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Compare Two Expressions Without Calculating Everything

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Arithmetic Expressions · Comparing expressions through reasoning · 3:16

You'll learn: Compare two expressions by tracking how their parts differ, without calculating everything.

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Compare Two Expressions Without Calculating Everything

3:16

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Compare Two Expressions Without Calculating Everything

You'll learn: Compare two expressions by tracking how their parts differ, without calculating everything.

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Same topic

Comparing expressions through reasoning

1

Change an Expression While Keeping Its Value
3:17
Change an Expression While Keeping Its Value
You'll learn: Change parts of an expression in balancing ways so its value stays the same.

Next topic

Brackets and meaning

2

How Do Brackets Change a Calculation's Meaning?
3:09
How Do Brackets Change a Calculation's Meaning?
You'll learn: Brackets group quantities, so the same numbers with different brackets can mean different calculations.
Evaluate a Bracketed Expression One Group at a Time
3:15
Evaluate a Bracketed Expression One Group at a Time
You'll learn: Evaluate the bracketed groups first, then combine the results.

Next topic

Identifying terms

2

Rewrite Subtraction as Addition of an Opposite
3:25
Rewrite Subtraction as Addition of an Opposite
You'll learn: Subtracting a number is the same as adding its opposite, which turns expressions into sums of terms.
Identify Whole Terms Before Evaluating an Expression
3:28
Identify Whole Terms Before Evaluating an Expression
You'll learn: Products and quotients form single terms; identify the terms first, then add them.

Next topic

Swapping and grouping terms

2

Reorder Signed Terms Without Changing Their Value
3:29
Reorder Signed Terms Without Changing Their Value
You'll learn: Signed terms can be added in any order and grouping without changing the value.
When Does Swapping Numbers Change an Expression?
3:14
When Does Swapping Numbers Change an Expression?
You'll learn: Swapping numbers inside a subtraction or division changes the value; swapping whole signed terms does not.

Next topic

Removing brackets and compensating changes

2

Remove Brackets Without Losing the Signs
3:21
Remove Brackets Without Losing the Signs
You'll learn: A minus sign before a bracket flips the sign of every term inside when the bracket is removed.
Subtract 9 by Subtracting 10 and Adding 1
3:26
Subtract 9 by Subtracting 10 and Adding 1
You'll learn: Changing one term changes the total by the same amount, so subtract 10 and add 1 to subtract 9.

Next topic

Distribution and expression transformations

3

Why Can Multiplication Spread Across a Sum or Difference?
3:22
Why Can Multiplication Spread Across a Sum or Difference?
You'll learn: A number times a sum equals the sum of the separate products, shown with a grid of objects.
Use a Common Factor to Put Terms Back into Brackets
3:18
Use a Common Factor to Put Terms Back into Brackets
You'll learn: Take out a common factor to put terms back into brackets.
Adjust a Product Without Changing Its Value
3:15
Adjust a Product Without Changing Its Value
You'll learn: Multiply one factor and divide another by the same number to keep a product unchanged.

Next topic

Expression-building exploration

1

Build Different Expressions for the Same Target Number
3:15
Build Different Expressions for the Same Target Number
You'll learn: Build several different expressions that hit the same target using restricted numbers and operations.

Next topic

Arithmetic Expressions

2

What Is an Arithmetic Expression?
3:54
What Is an Arithmetic Expression?
You'll learn: What Is an Arithmetic Expression?
Different Expressions Can Have the Same Value
3:58
Different Expressions Can Have the Same Value
You'll learn: Different Expressions Can Have the Same Value