10 Questions
What is a one-step equation?
An equation containing a variable where only one operation is needed to find its value
If the equation is x + 5 = 12, what operation should be used to solve it?
Subtraction
What does the numerator represent in a fraction?
The top part of the fraction
In a one-step equation with multiplication, what is used to isolate the variable?
Division
Why is it important to identify which operation is involved in a one-step equation?
To use the inverse operation to solve the equation
What is the first step needed to add fractions with different denominators?
Find the least common multiple of the denominators
In the case of multiplying fractions, what do you need to do?
Multiply the numerators and denominators
How can dividing by a number be simplified when dealing with fractions?
Multiplying by its reciprocal
What operation is needed to solve a one-step equation involving fractions?
Addition
How can you rewrite a whole number like 3 as a fraction with a denominator of 1?
$\frac{3}{1}$
Study Notes
One-Step Equations
- An equation is a mathematical statement showing that two expressions have the same value.
- A one-step equation is an equation containing a variable where one operation must be performed to find the value of that variable.
Solving One-Step Equations
- The goal is to notice which operation is being performed and use the inverse operation to solve.
- Examples:
- x + 3 = 6: subtract 3 from both sides to solve for x.
- 2x = 8: divide both sides by 2 to solve for x.
One-Step Equations with Fractions
- A fraction is a number in the form of a/b, where a and b are whole numbers.
- In a fraction, a is called the numerator, and b is called the denominator.
Fractions Operations
- Adding Fractions:
- If two fractions have the same denominator, add the numerators and keep the denominator.
- If fractions do not have the same denominator, find the least common multiple of the denominators and multiply the top and bottom of each fraction by a number to create a common denominator.
- Subtracting Fractions:
- Once a common denominator is achieved, subtract the numerators and keep the denominators the same.
- Multiplying Fractions:
- Multiply the numerators and multiply the denominators.
- Dividing Fractions:
- Divide the numerators and divide the denominators.
- Dividing by a fraction is the same as multiplying by its reciprocal.
Solving One-Step Equations with Fractions
- Recognize the operation in the equation and use the inverse operation to solve.
- Example 1:
- x - 1/2 = 3/4: add 1/2 to both sides and find a common denominator to add the fractions.
- Example 2:
- x/2 = 3/4: multiply both sides by 2 to eliminate the fraction on the left side.
- Divide both sides by 3/4, which is the same as multiplying by its reciprocal, 4/3.
Learn how to solve one-step equations, which are mathematical statements containing variables that require one operation to find the value. Practice simplifying the equations by performing addition, subtraction, multiplication, or division on both sides to isolate the variable.
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