Cancel in Ratios

Cancel in Ratios

What is it?

(n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write the extra factors out.

In simple words

• (n+1)!
• 8!/6! = 8*7
• (n+2)!/n! = (n+1)(n+2)
• State the rule, show the working, and check the answer.

Important terms

CANCEL IN RATIOS: (n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write the extra factors out.

CANCEL IN RATIOS: (n+1)!

What you should learn

• State the rule or meaning of cancel in ratios in easy words.
• Apply cancel in ratios in a clear step-by-step solution.
• Check the conditions, working, and final answer for accuracy.

Examples

• 8!/6! = 8*7
• (n+2)!/n! = (n+1)(n+2)
• Leave 0! as 1

MAIN IDEA

(n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write the extra factors out.

EXAM USE

Write the rule first: (n+1)! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Full school-level explanation

(n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write the extra factors out.

Understand the idea, then apply it:

WHAT — CANCEL IN RATIOS

(n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write the extra factors out.

WHY — Why it matters

This rule is a separate learning unit inside factorial n!. It can be defined, applied, and checked in its own FBISE question.

HOW — How to answer

Write the rule first: (n+1)! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

MAIN IDEA

(n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write the extra factors out.

Remember

• write extra factors

Examples

• 8!/6! = 8*7
• (n+2)!/n! = (n+1)(n+2)
• Leave 0! as 1

EXAM USE

Write the rule first: (n+1)! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Remember

• focused answer
• accurate support

Examples

• State the central idea
• Use one accurate detail
• Check the final response

How to answer a cancel in ratios question

How it works

• Read the exact command word and identify what the question asks.
• State the matching idea, rule, or meaning before adding detail.
• Use the unit evidence or mathematical working that directly supports the answer.
• Check accuracy, relevance, and answer length before finishing.

Remember

• write extra factors
• n! = 12...*n
• 0! = 1
• 0! is 1
• write extra factors
• focused answer
• accurate support
• write extra factors

Deeper understanding

Go beyond memorising Cancel in Ratios. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

What to Know

Example or Evidence

How to Answer

Exam focus

Quick revision

• write extra factors
• n! = 12...*n
• 0! = 1
• 0! is 1
• CANCEL IN RATIOS: (n+1)! / n! = n+1. n! / (n-2)! = n(n-1) if n>=2. Never cancel inside n! as if it were n * !. Write t
• CANCEL IN RATIOS: (n+1)!

0! = 1. If you put 0, nCr formulas break at r=0.

For long answers on Cancel in Ratios: define clearly → explain the main parts → give one example → state one exam caution.