Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 20, 2023

Express $\frac{35}{49}$ as a simplified fraction.

STEP 1

Assumptions1. We are given the fraction $\frac{35}{49}$ . . We need to express this fraction in its lowest terms.

STEP 2

To express a fraction in its lowest terms, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

STEP 3

Let's find the GCD of35 and49.The factors of35 are1,5,7, and35. The factors of49 are1,7, and49.
The greatest common factor of35 and49 is7.

STEP 4

Now that we have the GCD, we can divide both the numerator and the denominator of the fraction by the GCD to express the fraction in its lowest terms.
$\frac{35}{49} = \frac{35/7}{49/7}$

STEP 5

Calculate the new numerator and denominator.
$\frac{35/7}{49/7} = \frac{5}{7}$ So, the fraction $\frac{35}{49}$ in its lowest terms is $\frac{5}{7}$ .

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