Arithmetic guides
Fractions, percentages, ratios, roots and everyday number skills explained step by step.
25 guides · each with a free step-by-step calculator
How to Add Numbers Step by Step
Ever counted your allowance twice and got two different totals? Addition is the fix. It's the very first math skill you learn, and by the end of this guide you'll add any two numbers correctly, every time.
How to Subtract Numbers (Step-by-Step Guide)
You hand over a $50 bill and wait for your change — how much should come back? Subtraction answers that instantly. It's the opposite of addition, and this guide walks you through it one column at a time.
How to Multiply Numbers Step by Step
Need to buy 14 boxes of 23 pencils and don't want to count one by one? Multiplication gets you the answer in seconds. This guide teaches long multiplication step by step, so bigger numbers stop feeling scary.
How to Divide Numbers Step by Step
Six friends, one bag of 84 candies — how many does each person get? Division answers that in one step. It's the opposite of multiplication, and this guide shows you exactly how to work it out.
How to Calculate a Percentage (Step-by-Step)
You scored 18 out of 25 on a quiz — is that a good grade? Turning it into a percentage tells you instantly. By the end of this guide you'll be able to find any percentage in three quick steps.
How to Find Percentage Increase or Decrease
Shoes that cost $50 last month now cost $65 — how big is that jump, really? Percentage change turns any rise or fall into one easy-to-compare number, and this guide shows you exactly how to find it.
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How to Calculate Your Age From Birth Year
Ever glanced at an old photo's date and wondered how old the person in it must be now? Working out age from a birth year is one of the simplest subtraction problems there is, and this guide walks you through it.
How to Convert Length Units (Meters, Feet & More)
A friend from the US asks how far a "100 meter dash" really is, and you draw a blank on feet. Converting length units solves that instantly, and this guide shows you the one method that works for any pair of units.
How to Find the HCF (GCD) of Two Numbers
You've got 36 chocolate bars and 24 candies and want identical gift bags with nothing left over — what's the biggest number of bags you can make? That's exactly what the HCF finds, and this guide shows the fast way to get it.
How to Find the LCM of Two Numbers
Bus A leaves every 8 minutes, Bus B every 12 — how long until they leave together again? That's the LCM at work. It's the smallest number both of your numbers divide into, and this guide shows the quickest way to find it.
How to Add Fractions Step by Step
You hiked 2/5 of a trail before lunch and 1/4 more after — how much of the trail is that in total? You can't just add 2 + 1 and 5 + 4. This guide shows the cross-multiplication trick that makes adding fractions easy every time.
How to Subtract Fractions Step by Step
A jug is 5/6 full of juice, and you pour out 1/3 of a jug to make a smoothie — how much is left? Subtracting fractions with different denominators trips up a lot of people, but the same cross-multiplication trick from adding fractions solves it easily.
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How to Multiply Fractions Step by Step
3/5 of your garden is flowers, and 2/3 of that flower patch is roses — what fraction of the whole garden is roses? Multiplying fractions finds a fraction of a fraction, and it's actually easier than adding them.
How to Divide Fractions Step by Step
You have 3/4 of a liter of juice and want to pour it into 1/8-liter cups — how many full cups can you fill? Dividing fractions answers exactly this kind of "how many fit inside" question, using one simple flip-and-multiply trick.
How to Simplify a Fraction (Lowest Terms)
18 out of 24 students in a class passed a test — but "18/24" is clunky to say out loud. Simplifying a fraction rewrites it with the smallest possible numbers, without changing its value, and this guide shows you exactly how.
How to Simplify a Ratio to Lowest Terms
A paint mix uses 15 parts blue to 25 parts white — awkward to say, easy to fix. Simplifying a ratio writes a comparison using the smallest possible whole numbers, and it uses the exact same trick as simplifying a fraction.
How to Solve a Proportion (Cross Multiply)
A recipe uses 3 eggs for every 5 cups of flour — if a bakery uses 12 eggs, how much flour keeps the same ratio? A proportion finds that missing number, and cross multiplication solves it in three quick steps.
How to Find Prime Factors of a Number
Want to arrange 84 students into equal groups and need every possible group size? Prime factorization breaks a number down into the smallest building blocks that multiply together to make it, revealing every option at once.
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How to Find a Square Root by Hand
A square community garden covers 225 square meters — how long is each side? A square root answers that instantly. It's the reverse of squaring a number, and this guide shows you how to find one, even when it isn't a whole number.
How to Find a Cube Root by Hand
A cube-shaped storage box holds 512 cubic centimeters — how long is each side? A cube root answers that. It's the reverse of cubing a number, and unlike square roots, it even works for negative numbers.
What Is an Exponent? Powers Explained Simply
A storage cube has sides of 5 cm — writing its volume as 5×5×5 gets old fast. An exponent is the shortcut: just write 5³. This guide explains exponents in plain English and shows you how to calculate them.
How to Write a Number in Scientific Notation
Earth sits about 93,000,000 miles from the Sun — writing that out every time is a hassle. Scientific notation shrinks huge (or tiny) numbers into a compact form, and this guide shows you exactly how to build one.
How to Find the Quotient and Remainder
23 cookies, 4 friends — everyone gets a fair share, but a few cookies won't split evenly. Division with remainder tells you exactly how many whole cookies each friend gets, plus how many are left over.
How to Calculate Percentage From Marks
You scored 68 out of 80 on a math exam — but what grade does that translate to? Turning marks into a percentage makes it instantly easy to compare against a grading scale, and this guide shows you how.
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How to Calculate Your GPA (Grade Point Average)
One semester, 54 total grade points, 18 credit hours — what's your GPA? Your Grade Point Average sums up how you're doing across every class into a single number, weighted fairly by how much each class counts.
