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elementary-math Module
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Lesson Directive // Fraction OperationsREF_CORE

Adding & Subtracting

aabb++ccdd==adad++bcbcbdbd

Hover over a variable in the formula above, or see glossary below:

aa
Numerator 1
Integer
bb
Denominator 1
Integer ≠ 0
cc
Numerator 2
Integer
dd
Denominator 2
Integer ≠ 0

To add or subtract fractions, they must share a common denominator. Find the LCM (Lowest Common Multiple) of the denominators, convert both fractions, then add or subtract the numerators.

INSIGHT: You can only add like parts — you cannot add thirds and quarters directly.

Multiplying

To multiply two fractions, multiply the numerators together and the denominators together: \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}.

INSIGHT: No common denominator needed — multiplication is simpler than addition!

Dividing (Keep-Change-Flip)

To divide by a fraction, multiply by its reciprocal: \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}.

INSIGHT: Dividing by $\frac{1}{2}$ is the same as multiplying by 2.
Detailed Theory & ReferencesEXT_DOC

Operations with Fractions

A fraction ab\frac{a}{b} represents aa equal parts of a whole that is divided into bb parts.

Addition and Subtraction

Fractions can only be added or subtracted when they share a common denominator: 13+14=412+312=712\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}

Multiplication

Multiply numerator by numerator, denominator by denominator: ab×cd=a⋅cb⋅d\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

Division (Keep-Change-Flip)

To divide by a fraction, multiply by its reciprocal: ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

References

AI NOTICE

AI Assistance Disclaimer: This module uses AI-assisted educational models and interactive visual representations to help explain scientific and mathematical concepts. For formal research or academic evaluation, please verify formulas and data against standard primary reference materials.