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What is \(\frac{6}{7} - \frac{2}{14}\)?

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Explanation: Convert \(\frac{2}{14}\) to \(\frac{1}{7}\), then subtract: \(6-1=5\), so \(\frac{5}{7}\).

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Fractions

Fractions Practice Quiz with a Step-by-Step Interactive Lesson

Use the quiz at the top of the page to practice fractions skills: simplifying fractions, equivalent fractions, comparing fractions, and fraction operations. If you want a refresher, click Start lesson to open a clear, step-by-step fractions guide.

How this fractions practice works

1. Take the quiz: answer the fraction questions at the top of the page.
2. Open the lesson (optional): review the methods for common denominators, simplifying, and fraction multiplication.
3. Retry: return to the quiz and apply what you reviewed immediately.

What you’ll learn in the fractions lesson

Meaning & vocabulary

Numerator and denominator
Unit fractions, proper and improper fractions
Mixed numbers and simplest form

Models & equivalence

Fractions as parts of a whole and points on a number line
Equivalent fractions by scaling: \(\frac{a}{b}=\frac{ka}{kb}\)

Simplifying & comparing

Simplify fractions using the greatest common factor (GCF)
Compare and order fractions using benchmarks and common denominators

Fraction operations

Add and subtract fractions (like and unlike denominators)
Multiply fractions (and simplify by cancelling)
Divide fractions with the reciprocal (extension skill)

Back to the quiz

When you’re ready, return to the quiz at the top of the page and continue practicing fractions.

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Fractions
Lesson

Step-by-step guide

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Fractions Lesson

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Lesson Overview

Lesson overview

Purpose: Build a clear understanding of fractions and learn reliable methods for simplifying, comparing, and doing fraction operations.

Success criteria

Explain \(\frac{a}{b}\) as \(a\) parts out of \(b\) equal parts (and as division \(a\div b\), with b≠ 0).
Identify numerator (top) and denominator (bottom), and read fractions correctly.
Create and recognize equivalent fractions and simplify to lowest terms using the GCF.
Compare and order fractions using benchmarks and common denominators.
Add and subtract fractions (like and unlike denominators) and simplify answers.
Multiply fractions (including by whole numbers) and simplify by cancelling common factors.
Connect fractions to decimals, percents, measurement, and real life (recipes, time, probability).

Key vocabulary

Numerator: the top number that tells how many parts you have.
Denominator: the bottom number that tells how many equal parts make one whole.
Equivalent fractions: different-looking fractions that represent the same value (like \(\frac{1}{2}=\frac{2}{4}\)).
Simplest form (lowest terms): a fraction simplified so the numerator and denominator have no common factor greater than 1.

Quick pre-check

Pre-check 1: In the fraction \(\frac{3}{5}\), which number is the denominator?

\(3\) \(5\) \(3+5\) \(3\times 5\)

Hint: The denominator is the bottom number.

Pre-check 2: Simplify \(\frac{6}{12}\).

Hint: Divide numerator and denominator by the same number (try 6).

Parts of a Whole

Fractions as parts of a whole (and points on a number line)

Learning goal: Read and interpret fractions using numerator/denominator and connect fractions to a whole.

Key idea

A fraction \(\frac{a}{b}\) describes a whole that has been split into \(b\) equal parts. The denominator \(b\) tells the number of equal parts in one whole. The numerator \(a\) tells how many parts you have.

Examples: Unit fraction: \(\frac{1}{b}\) (one equal part).
Proper fraction: \(\frac{a}{b}\) with \(a<b\) (less than 1).
Improper fraction: \(\frac{a}{b}\) with \(a\ge b\) (at least 1).

Worked example

Example: What does \(\frac{3}{4}\) mean?

The denominator \(4\) means the whole is split into 4 equal parts.
The numerator \(3\) means you have 3 of those parts.
So \(\frac{3}{4}\) is three out of four equal parts.

Try it

Try it 1: Write the fraction for “3 parts out of 5 equal parts”.

Hint: Numerator = parts you have (3). Denominator = equal parts in the whole (5).

Try it 2: Which of the following is equivalent to \(\frac{3}{5}\)?

\(\frac{6}{10}\) \(\frac{3}{10}\) \(\frac{5}{3}\) \(\frac{15}{5}\)

Hint: Multiply numerator and denominator by the same number (for example, by 2).

Summary

The denominator tells how many equal parts are in one whole.
The numerator tells how many parts you have.
Equivalent fractions represent the same value even if they look different.

Equivalent Fractions

Equivalent fractions and simplifying (reducing)

Learning goal: Make equivalent fractions and simplify fractions to lowest terms correctly.

