Simplify: \(-\frac{5}{16} + \frac{11}{18} + \left(-\frac{7}{24}\right)\)
Answer (1)
To simplify the expression − 16 5 + 18 11 + ( − 24 7 ) , we need to find a common denominator for the fractions involved.
Identify the Denominators: The denominators we have are 16, 18, and 24.
Find the Least Common Denominator (LCD):
Prime factorization of 16 is 2 4 .
Prime factorization of 18 is 2 × 3 2 .
Prime factorization of 24 is 2 3 × 3 .
The LCD is the highest power of each prime that appears in the factorizations: 2 4 × 3 2 = 144 .
Convert Each Fraction to Have the LCD as the Denominator:
For − 16 5 , multiply both numerator and denominator by 9 to get − 144 45 .
For 18 11 , multiply both numerator and denominator by 8 to get 144 88 .
For − 24 7 , multiply both numerator and denominator by 6 to get − 144 42 .
Add the Fractions:
Combine the fractions: − 144 45 + 144 88 − 144 42 .
Add the numerators: − 45 + 88 − 42 = 1 .
The result is 144 1 .
The simplified result of the expression is 144 1 . This fraction is already in its simplest form.
