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If you’re learning about fractions, you’ve probably heard the term “equivalent fractions” before. But what exactly are they? Simply put, equivalent fractions are fractions that represent the same value but are written in different ways. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent half of a whole. Similarly, $\frac{3}{6}$ and $\frac{5}{10}$ are equivalent fractions because they also both represent half of a whole. Understanding equivalent fractions is important because they allow us to compare and manipulate fractions more easily. ...

How can you identify common factors in expressions? If you’ve ever struggled with algebra, you’ve probably encountered expressions that seemed too complex to solve. However, understanding common factors in expressions can help simplify even the most daunting equations. In mathematics, a factor is a number or expression that divides another number or expression evenly. When working with algebraic expressions, identifying and factoring out common factors can help you solve equations more efficiently. ...

How do you factor $$x^2 - 81$$? This type of expression is known as the difference of squares which is an important method of factorisation found in algebraic equations. In its simplest form, the difference of squares tells us that the difference of two square terms will equal the product of the sum and the difference of their individual square terms. It is written like this: $$ a^2 - b^2 = (a - b)(a + b) $$ ...

What is a square number? When it comes to learning mathematics, one of the fundamental concepts is understanding what a square number is. Square numbers are essential for many mathematical operations, and they are used in various fields, including science and engineering. A square number is the result of multiplying a number by itself. For example, $$3 \times 3 = 9$$, making $$9$$ a square number. Square numbers are used in algebra, geometry, and even in everyday life. They are essential for calculating areas and volumes, and they are used in many scientific calculations. Understanding square numbers is the foundation of many mathematical operations, and it is essential for anyone who wants to excel in maths. ...

What is the distributive property in algebra? The distributive property, also known as the distributive law in algebra, is a fundamental principle governing mathematical operations. In simple terms, it states that multiplication can be distributed across addition or subtraction in an expression or equation. For instance, consider the expression $3 \times (4 + 2)$. By applying the distributive property, you can rewrite this expression as $(3 \times 4) + (3 \times 2)$, which equals $12 + 6 = 18$. ...

Understanding factorisation is crucial in many areas of math, particularly in algebraic expressions and quadratic equations. By factoring, we break down complex expressions into simpler ones, which makes solving problems and simplifying equations much easier. So how do you factorise $1 - x^2$? To factorise $1 - x^2$, apply the difference of two squares method. Applying The Difference Of Squares Method One effective technique for factorising $1 - x^2$ is by using the difference of squares method. This involves recognising that the expression can be written as $(1)^2 - (x)^2$, which follows the general form of $a^2 - b^2$. ...

If you’re studying algebra, you may have come across the FOIL method. FOIL is an acronym that stands for First, Outer, Inner, Last and is a technique used to expand two binomials – expressions that consist of two terms. The FOIL method helps you remember the order in which to multiply the terms of each binomial and ensures you don’t accidentally miss any combinations. The FOIL method is a simple and efficient way to multiply binomials. ...

If you are a student of algebra, you might have come across the concept of factorising a quadratic expression. Factorising is an essential skill in algebra, and it involves breaking down an algebraic expression into simpler terms. One of the most common methods of factorising quadratic expressions is the technique known as the difference of two squares method. This technique applies to expressions in the format: $$ a^2 - b^2 $$ ...

If you’re studying maths, you’re likely to come across the term square number at some point. But what exactly is a square number? Put simply, a square number is a number that is the result of an integer being multiplied to itself. For example, $3 \times 3 = 9$, so $9$ is a square number. Understanding square numbers is important in maths, as they are used in a variety of calculations. For instance, they are often used in geometry to calculate the area of a square. They are also used in algebra to solve equations. By learning about square numbers, you’ll be able to better understand these and other mathematical concepts. ...

If you’ve ever taken an algebra class, you’ve probably heard the term coefficient. But what exactly is a coefficient? A coefficient is a number that is multiplied by a variable in an algebraic expression. It’s usually an integer, but it can also be a fraction or decimal. For example: In $3x + 4y$, the coefficients are $3$ and $4$ In $\frac{2}{5}x - 7$, the coefficient of $x$ is $\frac{2}{5}$, and $-7$ is a constant Coefficient Definition In algebra, a coefficient is the numerical or literal factor multiplied by a variable. It comes before the variable in an expression. ...