When adding and subtracting fractions, we need to get the denominators to be the same. This process is called finding the Least Common Multiple (LCM) of both numbers in the denominators. The LCM is the lowest number that 4 and 6 can form through factors.
So, we need to find the LCM of 4 and 6, so we’ll list the multiples of both numbers to find a common factor.
LCM of 4 and 6:
4: 4, 8, 12, 16
4•1=4, 4•2=8, 4•3=12, and 4•4=15
6: 6, 12, 18
6•1=6, 6•2=12, 6•3=18
The LCM is the product of two factors of different numbers. Looking at the list, the least common multiple is 12 because 12 is a product of two factors of 4 and 6. Therefore, the goal is to get both denominators equal to 12 through multiplication.
3/4 - 1/6
To do this, we need to multiply each fraction by a factor that produces 12. We know that 4•3=12 and 6•2=12, meaning to get 12 as both denominators, we must multiply 3/4 by 3 and 1/6 by 2. Remember, to preserver the fraction’s proportionality, we need to multiply the entire fraction by these factors, meaning the numerator and denominator.
3•3/4•3 - 2•1/2•6
Because 4•3=12 and 6•2=12, the denominators will both be twelve, but the numerators of both fractions also must be multiplied.
9/12 - 2/12
Now that we have common denominators, we can subtract the fractions. The rule for subtracting and adding fractions is to add the denominators and keep the denominators untouched.
9/12 - 2/12 = 9-2/12
Answer: 7/12