🔮 Algebra Realm · Equations

Unknown in numerator

Unknown in numerator focuses on how to solve a fraction equation when an expression containing the unknown is divided by a known number. In this lesson, focus on an equation is a balanced statement.

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Understand Unknown in numerator

Unknown in numerator focuses on how to solve a fraction equation when an expression containing the unknown is divided by a known number. In this lesson, focus on an equation is a balanced statement.

An equation is a balanced statement. Undo operations in a controlled order while performing the same change to both sides. For unknown in numerator, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Unknown in numerator: An equation is a balanced statement. Substitute the proposed solution into the original equation and verify that both sides match. Keep the unknown in numerator representation visible until the final line.

Picture the idea

Move algebra tiles across a balance scale and record each legal inverse operation as a solver step. Use the model to explain one change you notice while working on unknown in numerator.

Check as you go

Substitute the proposed solution into the original equation and verify that both sides match. Write that check beside the final unknown in numerator answer.

Key vocabulary

equationinverse operationbalanceunknownsolutioninnumerator

Rules and key facts

x/5 = 3 gives x = 15.

  • Simplify either side if needed.
  • Choose an inverse operation that removes one obstacle around the unknown.
  • Apply the same operation to both sides.
  • Continue until the unknown is isolated, then substitute to check. Record the check explicitly for unknown in numerator.

Step-by-step method

  1. Simplify either side if needed.
  2. Choose an inverse operation that removes one obstacle around the unknown.
  3. Apply the same operation to both sides.
  4. Continue until the unknown is isolated, then substitute to check. Record the check explicitly for unknown in numerator.

What you need first

  • Recognise the vocabulary: equation, inverse operation, balance.
  • Be able to explain the purpose of unknown in numerator before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Unknown prices
  • Formula calculations

Visual / interactive

See the idea, then move it around

Skip to Practice

Move algebra tiles across a balance scale and record each legal inverse operation as a solver step. Use the model to explain one change you notice while working on unknown in numerator.

Interactive maths model 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: Unknown in numerator — Solve 3/x = 2. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 2x. Divide by 2: x = 1.5. Final answer: 1.5. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Simplify either side if needed.
  2. Choose an inverse operation that removes one obstacle around the unknown.
  3. Apply the same operation to both sides.
Secure example

Use the normal method

Given information: Unknown in numerator — Solve 3/x = 14. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 14x. Divide by 14: x = 0.2143. Final answer: 0.2143. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Substitute and divide to check the original fraction.

Challenge example

Stretch the idea

Given information: Unknown in numerator — Solve 3/x = 13. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 13x. Divide by 13: x = 0.2308. Final answer: 0.2308. 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: Unknown in numerator — Solve 3/x = 12. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 12x. Divide by 12: x = 0.25. Final answer: 0.25. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Box the entire numerator before clearing the denominator.

Common mistakes

  • Changing one side only. This is a key trap when answering unknown in numerator questions.
  • Skipping a line and losing a negative sign or denominator.

How to check your answer

Substitute the proposed solution into the original equation and verify that both sides match. Write that check beside the final unknown in numerator answer.

Extension challenge

Create a unknown in numerator problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Unknown in numerator challenge

Use balance battle controls to solve three checked unknown in numerator rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Challenge Unknown in numerator Arcane Boss

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Unknown in numerator Arcane Boss

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Study cards

Core idea

Unknown in numerator: An equation is a balanced statement. Substitute the proposed solution into the original equation and verify that both sides match. Keep the unknown in numerator representation visible until the final line.

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Key vocabulary

equation · inverse operation · balance · unknown · solution · in · numerator

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Rules

Simplify either side if needed. Choose an inverse operation that removes one obstacle around the unknown. Apply the same operation to both sides. Continue until the unknown is isolated, then substitute to check. Record the check explicitly for unknown in numerator.

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Formula / fact

x/5 = 3 gives x = 15.

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Foundation example

Given information: Unknown in numerator — Solve 3/x = 2. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 2x. Divide by 2: x = 1.5. Final answer: 1.5. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Unknown in numerator — Solve 3/x = 14. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 14x. Divide by 14: x = 0.2143. Final answer: 0.2143. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Unknown in numerator — Solve 3/x = 13. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 13x. Divide by 13: x = 0.2308. Final answer: 0.2308. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Unknown in numerator — Solve 3/x = 12. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 12x. Divide by 12: x = 0.25. Final answer: 0.25. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Changing one side only. This is a key trap when answering unknown in numerator questions.

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Exam tip

For unknown in numerator, show the key representation before the final calculation. Use this final check: Substitute the proposed solution into the original equation and verify that both sides match.

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Real-world use

Unknown prices, Formula calculations

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Checklist

I can explain unknown in numerator, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Unknown in numerator

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Simple explanation

Unknown in numerator: An equation is a balanced statement. Substitute the proposed solution into the original equation and verify that both sides match. Keep the unknown in numerator representation visible until the final line.

Think of unknown in numerator 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. Simplify either side if needed.
  2. Choose an inverse operation that removes one obstacle around the unknown.
  3. Apply the same operation to both sides.
  4. Continue until the unknown is isolated, then substitute to check. Record the check explicitly for unknown in numerator.

Hint 1

Start by naming the given information and the exact result required for unknown in numerator.

Hint 2

Simplify either side if needed.

Full worked solution

Given information: Unknown in numerator — Solve 3/x = 2. Give x as a decimal if needed. Method choice: use the unknown in numerator method and show each step with the stated values. Calculation or reasoning: Multiply by x: 3 = 2x. Divide by 2: x = 1.5. Final answer: 1.5. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Simplify either side if needed. → Choose an inverse operation that removes one obstacle around the unknown. → Apply the same operation to both sides. → Continue until the unknown is isolated, then substitute to check. Record the check explicitly for unknown in numerator.

Common mistake warning

Changing one side only. This is a key trap when answering unknown in numerator questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain unknown in numerator in my own words.
  • I can use these words accurately: equation, inverse operation, balance.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Changing one side only.
  • I can apply this check: Substitute the proposed solution into the original equation and verify that both sides match.
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