Solving equations with fractions in grade 10 involves eliminating the fractions to simplify the equation and then solving for the unknown variable. Here's a breakdown of the process:
Steps to Solve Equations with Fractions
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Find the Common Denominator: Identify the least common denominator (LCD) of all the fractions in the equation. This is the smallest number that all the denominators can divide into evenly.
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Multiply Each Term by the Common Denominator: Multiply both sides of the equation (every single term) by the LCD. This will eliminate the fractions. According to the provided reference material, this is a crucial first step.
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Simplify the Equation: After multiplying by the LCD, simplify the equation by performing any necessary arithmetic operations, such as distributing and combining like terms.
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Solve for the Variable: Use algebraic techniques to isolate the variable on one side of the equation. This may involve adding, subtracting, multiplying, or dividing both sides of the equation by constants.
Example
Let's look at a simplified example based on the reference material:
Equation: x/6 = 1/4
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Find the Common Denominator: The least common denominator of 6 and 4 is 12.
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Multiply Each Term by the Common Denominator: Multiply both sides of the equation by 12:
12 (x/6) = 12 (1/4) -
Simplify the Equation: Simplify both sides:
2x = 3 -
Solve for the Variable: Divide both sides by 2 to isolate x:
x = 3/2
Therefore, the solution to the equation is x = 3/2.
Further Considerations
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More Complex Equations: Equations may involve more than two fractions and may include variables in the numerators and denominators. The same principles apply: find the LCD and multiply every term by it.
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Checking Your Solution: It's always a good idea to substitute your solution back into the original equation to ensure that it is correct.
By following these steps, you can confidently solve equations with fractions in grade 10.
