SOLID STATE PRESS
← Back to catalog
Fractions Fundamentals cover
Coming soon
Coming soon to Amazon
This title is in our publishing queue.
Browse available titles
Mathematics

Fractions Fundamentals

A Clear Primer for High School and Early College

Fractions show up on nearly every math test from pre-algebra through college placement — and for a lot of students, the rules never quite clicked the first time. Whether you're staring down a standardized exam, trying to get unstuck before a unit test, or a parent looking for a fractions decimals and percents quick review to work through with your kid, this guide gets you up to speed without the filler.

**Fractions Fundamentals** covers exactly what it promises: what a fraction really means, how to simplify using the greatest common factor, how to add and subtract with unlike denominators, how to multiply and divide (including mixed numbers), and how to compare and convert fractions to decimals and percents. Every rule is explained in plain language, backed by worked examples, and paired with the misconceptions that trip students up most.

This is a TLDR study guide — short by design. At 10–20 pages, it respects your time and gets to the point. It is built for high school students (grades 9–12) and early college students who need a focused refresher, not a 300-page textbook. Tutors and parents will find it equally useful as a session-planning reference.

If you want a fractions study guide for high school students that you can read in one sitting and actually use on test day, this is it.

Pick it up, work the examples, and walk into your next exam with the concept locked in.

What you'll learn
  • Explain what a fraction represents and identify the numerator, denominator, and types of fractions
  • Find equivalent fractions, simplify to lowest terms, and convert between mixed numbers and improper fractions
  • Add and subtract fractions using a common denominator, including with mixed numbers
  • Multiply and divide fractions, including the 'keep-change-flip' rule and why it works
  • Compare fractions and convert between fractions, decimals, and percents
What's inside
  1. 1. What a Fraction Actually Is
    Introduces fractions as parts of a whole and as division, defines numerator and denominator, and classifies proper, improper, and mixed numbers.
  2. 2. Equivalent Fractions and Simplifying
    Shows how multiplying or dividing top and bottom by the same number produces equivalent fractions, and how to reduce to lowest terms using the GCF.
  3. 3. Adding and Subtracting Fractions
    Covers common denominators, the LCD, and step-by-step addition and subtraction including mixed numbers and borrowing.
  4. 4. Multiplying and Dividing Fractions
    Explains multiplication straight across, why dividing by a fraction means multiplying by its reciprocal, and how to handle mixed numbers.
  5. 5. Comparing Fractions and Converting to Decimals and Percents
    Three reliable ways to compare fractions and how to move fluidly between fractions, decimals, and percents.
Published by Solid State Press
Fractions Fundamentals cover
TLDR STUDY GUIDES

Fractions Fundamentals

A Clear Primer for High School and Early College
Solid State Press

Fractions Fundamentals

A Clear Primer for High School and Early College

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you're a high school student who needs a fractions study guide to get ready for a quiz, a final, or the math section of the SAT or ACT, this book was written for you. It also works as a middle school math fractions refresher for students entering pre-algebra or algebra 1, and as pre-algebra fractions help for parents and tutors who need a clear, fast resource to work through alongside a student.

The book covers what fractions mean, equivalent fractions, and simplifying fractions — with practice-focused explanations that double as a simplifying fractions practice resource for teens. From there it moves into how to add and subtract fractions, step-by-step guidance on multiplying and dividing fractions explained simply, and a final section on converting fractions to decimals and percents for a complete fractions, decimals, and percents quick review. About 15 pages, no filler.

Read straight through, work every example as you go, then use the problem set at the end to check what you actually retained.

Contents

  1. 1 What a Fraction Actually Is
  2. 2 Equivalent Fractions and Simplifying
  3. 3 Adding and Subtracting Fractions
  4. 4 Multiplying and Dividing Fractions
  5. 5 Comparing Fractions and Converting to Decimals and Percents
Chapter 1

What a Fraction Actually Is

A fraction is a way of writing one number divided by another — and that single idea explains everything else about how fractions work.

Picture a chocolate bar with 8 equal pieces. You eat 3 of them. The portion you ate is $\frac{3}{8}$ of the bar. The bottom number, 8, tells you how many equal parts the whole was cut into. The top number, 3, tells you how many of those parts you're talking about. That relationship is worth locking in before moving forward.

The bottom number is called the denominator. It names the size of each piece — eighths, thirds, tenths, whatever. The top number is called the numerator. It counts how many pieces you have. A helpful memory hook: denominator starts with "d," like divide or down — it's always on the bottom.

$\frac{\text{numerator}}{\text{denominator}} = \frac{\text{how many pieces you have}}{\text{how many pieces make a whole}}$

Fractions as Division

Here is the second way to read a fraction, and it matters just as much as the "parts of a whole" picture: $\frac{3}{8}$ also means $3 \div 8$. The fraction bar is a division sign. If you punch $3 \div 8$ into a calculator, you get $0.375$ — and that is exactly what $\frac{3}{8}$ equals as a decimal. You will use this connection directly in Section 5 when converting fractions to decimals.

This means fractions and division are the same operation written differently. $\frac{12}{4}$ means $12 \div 4 = 3$. $\frac{7}{1}$ means $7 \div 1 = 7$. Any whole number can be written as a fraction by putting it over 1.

Example. A recipe makes 5 equal servings. You are cooking for 3 people. What fraction of the full recipe do you need?

Solution. You need 3 out of 5 servings, so the fraction is $\frac{3}{5}$. As a division problem, that's $3 \div 5 = 0.6$, meaning you need 60% of the full recipe.

Three Types of Fractions

Once you understand the numerator and denominator, you can classify any fraction in a few seconds.

Keep reading

You've read the first half of Chapter 1. The complete book covers 5 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon