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Divide fractions using the Keep-Change-Flip method with step-by-step solutions.
Problem: 3/4 ÷ 2/5
Keep: 3/4
Change: ÷ becomes ×
Flip: 2/5 becomes 5/2
Multiply: 3/4 × 5/2 = 15/8
Convert: 15/8 = 1 7/8
Answer: 1 7/8 or 1.875
Dividing by a fraction is the same as multiplying by its reciprocal. When you divide by 2/5, you're asking "how many 2/5's fit into the first fraction?" This is equivalent to multiplying by 5/2.
Think of it this way: Dividing by 2 is the same as multiplying by 1/2. Similarly, dividing by 2/5 is the same as multiplying by 5/2.
Keep-Change-Flip (also called KCF) is a simple three-step method for dividing fractions: (1) Keep the first fraction the same, (2) Change the division sign to multiplication, (3) Flip the second fraction upside down (reciprocal). Then multiply as normal. For example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
A reciprocal is a fraction flipped upside down. The reciprocal of a/b is b/a. When you multiply a fraction by its reciprocal, you always get 1. For example, 3/4 × 4/3 = 12/12 = 1. The reciprocal of 5 is 1/5, and the reciprocal of 2/3 is 3/2.
Dividing by a number is the same as multiplying by its reciprocal. This mathematical property makes division equivalent to multiplication by the flipped fraction. It works because (a/b) ÷ (c/d) = (a/b) × (d/c) - these two operations give the same result.
Yes! First convert the whole number to a fraction by putting it over 1. For example, to divide 3/4 ÷ 2, rewrite it as 3/4 ÷ 2/1. Then apply Keep-Change-Flip: 3/4 × 1/2 = 3/8.
Convert both mixed numbers to improper fractions first. Then use the Keep-Change-Flip method. Finally, convert the answer back to a mixed number if desired. For example: 2 1/2 ÷ 1 1/4 = 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2.
When dividing fractions, you can get an answer greater than 1 (an improper fraction). This happens when the first fraction is larger than the second. You can leave it as an improper fraction or convert it to a mixed number. For example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2.