Key idea

You can create an equivalent fraction by multiplying the numerator and denominator by the same nonzero number: \[ \frac{a}{b}=\frac{ka}{kb}\quad (k\neq 0) \] You can simplify a fraction by dividing the numerator and denominator by the same number greater than 1. The best choice is the greatest common factor (GCF).

Worked example

Example: Simplify \(\frac{9}{12}\)

The GCF of 9 and 12 is 3.
Divide both by 3: \(\frac{9}{12}=\frac{9\div 3}{12\div 3}=\frac{3}{4}\).
So the simplified fraction is \(\frac{3}{4}\).

Try it

Try it 1: Simplify \(\frac{12}{18}\).

Hint: The GCF of 12 and 18 is 6. Divide top and bottom by 6.

Try it 2: Which of the following is equivalent to \(\frac{1}{6}\)?

\(\frac{2}{12}\) \(\frac{3}{12}\) \(\frac{1}{3}\) \(\frac{6}{1}\)

Hint: Multiply \(\frac{1}{6}\) by \(\frac{2}{2}\) to get \(\frac{2}{12}\).

Summary

Multiply or divide the numerator and denominator by the same number to make an equivalent fraction.
Simplify to lowest terms using the GCF.

Compare Fractions

Comparing fractions (which is bigger?)

Learning goal: Compare fractions accurately using common denominators and benchmarks like \(\frac{1}{2}\) and 1.

Key idea

Same denominator: compare numerators (bigger numerator → bigger fraction).
Same numerator: smaller denominator → bigger fraction (because parts are larger).
Different denominators: rewrite using a common denominator (often the LCM), then compare.

Worked example

Example: Compare \(\frac{7}{10}\) and \(\frac{3}{5}\)

Rewrite \(\frac{3}{5}\) with denominator 10: \(\frac{3}{5}=\frac{3\times 2}{5\times 2}=\frac{6}{10}\).
Now compare: \(\frac{7}{10}\) vs \(\frac{6}{10}\).
Because \(7>6\), \(\frac{7}{10} > \frac{3}{5}\).

Try it

Try it 1: Which is larger: \(\frac{7}{10}\) or \(\frac{3}{5}\)? Type the larger fraction.

Hint: Rewrite \(\frac{3}{5}\) as \(\frac{6}{10}\), then compare.

Try it 2: Type a fraction equivalent to \(\frac{1}{2}\): \(\frac{2}{4}\), \(\frac{3}{6}\), or \(\frac{4}{8}\).

Hint: Equivalent fractions come from multiplying numerator and denominator by the same number.

Summary

Use common denominators to compare fractions with different denominators.
Benchmarks like \(\frac{1}{2}\) and 1 help you reason quickly.

Add & Subtract

Add and subtract fractions (common denominators)

Learning goal: Add and subtract fractions correctly by using like denominators or finding a least common denominator (LCD).

Key idea

Like denominators: add/subtract the numerators and keep the denominator.
\(\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}\), and \(\frac{a}{b}-\frac{c}{b}=\frac{a-c}{b}\).

Unlike denominators: find a common denominator (often the LCD / LCM), rewrite both fractions as equivalent fractions, then add/subtract, and simplify.

Worked example

Example: \(\frac{2}{3}-\frac{1}{6}\)

The LCM of 3 and 6 is 6.
Rewrite \(\frac{2}{3}\) as \(\frac{4}{6}\).
Now subtract: \(\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}\).

Try it

Try it 1: Compute \(\frac{5}{9} + \frac{2}{3}\). Give a simplified answer (improper fraction or mixed number).

Hint: Rewrite \(\frac{2}{3}\) with denominator 9: \(\frac{2}{3}=\frac{6}{9}\).

Worked solution

Find a common denominator: LCM\((9,3)=9\).
\(\frac{2}{3}=\frac{2\times 3}{3\times 3}=\frac{6}{9}\).
Add: \(\frac{5}{9}+\frac{6}{9}=\frac{11}{9}\).
As a mixed number: \(\frac{11}{9}=1\frac{2}{9}\).

Try it 2: Compute \(\frac{7}{10} - \frac{3}{5}\).

Hint: Rewrite \(\frac{3}{5}\) as \(\frac{6}{10}\), then subtract numerators.

Summary

To add/subtract fractions, you need like denominators.
Use the LCD (LCM of denominators), rewrite as equivalent fractions, then add/subtract and simplify.

Multiply Fractions

Multiply fractions (and simplify by cancelling)

Learning goal: Multiply fractions accurately and simplify efficiently.

