One-Step Equations Quiz: Solving Equations Made Easy

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Questions and Answers

What is a one-step equation?

An equation showing that two expressions have different values
An equation where multiple operations need to be performed to find the value of the variable
An equation containing a variable where only one operation is needed to find its value (correct)
An equation where the variable is already isolated

If the equation is x + 5 = 12, what operation should be used to solve it?

Subtraction (correct)
Addition
Division
Multiplication

What does the numerator represent in a fraction?

The bottom part of the fraction
The top part of the fraction (correct)
The whole number part of the fraction
The number of equal parts into which the whole is divided

In a one-step equation with multiplication, what is used to isolate the variable?

Division (C)

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Why is it important to identify which operation is involved in a one-step equation?

To use the inverse operation to solve the equation (C)

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What is the first step needed to add fractions with different denominators?

Find the least common multiple of the denominators (C)

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In the case of multiplying fractions, what do you need to do?

Multiply the numerators and denominators (C)

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How can dividing by a number be simplified when dealing with fractions?

Multiplying by its reciprocal (C)

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What operation is needed to solve a one-step equation involving fractions?

Addition (B)

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How can you rewrite a whole number like 3 as a fraction with a denominator of 1?

$\frac{3}{1}$ (B)

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Flashcards

One-step equation

An equation needing only one step to find the variable's value.

Solve x + 5 = 12

Subtract 5 from both sides to isolate x.

Numerator in a fraction

The top number in a fraction.

Isolate variable (multiplication)

Divide both sides of the equation by the number next to the variable.

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Equation operation identification

Knowing the operation (+, -, ×, ÷) in an equation is crucial for solving it.

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Add fractions (different denominators)

Find the least common multiple (LCM) of the denominators to get a common denominator.

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Multiply fractions

Multiply the numerators and denominators separately.

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Divide by a number (fractions)

Multiply by its reciprocal.

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One-step equation (fractions)

Solve using addition/subtraction or multiplication/division with fractions.

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Whole number to fraction

Express a whole number as a fraction with a denominator of 1.

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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.