This page covers Fractions & Decimals at the Middle School (Grades 6–8) level, delivered as a formula cheat sheet. Rational numbers done properly — equivalent fractions, operations on unlike denominators, converting. The material here corresponds to Grades 6–8 courses: Math 6 and Math 7.
The key formulas for Fractions & Decimals at the Middle School (Grades 6–8) level are organised below. Each formula is accompanied by a note on when it applies and what common variations exist.
The skills covered by these formulas are: Equivalent fractions, Adding and subtracting unlike denominators, Multiplying and dividing fractions, Decimal operations, Converting fractions to decimals.
For each formula, read the conditions carefully. Many errors in Fractions & Decimals come from applying a formula outside its domain of validity — using a geometric formula that assumes a right angle when the angle is not specified, or applying a probability rule that requires independence when the events are dependent.
Use this sheet as a revision tool after you have worked through problems — not as a first introduction to the material. A formula you have derived or used is one you will remember; a formula you have only read is one you will forget under exam pressure.
Worked Example
A standard fractions decimals problem at the middle school grade 6 8 level.
Work through step by step: identify what is given, what is asked, apply the relevant technique, and check your answer against the original conditions.
Adding numerators and denominators directly: ½ + ⅓ ≠ 2/5. You cannot add fractions with different denominators without converting to a common denominator first.
Frequently Asked Questions
How is Fractions & Decimals different at the Middle School level compared to earlier levels?
At the Middle School (Grades 6–8) level, Fractions & Decimals builds on Grades 6–8 prerequisites. Students are expected to have completed Math 6 before tackling this material.
Which exams test Fractions & Decimals at this level?
SAT/ACT Math, Common Core Grade 4–6.
What is the single most effective way to practise Fractions & Decimals for Middle School students?
The most effective practice at the Middle School (Grades 6–8) level is deliberate work on novel problem setups — not repeated drilling of the same template. Attempt problems before looking at solutions, and review errors by identifying the specific step where the reasoning broke down.