Free Math Worksheets

- The coefficient is the number multiplying the variable. - A minus sign in front of a variable represents an implied factor. - Rewrite division by a number as multiplication by its reciprocal. - Multiplying a variable by \(1\) does not change its value.

1. A coefficient is the numerical factor multiplying a variable. 2. In \(-x\), the implied numerical factor is \(-1\), so the coefficient is \(-1\). 3. In \(1.2y\), the coefficient is \(1.2\). 4. Rewrite \(\frac{z}{10}\) as \(\frac{1}{10}z\), so the coefficient is \(\frac{1}{10}\), or \(0.1\). 5. In \(-\frac{4}{5}a\), the coefficient is \(-\frac{4}{5}\), or \(-0.8\). 6. The expression \(b\) means \(1\times b\), so the coefficient is \(1\).

a) \(-1\) b) \(1.2\) c) \(\frac{1}{10}\), or \(0.1\) d) \(-\frac{4}{5}\), or \(-0.8\) e) \(1\)

- Rewrite subtraction as addition of a negative term. - Keep each minus sign attached to the term that follows it. - Identify every term before rewriting the expression.

1. The signed terms in \(7x-4y\) are \(7x\) and \(-4y\). Written as a sum, the expression is \((7x)+(-4y)\). 2. The signed terms in \(-a^2+5a-9\) are \(-a^2\), \(5a\), and \(-9\). Written as a sum, the expression is \((-a^2)+(5a)+(-9)\). 3. The signed terms in \(3u^2-uv+2v^2\) are \(3u^2\), \(-uv\), and \(2v^2\). Written as a sum, the expression is \((3u^2)+(-uv)+(2v^2)\).

1) \((7x)+(-4y)\) 2) \((-a^2)+(5a)+(-9)\) 3) \((3u^2)+(-uv)+(2v^2)\)

- Use the order of operations to decide which operation is performed last. - Imagine substituting numbers for the variables and completing the calculation. - The last operation determines the name of the entire expression.

1. In \(x(y+5)\), the addition inside parentheses is performed first and multiplication is performed last. The expression is a product. 2. In \(a^2-10\), exponentiation is performed first and subtraction is performed last. The expression is a difference. 3. In \((p-q)\div4\), subtraction inside parentheses is performed first and division is performed last. The expression is a quotient. 4. In \(7+3n\), multiplication is performed before addition, so addition is performed last. The expression is a sum. 5. In \((m+1)^2\), addition inside parentheses is performed first and exponentiation is performed last. The expression is a power.

1) Multiplication; product 2) Subtraction; difference 3) Division; quotient 4) Addition; sum 5) Exponentiation; power

- A variable with no visible numerical factor has an implied coefficient. - Include each term’s sign as part of its numerical factor. - Rewrite subtraction as addition of a negative term.

1. Rewrite each subtraction as addition of a negative term: \((-5x^2)+x+(-0.8)\). 2. The numerical factor of \(-5x^2\) is \(-5\). 3. The term \(x\) means \(1\times x\), so its coefficient is \(1\). 4. The numerical factor of the constant term \(-0.8\) is \(-0.8\).

a) \((-5x^2)+x+(-0.8)\) b) The numerical factors are \(-5\), \(1\), and \(-0.8\). The coefficient of the \(x\)-term is \(1\).

- Identify the operation inside the parentheses before the multiplication. - Substitute the given value for part b). - A product is \(0\) when at least one factor is \(0\).

1. The expression means four times the difference between \(x\) and \(2.5\). 2. For \(x=5.5\), \(4\times(5.5-2.5)=4\times 3=12\). 3. Since \(4\ne 0\), the product equals \(0\) only when \(x-2.5=0\). 4. Therefore, \(x=2.5\).

a) Four times the difference between \(x\) and \(2.5\) b) \(12\) c) \(x=2.5\), because the factor \(x-2.5\) must equal \(0\).