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De Morgan's laws for logic tell us how to distribute a negation over a conjunction or disjunction.

We can use multiplication as repeated addition and the relationship between multiplication and division to solve division problems.

We can use place value strategies to divide some large numbers quickly and efficiently.

We can use rounding to estimate the result of a division problem.

To determine the missing length, we consider the area of the blue rectangle (the one on the righthand side).

We can use area models to represent division problems involving threedigit numbers.

Let's write down the multiplication and division problems this area model represents:

Box models allow us to solve division problems by breaking them down into smaller, easier steps.

The advantage of box models over area models is that box models can be used to solve division problems with remainders.

Box models are powerful because they provide a general method for dividing large numbers. And, as we've seen, they can also handle cases with remainders.

A fraction is a number that represents part of a whole.

In this lesson, we'll learn how to write fractions in words.

In this lesson, we'll learn how to write nonunit fractions in words.

Let's look at the following fraction model, where each circle represents one whole.

Two fractions are equivalent (equivalent) if their area models have the same shape and have the same shaded area.

We can generate equivalent fractions by multiplying the numerator and denominator by any whole number.

A fraction is written in lowest terms when the greatest common factor of the numerator and denominator equals $1.$

Every fraction represents a division the division of the numerator by the denominator. For example:

Another way to represent an improper fraction is to write it as a mixed number.

In this lesson, we'll learn how to write the result of a division problem as a mixed number.

To convert an improper fraction to an equivalent mixed number, we proceed as follows:

Let's convert the following mixed number to an improper fraction:

Let's remind ourselves of the symbols we use to compare numbers:

We can compare two fractions that are one piece short of a whole by finding which is closer to one whole.

A fraction is equivalent to $\dfrac12$ if its numerator is onehalf of its denominator.

When adding fractions using models, we join the shaded parts that refer to the same whole.

When adding two fractions with the same denominator, we

When subtracting two fractions with the same denominator, we

Fraction addition often arises in realworld situations.

Subtraction of fractions often arises in realworld situations.

Let's take a look at the following fraction model (sometimes called a tape diagram):

Let's consider the following decomposition of the fraction $\dfrac67{:}$

To add two mixed numbers, we add whole numbers to whole numbers and fractions to fractions.

To subtract mixed numbers with like denominators, we subtract

Let's consider the following subtraction problem:

Suppose Linda prepares some fruit juice for a hot summer day. The recipe tells her to mix $2\, \dfrac{1}{5}\,\textrm{L}$ of apple juice with $1\, \dfrac{2}{5}\,\textrm{L}$ of cherry juice. If Linda follows the recipe exactly, how many l

Suppose Bethany promised to work for $9\,\dfrac23\,\rm{hr}$ this week in her mother's store. If she worked for $2\,\dfrac13\,\rm{hr}$ in the first two days, how many hours does she have left to work over the remaining days?

Decimals are a way of expressing fractions in an equivalent form that's often easier to work with.

The original HTML source mainly contains a series of script and style imports for a math related web application, and there is no actual math related text content to extract. However, here are the MathML formulas converted to LaTeX:

If two whole numbers have different numbers of digits, then the number containing more digits is the larger number.

We've seen how to express fractions with denominators of $10,100,$ and $1,000$ as decimals. But what about fractions with other denominators? How do we express those fractions as decimals?

Whenever we write a mixed number as a decimal, our decimal will have

We've seen how to convert fractions to decimals. We can also convert from decimals to fractions.

Whenever we write a decimal as a mixed number, our mixed number will have

Let's use an area model to convert this fraction into a decimal fraction with a denominator of 100.

When solving problems with units, we often want to convert from one unit of measurement to another.

When solving problems with units, we often want to convert from one unit of measurement to another.

The volume of an object is the amount of threedimensional space that the object takes up.