divid the fraction 14/27 by the fraction 2/3 and reduce your answe to the lowest terms
14/27/2/3
=14/27x3/2 (division convert to multiply and numerator will switch to denominator.
=7/9 answer
To divide fractions, we need to follow these steps:
Step 1: Invert the second fraction (the one we want to divide by) by swapping the numerator and denominator.
- Inverting 2/3, we get 3/2.
Step 2: Multiply the first fraction by the inverted second fraction.
- Multiply 14/27 by 3/2: (14/27) * (3/2) = (14 * 3) / (27 * 2).
Step 3: Simplify the resulting fraction by reducing it to its lowest terms.
- 14 * 3 = 42.
- 27 * 2 = 54.
- So, the simplified fraction is 42/54.
To reduce a fraction to its simplest form, we need to find the greatest common divisor (GCD) of the numerator and denominator.
Step 4: Find the GCD of 42 and 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 largest common factor (GCD) is 6.
Step 5: Divide both the numerator and denominator by the GCD (6 in this case).
- 42 ÷ 6 = 7.
- 54 ÷ 6 = 9.
Therefore, the final answer, reduced to the lowest terms, is 7/9.