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Which Arithmetic Laws Still Work for Fractions?

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The World of Numbers · Rational numbers and arithmetic · 3:37

You'll learn: Explain closure, commutativity of addition/multiplication and distributivity.

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Which Arithmetic Laws Still Work for Fractions?

3:37

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Which Arithmetic Laws Still Work for Fractions?

You'll learn: Explain closure, commutativity of addition/multiplication and distributivity.

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Same topic

Rational numbers and arithmetic

6

From Parts of a Whole to Rational Numbers
3:24
From Parts of a Whole to Rational Numbers
You'll learn: Define p/q with integer numerator and non-zero integer denominator. Include negative fractions and integers.
Different Fractions Can Name the Same Number
3:32
Different Fractions Can Name the Same Number
You'll learn: Generate equivalent signed fractions and reduce to lowest terms.
Check Fraction Equality with Cross Products
3:12
Check Fraction Equality with Cross Products
You'll learn: Use ad=bc to check equality when denominators are non-zero.
Add and Subtract Rational Numbers
3:36
Add and Subtract Rational Numbers
You'll learn: Find a common denominator, combine signed numerators and simplify.
Multiply and Divide Rational Numbers
3:31
Multiply and Divide Rational Numbers
You'll learn: Multiply numerators and denominators and divide by a non-zero fraction using its reciprocal.
Does This Fraction Equation Have Just One Answer?
3:17
Does This Fraction Equation Have Just One Answer?
You'll learn: Simplify both sides and recognise an identity rather than a unique solution.

Next topic

Rational numbers on the number line

5

Place Positive, Negative and Improper Fractions on a Line
3:23
Place Positive, Negative and Improper Fractions on a Line
You'll learn: Divide unit intervals equally and locate fractions on either side of zero.
Absolute Value Measures Distance, Not Direction
3:29
Absolute Value Measures Distance, Not Direction
You'll learn: Explain absolute value and distance between two rational points.
There Is Always Another Rational Number Between Two
3:34
There Is Always Another Rational Number Between Two
You'll learn: Use averaging to generate a number strictly between two distinct rational numbers.
Find Several Rational Numbers in One Interval
3:40
Find Several Rational Numbers in One Interval
You'll learn: Use common denominators or repeated averaging to list the required number of interior points.
Find Numbers Between Very Close Decimals
3:44
Find Numbers Between Very Close Decimals
You'll learn: Refine decimal places to reveal rational values in a narrow interval.

Next topic

Rational-number applications

2

How Many Complete Kurtas Can the Tailor Make?
3:31
How Many Complete Kurtas Can the Tailor Make?
You'll learn: Divide mixed-number measurements and interpret a whole-object result.
Solve a Rational-Number Equation and Reason About Its Sign
3:18
Solve a Rational-Number Equation and Reason About Its Sign
You'll learn: Solve a fractional-coefficient equation and infer a product’s sign from a relation.

Next topic

Irrational lengths and proofs

2

A Unit Square Reveals a New Kind of Number
3:25
A Unit Square Reveals a New Kind of Number
You'll learn: Use the diagonal of a unit square to motivate √2 and irrational numbers.
Why √2 Cannot Be a Fraction
3:25
Why √2 Cannot Be a Fraction
You'll learn: Follow the contradiction proof from a lowest-terms fraction to both numerator and denominator being even.