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Solve the Fraction Division Fill-in-the-Blank Problem: 12/15 ÷ ____
Mathematics
Grade 6 (Primary School)
Question Content
Complete the expression: 12/15 ÷ ____, where the blank needs to be filled with a value such that the expression is solvable (the problem is incomplete as it lacks a result or additional constraint, but it is a fraction division problem structure)
Correct Answer
Note: The problem is incomplete. If assuming a common scenario where the result is 1, the answer is 12/15 (or simplified to 4/5); if no result is specified, any non-zero number is a valid fill-in value for a solvable division expression.
Detailed Solution Steps
1
Step 1: Recognize that this is a fraction division problem. For a division expression a ÷ b, b cannot be 0 (division by zero is undefined).
2
Step 2: If we assume the problem intends the result to be 1 (a common fill-in-the-blank scenario), we use the rule that a number divided by itself equals 1. So 12/15 ÷ 12/15 = 1, and simplifying 12/15 gives 4/5.
3
Step 3: If there is no specified result, any non-zero rational number can be placed in the blank to create a valid solvable expression.
Knowledge Points Involved
1
Fraction Division Basics
Fraction division follows the rule: a/b ÷ c/d = a/b × d/c (multiplying by the reciprocal of the divisor). The divisor cannot be zero, as division by zero is mathematically undefined. This applies to all non-zero rational numbers as divisors.
2
Simplifying Fractions
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For 12/15, the GCD of 12 and 15 is 3, so 12÷3 / 15÷3 = 4/5. Simplified fractions are equivalent to the original fraction and make calculations easier.
3
Property of Division (Dividing a Number by Itself)
Any non-zero number divided by itself equals 1. This is a basic arithmetic property, applicable to integers, fractions, and decimals, as long as the number is not zero (since 0/0 is undefined).
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