\frac{3}{a} + \frac{4}{6}
Answer (2)
Simplify the fraction 6 4 to 3 2 .
Find a common denominator for a 3 and 3 2 , which is 3 a .
Rewrite the fractions with the common denominator: 3 a 9 + 3 a 2 a .
Combine the fractions to get the simplified expression: 3 a 2 a + 9 .
Explanation
Understanding the Problem We are given the expression a 3 + 6 4 and asked to simplify it.
Simplifying the Fraction First, we simplify the fraction 6 4 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us 6 4 = 6 ÷ 2 4 ÷ 2 = 3 2 .
Finding a Common Denominator Now we rewrite the expression as a 3 + 3 2 . To combine these fractions, we need to find a common denominator. The least common multiple of a and 3 is 3 a .
Rewriting with Common Denominator We rewrite each fraction with the common denominator 3 a : a 3 = a × 3 3 × 3 = 3 a 9 3 2 = 3 × a 2 × a = 3 a 2 a .
Combining the Fractions Now we can combine the fractions: 3 a 9 + 3 a 2 a = 3 a 9 + 2 a .
Final Answer Therefore, the simplified expression is 3 a 2 a + 9 .
Examples
In real life, simplifying expressions like this can help in various scenarios. For example, if you are calculating the total cost of items where one item's price depends on a variable 'a', and another item has a fixed price, simplifying the expression helps in easily calculating the total cost for different values of 'a'. Suppose you are buying 'a' number of apples at 3 e a c han d a l so b u y in g a f i x e d i t e m cos t in g \frac{4}{6} d o ll a rs . T h e t o t a l cos tw o u l d b e \frac{3}{a} + \frac{4}{6} , w hi c h s im pl i f i es t o \frac{2a+9}{3a}$. This simplified form makes it easier to calculate the total cost for different quantities of apples.
To simplify a 3 + 6 4 , first reduce 6 4 to 3 2 . Next, find a common denominator of 3 a to combine them, giving you the final result of 3 a 2 a + 9 .
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