In this Grade 6 chapter summary from Yoshiwara Elementary Algebra, students review key concepts from Chapter 5, including exponent rules, square roots and cube roots, the Pythagorean theorem, and the FOIL method for multiplying binomials. The lesson consolidates skills such as applying the order of operations with powers and roots, calculating volume and surface area using formulas, and distinguishing between rational and irrational numbers. It also introduces vocabulary like monomial, binomial, trinomial, and quadratic trinomial to describe algebraic expressions.
Section 1
📘 Exponents and Roots
This lesson introduces exponents for repeated multiplication, like , and roots as their inverse, like . You'll master simplifying expressions and applying these powerful tools to solve geometric and algebraic problems.
This is just the beginning. Next, you'll tackle interactive examples on order of operations and apply your skills in practice problems involving geometric formulas.
Section 2
Order of operations
1 Perform any operations inside parentheses, or above or below a fraction bar.
2 Compute all indicated powers.
3 Perform all multiplications and divisions in the order in which they occur from left to right.
Section 3
Square and cube roots
Square Root.
The number is called a square root of a number if . Every positive number has two square roots, one positive and one negative.
Cube Root.
The number is called a cube root of a number if . Every number has exactly one cube root.
Section 4
Decimal form of a rational number
A rational number is one that can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal representation of a rational number has one of two forms.
1 The decimal representation terminates, or ends.
2 The decimal representation repeats a pattern.
Section 5
Pythagorean theorem
If stands for the length of the hypotenuse of a right triangle, and the lengths of the two legs are represented by and , then
Section 6
Products of binomials
We use the distributive law to expand the product of two binomials. The letters F, O, I, L indicate the four steps in computing the product:
1 F stands for the product of the First terms in each binomial.
2 O stands for the product of the Outer terms.
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Section 1
📘 Exponents and Roots
This lesson introduces exponents for repeated multiplication, like , and roots as their inverse, like . You'll master simplifying expressions and applying these powerful tools to solve geometric and algebraic problems.
This is just the beginning. Next, you'll tackle interactive examples on order of operations and apply your skills in practice problems involving geometric formulas.
Section 2
Order of operations
1 Perform any operations inside parentheses, or above or below a fraction bar.
2 Compute all indicated powers.
3 Perform all multiplications and divisions in the order in which they occur from left to right.
Section 3
Square and cube roots
Square Root.
The number is called a square root of a number if . Every positive number has two square roots, one positive and one negative.
Cube Root.
The number is called a cube root of a number if . Every number has exactly one cube root.
Section 4
Decimal form of a rational number
A rational number is one that can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal representation of a rational number has one of two forms.
1 The decimal representation terminates, or ends.
2 The decimal representation repeats a pattern.
Section 5
Pythagorean theorem
If stands for the length of the hypotenuse of a right triangle, and the lengths of the two legs are represented by and , then
Section 6
Products of binomials
We use the distributive law to expand the product of two binomials. The letters F, O, I, L indicate the four steps in computing the product:
1 F stands for the product of the First terms in each binomial.
2 O stands for the product of the Outer terms.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter