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Fractions and mixed numbers

Arithmetic sequences with fractions

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

What is the next fraction in this sequence?

$\frac{6}{7},\;\frac{5}{7},\;\frac{4}{7},\;\frac{3}{7}$

Look at the numerators of the fractions. The numerator decreases by 1 each time.

The rule for the pattern is: subtract $\frac{1}{7}$.

Subtract $\frac{1}{7}$ from the last fraction

$\frac{3}{7}\;-\;\frac{1}{7}\;=\;\frac{2}{7}$

The next fraction in the pattern is $\frac{2}{7}$. The pattern is:

$\frac{6}{7},\;\frac{5}{7},\;\frac{4}{7},\;\frac{3}{7},\;\frac{2}{7}$

What is the next fraction in this sequence? $\frac{5}{3},\;\frac{6}{3},\;\frac{7}{3},\;\frac{8}{3}$
 Solution: