Number foundations · Topic 2 of 15

Fractions & Mixed Numbers

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Math · fractions

A fraction is parts over equal parts; equivalent fractions scale top and bottom alike; simplify with the GCF and convert mixed numbers both ways.

01 · Simplest formSimplify: divide top and bottom by the GCF

02 · Mixed → improperMixed → improper: (whole × bottom + top)/bottom

03 · Improper → mixedImproper → mixed: divide, remainder over bottom

Denominator = equal parts in the whole; numerator = parts you have must know

Proper < 1; improper ≥ 1; mixed = whole + proper fraction

Same nonzero × or ÷ on top and bottom keeps the value (3/8 = 12/32) must know

Simplify: divide top and bottom by the GCF until only 1 is shared must know

Same denominator: the larger numerator is larger (7/10 > 3/10)

How to solve it

Mixed → improper: (whole × denominator + numerator) over the denominator

Improper → mixed: divide; quotient = whole, remainder over the denominator

GCF = the largest factor both numbers share (30 and 42 → 6)

3 2/5 = (3 × 5 + 2)/5 = 17/5

23/6 = 3 r 5 = 3 5/6

6 of 8 portions = 6/8 = 3/4 of the meal

Commonly confused

	Mixed → improper	Improper → mixed
Operation	Multiply, then add	Divide
New numerator / whole	Whole × denominator + numerator	Whole = the quotient; remainder = new numerator
Denominator	Stays the same	Stays the same
Example	3 2/5 = (15 + 2)/5 = 17/5	23/6 = 3 r 5 = 3 5/6

Bigger denominator = smaller pieces: 1/8 < 1/6

Never add to top and bottom: 2/3 ≠ 3/4

Unlike denominators: compare over a common denominator or as decimals

Show 3 more facts

Same top and bottom = 1 whole (4/4 = 1)

Cross-multiply to compare: a/b vs c/d → compare a×d with b×c

Simplify by prime factors: 12/18 = (2·2·3)/(2·3·3) = 2/3

Pearl

Whatever you do to the top, do to the bottom — multiply or divide, never add.

Practice this topic, then test the whole section.

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