🛡️ Geometry Fortress · Turns

Angles from fractions of a turn

Angles from fractions of a turn connects a share of a full 360° rotation with an exact angle. Use the turn dial, calculate carefully and compare the result with familiar landmarks.

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Understand Angles from fractions of a turn

Angles from fractions of a turn connects a share of a full 360° rotation with an exact angle. Use the turn dial, calculate carefully and compare the result with familiar landmarks.

A full turn is 360°. A fraction of a turn is found by multiplying the fraction by 360, or by dividing 360 by the denominator before multiplying by the numerator. Keep the fraction visible so the angle can be checked against familiar quarter-, half- and three-quarter-turn landmarks.

Start here

Angles from fractions of a turn: use 360° for a full turn, calculate the requested share and compare the result with a familiar landmark.

Picture the idea

Fill a circular turn dial in equal sectors and watch the matching degree rotation grow as the numerator changes.

Check as you go

Convert the angle back into a fraction of 360 and compare it with the fraction in the question.

Key vocabulary

fraction of a turnfull turnnumeratordenominatorangledegrees

Rules and key facts

Given information: Angles from fractions of a turn — Convert 1/12 of a full turn to degrees. Method choice: A full turn is 360°. Multiply 360° by the fraction or percentage, then check the angle size is sensible. Calculation or reasoning: A full turn is 360°. Calculate 360 × 1/12 = 30°. Final answer: 30. Check: Multiply 360° by the fraction or percentage, then check the angle size is sensible.

  • Use 360° for one full turn.
  • Multiply 360° by the fraction of the turn.
  • For a missing turn, subtract the completed angle from 360°.
  • Check whether the angle size matches the fraction: less than half a turn should be below 180°.

Step-by-step method

  1. Use 360° for one full turn.
  2. Multiply 360° by the fraction of the turn.
  3. For a missing turn, subtract the completed angle from 360°.
  4. Check whether the angle size matches the fraction: less than half a turn should be below 180°.

What you need first

  • Recognise the vocabulary: angle, vertex, baseline.
  • Be able to explain the purpose of angles from fractions of a turn before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Construction plans
  • Bearings and turns

Visual / interactive

See the idea, then move it around

Skip to Practice

Fill a circular turn dial in equal sectors and watch the matching degree rotation grow as the numerator changes.

Turn fraction / percentage visualizer Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
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Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Angles from fractions of a turn — Convert 1/12 of a full turn to degrees. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: A full turn is 360°. Calculate 360 × 1/12 = 30°. Final answer: 30. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Use 360° for one full turn.
  2. Multiply 360° by the fraction of the turn.
  3. For a missing turn, subtract the completed angle from 360°.
Secure example

Use the normal method

Given information: Angles from fractions of a turn — A compass direction changes through 7/8 of a turn. Find the rotation in degrees. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: Multiply the full-turn angle by the fraction: 360 × 7/8 = 315°. Final answer: 315. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the angles from fractions of a turn result against the original information.

Challenge example

Stretch the idea

Given information: Angles from fractions of a turn — A clock hand moves 5/6 of a turn clockwise. Find the angle moved. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: Clockwise changes direction, not size. Calculate 360 × 5/6 = 300°. Final answer: 300. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Angles from fractions of a turn — A pointer has turned 4/5 of a full turn. How many degrees are left to complete the turn? Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: First find the completed angle: 360 × 4/5 = 288°. Then subtract: 360 − 288 = 72°. Final answer: 72. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Underline the units and command word. Show the key calculation and write the answer in context.

Common mistakes

  • Using the numerator as the divisor instead of the denominator.
  • Forgetting that a half turn is 180° and a quarter turn is 90°.

How to check your answer

Convert the angle back into a fraction of 360 and compare it with the fraction in the question.

Extension challenge

Create a angles from fractions of a turn problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Angles from fractions of a turn challenge

Use angle timer controls to solve three checked angles from fractions of a turn rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Boss challenge

Challenge Angles from fractions of a turn Guardian

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Angles from fractions of a turn Guardian

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Study cards

Core idea

Angles from fractions of a turn: use 360° for a full turn, calculate the requested share and compare the result with a familiar landmark.

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Key vocabulary

fraction of a turn · full turn · numerator · denominator · angle · degrees

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Rules

Use 360° for one full turn. Multiply 360° by the fraction of the turn. For a missing turn, subtract the completed angle from 360°. Check whether the angle size matches the fraction: less than half a turn should be below 180°.

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Formula / fact

Given information: Angles from fractions of a turn — Convert 1/12 of a full turn to degrees. Method choice: A full turn is 360°. Multiply 360° by the fraction or percentage, then check the angle size is sensible. Calculation or reasoning: A full turn is 360°. Calculate 360 × 1/12 = 30°. Final answer: 30. Check: Multiply 360° by the fraction or percentage, then check the angle size is sensible.

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Foundation example

Given information: Angles from fractions of a turn — Convert 1/12 of a full turn to degrees. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: A full turn is 360°. Calculate 360 × 1/12 = 30°. Final answer: 30. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Angles from fractions of a turn — A compass direction changes through 7/8 of a turn. Find the rotation in degrees. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: Multiply the full-turn angle by the fraction: 360 × 7/8 = 315°. Final answer: 315. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Angles from fractions of a turn — A clock hand moves 5/6 of a turn clockwise. Find the angle moved. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: Clockwise changes direction, not size. Calculate 360 × 5/6 = 300°. Final answer: 300. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Angles from fractions of a turn — A pointer has turned 4/5 of a full turn. How many degrees are left to complete the turn? Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: First find the completed angle: 360 × 4/5 = 288°. Then subtract: 360 − 288 = 72°. Final answer: 72. Check: substitute or compare with the original information to confirm the result fits the question.

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Common mistake

Using the numerator as the divisor instead of the denominator.

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Exam tip

For angles from fractions of a turn, show the conversion from a full 360° turn. Check with a familiar landmark: quarter turn 90°, half turn 180°, full turn 360°.

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Real-world use

Construction plans, Bearings and turns

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Checklist

I can explain angles from fractions of a turn, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Angles from fractions of a turn

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Simple explanation

Angles from fractions of a turn: use 360° for a full turn, calculate the requested share and compare the result with a familiar landmark.

Think of angles from fractions of a turn as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Use 360° for one full turn.
  2. Multiply 360° by the fraction of the turn.
  3. For a missing turn, subtract the completed angle from 360°.
  4. Check whether the angle size matches the fraction: less than half a turn should be below 180°.

Hint 1

A full turn is 360° and a half turn is 180°.

Hint 2

Multiply by the numerator and divide by the denominator.

Full worked solution

Given information: Angles from fractions of a turn — Convert 1/12 of a full turn to degrees. Method choice: use the angles from fractions of a turn method and show each step with the stated values. Calculation or reasoning: A full turn is 360°. Calculate 360 × 1/12 = 30°. Final answer: 30. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Use 360° for one full turn. → Multiply 360° by the fraction of the turn. → For a missing turn, subtract the completed angle from 360°. → Check whether the angle size matches the fraction: less than half a turn should be below 180°.

Common mistake warning

Using the numerator as the divisor instead of the denominator.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain angles from fractions of a turn in my own words.
  • I can use these words accurately: angle, vertex, baseline.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Reading the opposite protractor scale.
  • I can apply this check: Classify the result as acute, right, obtuse, straight or reflex and verify the size fits that class.
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