What is the gcf of 3/7 and 4/9?

Mathematics

1 answer:

LiRa [457]2 years ago

3 0

Answer:

1/63

Step-by-step explanation:

There are a couple of ways to do this.

Look for the GCF of the numerators when a common denominator is used.

GCF(3/7, 4/9) = GCF(27/63, 28/63) = (1/63)·GCF(27, 28)

GCF(3/7, 4/9) = 1/63

Use Euclid's algorithm. If the remainder from division of the larger by the smaller is zero, then the smaller is the GCF; otherwise, the remainder replaces the larger, and the algorithm repeats.

(4/9)/(3/7) = 1 remainder 1/63*

(3/7)/(1/63) = 27 remainder 0

The GCF is 1/63.

* The quotient is 28/27 = 1 +1/27 = 1 +(1/27)(3/7)/(3/7) = 1 +(1/63)/(3/7) or 1 with a remainder of 1/63.

_____

<em>Additional comment</em>

3/7 = (1/63) × 27

4/9 = (1/63) × 28

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