simplify 42/54
Understand the Problem
The question is asking us to simplify the fraction 42/54 to its lowest terms. To do this, we will find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by that number.
Answer
The simplified fraction is \( \frac{7}{9} \).
Answer for screen readers
The simplified fraction is ( \frac{7}{9} ).
Steps to Solve
- Find the GCD of 42 and 54
To simplify the fraction, we first need to find the greatest common divisor (GCD) of the numerator (42) and the denominator (54).
The factors of 42 are: $$ 1, 2, 3, 6, 7, 14, 21, 42 $$
The factors of 54 are: $$ 1, 2, 3, 6, 9, 18, 27, 54 $$
The common factors are: $$ 1, 2, 3, 6 $$
The greatest common factor is 6.
- Divide the numerator and denominator by the GCD
Now that we have the GCD (6), we will divide both the numerator and the denominator by 6.
For the numerator: $$ \frac{42}{6} = 7 $$
For the denominator: $$ \frac{54}{6} = 9 $$
- Write the simplified fraction
Now we can write the fraction in its simplest form:
$$ \frac{42}{54} = \frac{7}{9} $$
The simplified fraction is ( \frac{7}{9} ).
More Information
Simplifying fractions is an important skill in math, as it makes working with numbers easier. The GCD helps us reduce fractions to their simplest form, ensuring that we understand the relationship between numbers.
Tips
- Not finding the GCD correctly: Make sure to list all factors accurately.
- Forgetting to divide both the numerator and denominator: Both parts must be divided by the GCD to simplify the fraction properly.
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