Key idea

To multiply fractions, multiply numerators and multiply denominators: \[ \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd} \] Then simplify the result. A powerful strategy is to cancel common factors before multiplying.

Worked example

Example: \(\frac{5}{8}\times\frac{2}{5}\)

Multiply: \(\frac{5\times 2}{8\times 5}\).
Cancel the 5: \(\frac{5}{5}=1\).
You get \(\frac{2}{8}=\frac{1}{4}\). So the product is \(\frac{1}{4}\).

Try it

Try it: Compute \(\frac{4}{9}\times\frac{3}{8}\). Simplify your answer.

Hint: Multiply then simplify, or cancel first (3 cancels with 9, and 4 cancels with 8).

Worked solution

Cancel first: \(\frac{4}{9}\times\frac{3}{8}\).
\(3\) cancels with \(9\): \(\frac{3}{9}=\frac{1}{3}\).
\(4\) cancels with \(8\): \(\frac{4}{8}=\frac{1}{2}\).
Now multiply: \(\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}\).

Summary

Multiply top × top and bottom × bottom.
Cancel common factors to simplify and reduce mistakes.

Mixed Operations

Order of operations with fractions: multiply first

Learning goal: Evaluate expressions that mix fraction multiplication and addition/subtraction by doing multiplication/division first.

Key idea

When an expression contains \(+\) or \(−\) and also \( \times \) or \( \div \), do multiplication and division first, then add or subtract. Simplify whenever you can to keep numbers small.

Worked example

Example: \(\frac{1}{2} + \frac{3}{4}\times\frac{2}{3}\)

Step 1 (multiply first): \(\frac{3}{4}\times\frac{2}{3}=\frac{6}{12}=\frac{1}{2}\).
Step 2 (add): \(\frac{1}{2}+\frac{1}{2}=1\).
So the value is \(1\).

Try it

Try it 1: Calculate \(\frac{5}{6}\times\frac{4}{5}\). Simplify your answer.

Hint: Cancel the 5 first: \(\frac{5}{6}\times\frac{4}{5}=\frac{1}{6}\times 4\).

Try it 2: What is \(\frac{1}{4} + \frac{1}{2}\)? Give a simplified answer.

Hint: Rewrite \(\frac{1}{2}\) as \(\frac{2}{4}\), then add.

Summary

In mixed expressions, do multiplication/division before addition/subtraction.
Simplify (reduce/cancel) whenever possible to avoid big numbers.

Applications & Connections

Why fractions matter

Learning goal: Connect fractions to real life (recipes, measurement, probability) and to other math ideas.

Where you use fractions

Cooking & recipes: \(\frac{3}{4}\) cup, half a recipe, double a recipe.
Measurement: inches, centimeters, liters, and time (half an hour).
Probability: favorable outcomes / total outcomes.
Money: discounts and percentages (fractions, decimals, percents).

Worked example: scaling a recipe

Example: A recipe uses \(\frac{3}{4}\) cup of milk. You make half a recipe.

Half of \(\frac{3}{4}\) is \(\frac{1}{2}\times\frac{3}{4}=\frac{3}{8}\).
Answer: You need \(\frac{3}{8}\) cup of milk.

Try it

Try it 1: What is \(\frac{1}{6}\times\frac{3}{4}\)? Simplify your answer.

Hint: Multiply numerators and denominators, then simplify: \(\frac{3}{24}=\frac{1}{8}\).

Fun facts (a little history)

Many representations: Fractions can be shown with area models, number lines, and sets of objects.
Unit fractions: Ancient Egyptian mathematics often used sums of unit fractions (like \(\frac{1}{2}+\frac{1}{6}\)).
Connections: Fractions connect naturally to decimals (like \(\frac{1}{2}=0.5\)) and percents (like \(\frac{1}{2}=50\%\)).

Try it 2: Which of the following is equivalent to \(\frac{2}{3}\)?

\(\frac{2}{9}\) \(\frac{4}{6}\) \(\frac{3}{5}\) \(\frac{6}{4}\)

Hint: Multiply \(\frac{2}{3}\) by \(\frac{2}{2}\) to get \(\frac{4}{6}\).

Final recap

Fractions use a numerator (parts you have) and denominator (equal parts in a whole).
Equivalent fractions come from multiplying/dividing numerator and denominator by the same number.
Simplify using the GCF and check that your final answer is in lowest terms.
Add/subtract using a common denominator; multiply by multiplying across; simplify by cancelling.
Fractions appear in recipes, measurement, probability, and percentages.

Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the skill.