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by dividing or multiplying the numerator and the denominator of a fraction with the same number
ex:
* 1/2 = (1 x 5)/(2 x 5) = 5/10
(multiples both numerator and denominator with 5)
1/2 and 5/10 are equivalent fractions
* 14/35 = (14:7)/(35:7) = 2/5
(divide both numerator and denominator with common factor of 14 and 35)
14/35 and 2/5 are equivalent fractions
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Which factors can help you determine the number of possible solution to consider?
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What do they mean common factors?
All integers have factors. Some integers have some of the same factors as other integers. These are known as common factors. 3 is a common factor of 6 and 9.
How divisibility rules can help you find common factors?
Divisibility rules help you find the factors of a number. Once you've found the factors for two or more numbers, you can find what they have in common. Take 231 and 321. If you know the divisibility rules, you know that they are both divisible by 3, so 3 is a common factor.
How can you use the greatest common factor to find the simplest form?
To simplify or reduce an improper fraction, you can divide the numerator and denominator by the greatest common factor of both numbers. For example, if you are given the fraction 36/60; the common factors of the numerator (36) are 2, 3, 4, 6, 9, 12, and 18. The common factors of the denominator are 2, 3, 5, 6, 10, 12, and 20. We can see that 12 is the largest common factor between the numerator and denominator. Divide the numerator and denominator by 12: 36 / 12 = 3, and 60 / 12 = 5. We see that the fraction reduces to 3/5.
How does finding the GCF help you simplify a fraction?
When adding and subtracting unlike fractions, it is necessary to find a least common denominator. It's the same process as finding an LCM. You can simplify a fraction by finding the GCF of the numerator and denominator and dividing them both by it.
