Work out the missing value in the calculation below: 1/3 + ?/9 = 1
Understand the Problem
The question is asking to find the missing value in a mathematical equation involving fractions. The equation provided is 1/3 + (missing value) / 9 = 1. We need to solve for the missing value.
Answer
The missing value is \( x = 6 \).
Answer for screen readers
The missing value is ( x = 6 ).
Steps to Solve
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Set up the equation
We start with the equation: $$ \frac{1}{3} + \frac{x}{9} = 1 $$ where ( x ) is the missing value.
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Isolate the fraction with the variable
To isolate ( \frac{x}{9} ), we will subtract ( \frac{1}{3} ) from both sides: $$ \frac{x}{9} = 1 - \frac{1}{3} $$
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Evaluate the right side
Calculate ( 1 - \frac{1}{3} ). To do this, convert 1 into a fraction with a denominator of 3: $$ 1 = \frac{3}{3} $$ Therefore, $$ \frac{x}{9} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3} $$
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Clear the variable's fraction
Now, multiply both sides by 9 to solve for ( x ): $$ x = 9 \times \frac{2}{3} $$
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Calculate the final value
Perform the multiplication: $$ x = \frac{18}{3} = 6 $$
The missing value is ( x = 6 ).
More Information
When solving equations involving fractions, it’s often helpful to multiply both sides of the equation by the denominator to eliminate fractions. In this case, converting 1 to a fraction with a common denominator allowed for easier subtraction.
Tips
- One common mistake is forgetting to convert whole numbers into fractions before performing operations. Always ensure all terms are in the same format (usually fractions) when adding or subtracting.
- Another mistake is neglecting to simplify fractions adequately.
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