# Fractions differences in algebra

Context:It would normally follow on from work on sequences and fractions.

Question: Ruth was investigating fraction differences. She wrote down this sequence of fractions: 1/1, 1/2, 1/3, 1/4, 1,5 1,6 .. .. Then she worked out the difference between the consecutive fractions: 1/2, 1/6, 1/12, 1/20, 1/30, .. .. She Then worked out the differences between the Fractions in her second series. 1/3, 1/12 ... ... Investigate Further:

When Doing this make sure your look at these three things, 1:Making and monitoring decions to solve problems. 2.Communicating Mathematically. 3.Developing skills of Mathematical reasoning.

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#### Solution Preview

Fractions Questions

The first thing I look at is at the differences between numbers appearing in the sequence. Since these are fractions with 1 as the numerator, the easiest thing to look at is the differences in the denominators. For the first sequence, the difference in the denominators, 2-1=1, 3-2=1, 4-3=1, etc., is 1 and the pattern is obvious. For the second sequence, found by taking the differences between the elements of the first sequence, the difference in the denominators is:

6-2=4, 12-6=6, 20-12=8, 30-20=10

and the pattern 4,6,8,10,... is easily seen and can be continued to produce the next ...

#### Solution Summary

The fraction differences in algebra are found. The expert examines developing skills of mathematical reasoning.