flip method. Learn how to divide fractions easily.
• 3 1/2 ÷ 1 1/4 = 2 4/5
• 4 1/2 ÷ 1 1/2 = 3
• 2 2/3 ÷ 4 = 2/3
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Step 1: Convert: 3 1/2 = 7/2 and 1 1/4 = 5/4
Step 2: Keep: 7/2
Step 3: Change ÷ to ×
Step 4: Flip: 4/5
Step 5: Multiply: 7/2 × 4/5 = 28/10 = 14/5
Result: 14/5 = 2 4/5
Dividing by a fraction is the same as multiplying by its reciprocal. Think about it: dividing by 1/2 is the same as asking "how many halves fit into this number?" which is the same as multiplying by 2.
Example: 6 ÷ 1/2 = ?
• How many halves in 6? Answer: 12 halves
• This is the same as 6 × 2 = 12
• So 6 ÷ 1/2 = 6 × 2/1 = 12
It's a mnemonic for dividing fractions: Keep the first fraction unchanged, Change the division sign to multiplication, and Flip (find the reciprocal of) the second fraction. For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2. This works because dividing by a number is the same as multiplying by its reciprocal.
A reciprocal is what you get when you flip a fraction upside down. The reciprocal of 3/4 is 4/3. For whole numbers, put them over 1 first: the reciprocal of 5 (which is 5/1) is 1/5. When you multiply a number by its reciprocal, you always get 1.
No, you must convert mixed numbers to improper fractions before using the Keep, Change, Flip method. Trying to divide mixed numbers directly without converting will give you incorrect results. The conversion is a crucial first step in the process.
When you divide by a number less than 1 (like a proper fraction), you're asking 'how many of these small pieces fit into my number?' For example, 4 ÷ 1/2 asks 'how many halves in 4?' The answer is 8, which is bigger than 4. This is why dividing by fractions often increases the value.
Convert the whole number to a fraction by putting it over 1. For example, to divide by 3, use 3/1. Then apply Keep, Change, Flip: the reciprocal of 3/1 is 1/3. So dividing by 3 becomes multiplying by 1/3, which makes sense!
Multiply your answer by the divisor (second number). You should get the dividend (first number). For example, if 3 1/2 ÷ 1 1/4 = 2 4/5, check by calculating 2 4/5 × 1 1/4. If it equals 3 1/2, your answer is correct!