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Fractions and mixed numbers

Geometric sequences with fractions

A geometric sequence is a list of numbers with a definite pattern. Sometimes you may encounter a problem in geometric sequence that involves fractions.

What is the next fraction in this sequence?

$\frac{2}{4},\;\frac{2}{8},\;\frac{2}{16},\;\frac{2}{32}$

Look for a pattern. The numerator stays the same while the denominator increases. What is the pattern? Try multiplying.

If you multiply the first denominator, 4, by 2, you get 8. 8 is the second denominator.

Try multiplying 8 by 2. You get 16, which is the denominator of the third fraction.

Does this pattern hold true for the fourth fraction? Multiply 16 by 2 to check. 16 times 2 is 32, which is the denominator of the fourth fraction.

The pattern is to multiply the denominator by 2.

This is the same as multiplying the entire fraction by $\frac{1}{2}$

$\frac{2}{4}\;\cdot\;\frac{1}{2}=\;\frac{2}{8}$

$\frac{2}{8}\;\cdot\;\frac{1}{2}=\;\frac{2}{16}$

$\frac{2}{16}\;\cdot\;\frac{1}{2}=\;\frac{2}{32}$

$\frac{2}{32}\;\cdot\;\frac{1}{2}=\;?$

Multiply to find the next fraction in the pattern:

$\frac{2}{32}\;\cdot\;\frac{1}{2}=\;\frac{2}{64}$

The next fraction in the pattern is $\frac{2}{64}$

What is the next fraction in this sequence? $\frac{7}{3},\;\frac{7}{12},\;\frac{7}{48},\;\frac{7}{192}$
 Solution: