MathematicsChapter 5: Linear Equations and Inequalities
Cross Multiply
From a/b = c/d, cross multiply to get a*d = b*c.
Learning objectives
- Define and explain cross multiply.
- Apply cross multiply to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
From ab = cd, cross multiply to get a*d = b*c. Then expand and solve the linear equation. Example: x+13 = 42 gives 2(x+1)=12, so x+1=6 and x=5. The denominators must stay nonzero. Cross multiply is just multiplying both sides by b*d, so it is not a new law, only a shortcut.
Mathematical form
b = cd
d = b*c. Then expand and solve the linear eq
x=5. The denominators must stay nonzero. C
Where / symbols
- Cross Multiply
- From a/b = c/d, cross multiply to get a*d = b*c. Then expand and solve the linear equation. Example: (x+1)/3 = 4/2 gives 2(x+1)=12, so x+1=6 and x=5. The denominators must stay nonzero. Cross multiply is just multiplying both sides by b*d, so it is not a new law, only a shortcut.
Relationship
- ab = cd
- a*d = b*c
- x=5
Overview
Learn the idea, then use it:
Core Understanding
From ab = cd, cross multiply to get a*d = b*c. Then expand and solve the linear equation. Example: x+13 = 42 gives 2(x+1)=12, so x+1=6 and x=5. The denominators must stay nonzero. Cross multiply is just multiplying both sides by b*d, so it is not a new law, only a shortcut.
Examples a/b = c/d · a*d = b*c · x=5 · CROSS MULTIPLY: From a/b = c/d, cross multiply to get a*d = b*c. Then expand and solve the linear equation. Example: (x+1)/3 = 4/2 gives
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — CROSS MULTIPLY
From ab = cd, cross multiply to get a*d = b*c. Then expand and solve the linear equation. Example: x+13 = 42 gives 2(x+1)=12, so x+1=6 and x=5. The denominators must stay nonzero. Cross multiply is just multiplying both sides by b*d, so it is not a new law, only a shortcut.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge cross multiply with a neighbouring idea that uses a different definition, rule, or method.
Key points
- ab = cd
- a*d = b*c
- x=5
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Cross Multiply
Sticky Notes · Quick Revision
Core Idea
- From ab = cd, cross multiply to get a*d = b*c.
Key Points
- ab = cd
- a*d = b*c
- x=5
Simple Check
- Explain cross multiply in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge cross multiply with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- From ab = cd, cross multiply to get a*d = b*c.
- ab = cd
- a*d = b*c
- x=5
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