Dividing Expressions (Junior Cert Mathematics): Flashcards

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Dividing Expressions
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What does dividing expressions mean?

Simplifying a complicated expression into a simpler one

Two ways to divide expressions

Direct division and division by factorising first

What are coefficients?

Numbers in front of variables (e.g., 3 in 3x3x)

What are variables in algebra?

Letters like xx or yy representing unknowns

Rule for dividing same variable

Subtract the powers/exponents

Formula: xmxn\frac{x^m}{x^n} equals

xmnx^{m-n}

Steps in direct division method

Divide coefficients, then divide variables (subtract exponents)

Dividing polynomial by monomial: key rule

Divide each term separately

Steps for dividing by factorising

Factorise numerator and denominator, cancel common factors, simplify

Why can you cancel common factors?

A factor divided by the same factor equals 1

Simplify: 12x34x\frac{12x^3}{4x}

3x23x^2

Four factorising methods mentioned

HCF, grouping, quadratic factorisation, difference of two squares

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