In mathematics, numbers are used to quantify and measure objects and quantities. They are classified into different types such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Natural numbers are the counting numbers, which start from 1 and go up to infinity. They are represented as N = {1, 2, 3, 4, ...}.

Whole numbers include all the natural numbers along with the number 0. They are represented as W = {0, 1, 2, 3, 4, ...}.

Integers include all the whole numbers along with their negative counterparts and zero. They are represented as Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be represented as a/b, where a and b are integers and b ≠ 0.

Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They are non-repeating and non-terminating decimals. Examples include √2, π, and e.

Basic operations with numbers include addition, subtraction, multiplication, and division. These operations follow specific rules and properties.

- Practice identifying different types of numbers.
- Understand the properties of each type of number.
- Practice performing operations with different types of numbers.
- Memorize common irrational numbers and their decimal approximations.

Study GuideMultiply/Divide Fractions Worksheet/Answer key

Multiply/Divide Fractions Worksheet/Answer key

Multiply/Divide Fractions Worksheet/Answer key

Multiply/Divide Fractions Worksheet/Answer keyMultiplying and Dividing Fractions Worksheet/Answer key

Dividing Mixed Numbers Worksheet/Answer keyMultiplying Mixed Numbers

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Understand meanings of operations and how they relate to one another.

Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

Compute fluently and make reasonable estimates.

Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Grade 6 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of and fluency with multiplication and division of fractions and decimals

Students use the meanings of fractions, multiplication and division, and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and explain why they work. They use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain the procedures for multiplying and dividing decimals. Students use common procedures to multiply and divide fractions and decimals efficiently and accurately. They multiply and divide fractions and decimals to solve problems, including multi-step problems and problems involving measurement.

Connections to the Grade 6 Focal Points (NCTM)

Number and Operations: Students' work in dividing fractions shows them that they can express the result of dividing two whole numbers as a fraction (viewed as parts of a whole). Students then extend their work in grade 5 with division of whole numbers to give mixed number and decimal solutions to division problems with whole numbers. They recognize that ratio tables not only derive from rows in the multiplication table but also connect with equivalent fractions. Students distinguish multiplicative comparisons from additive comparisons.