Solved on Feb 01, 2024

Simplify the fraction $\frac{195}{315}$ .

STEP 1

Assumptions
1. We need to simplify the fraction $\frac{195}{315}$ .
2. Simplification of a fraction involves finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number.

STEP 2

First, we need to find the prime factors of the numerator (195) and the denominator (315) to determine the GCD.

STEP 3

Find the prime factors of 195.
$195 = 3 \times 5 \times 13$

STEP 4

Find the prime factors of 315.
$315 = 3 \times 3 \times 5 \times 7$

STEP 5

Identify the common prime factors between the numerator and the denominator. These will be used to find the GCD.
Common prime factors of 195 and 315 are $3$ and $5$ .

STEP 6

Calculate the GCD by multiplying the common prime factors.
$GCD = 3 \times 5 = 15$

STEP 7

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{195}{315} = \frac{195 \div 15}{315 \div 15}$

STEP 8

Perform the division for both the numerator and the denominator.
$\frac{195 \div 15}{315 \div 15} = \frac{13}{21}$

STEP 9

The fraction $\frac{195}{315}$ simplifies to $\frac{13}{21}$ .
This is the simplest form because 13 and 21 have no common factors other than 1.
The simplified fraction is $\frac{13}{21}$ .

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Simplify the fraction $\frac{195}{315}$ .

STEP 1

Assumptions
1. We need to simplify the fraction $\frac{195}{315}$ .
2. Simplification of a fraction involves finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number.

STEP 2

First, we need to find the prime factors of the numerator (195) and the denominator (315) to determine the GCD.

STEP 3

Find the prime factors of 195.
$195 = 3 \times 5 \times 13$

STEP 4

Find the prime factors of 315.
$315 = 3 \times 3 \times 5 \times 7$

STEP 5

Identify the common prime factors between the numerator and the denominator. These will be used to find the GCD.
Common prime factors of 195 and 315 are $3$ and $5$ .

STEP 6

Calculate the GCD by multiplying the common prime factors.
$GCD = 3 \times 5 = 15$

STEP 7

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{195}{315} = \frac{195 \div 15}{315 \div 15}$

STEP 8

Perform the division for both the numerator and the denominator.
$\frac{195 \div 15}{315 \div 15} = \frac{13}{21}$

STEP 9

The fraction $\frac{195}{315}$ simplifies to $\frac{13}{21}$ .
This is the simplest form because 13 and 21 have no common factors other than 1.
The simplified fraction is $\frac{13}{21}$ .

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Simplify the fraction 195315\frac{195}{315}315195​.

STEP 1

Assumptions1. We need to simplify the fraction 195315\frac{195}{315}315195​.2. Simplification of a fraction involves finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number.

STEP 2

First, we need to find the prime factors of the numerator (195) and the denominator (315) to determine the GCD.

STEP 3

Find the prime factors of 195.195=3×5×13195 = 3 \times 5 \times 13195=3×5×13

STEP 4

Find the prime factors of 315.315=3×3×5×7315 = 3 \times 3 \times 5 \times 7315=3×3×5×7

STEP 5

Identify the common prime factors between the numerator and the denominator. These will be used to find the GCD.Common prime factors of 195 and 315 are 333 and 555.

STEP 6

Calculate the GCD by multiplying the common prime factors.GCD=3×5=15GCD = 3 \times 5 = 15GCD=3×5=15

STEP 7

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.195315=195÷15315÷15\frac{195}{315} = \frac{195 \div 15}{315 \div 15}315195​=315÷15195÷15​

STEP 8

Perform the division for both the numerator and the denominator.195÷15315÷15=1321\frac{195 \div 15}{315 \div 15} = \frac{13}{21}315÷15195÷15​=2113​

STEP 9

The fraction 195315\frac{195}{315}315195​ simplifies to 1321\frac{13}{21}2113​.This is the simplest form because 13 and 21 have no common factors other than 1.The simplified fraction is 1321\frac{13}{21}2113​.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Simplify the fraction $\frac{195}{315}$ .

Assumptions
1. We need to simplify the fraction $\frac{195}{315}$ .
2. Simplification of a fraction involves finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number.

Find the prime factors of 195.
$195 = 3 \times 5 \times 13$

Find the prime factors of 315.
$315 = 3 \times 3 \times 5 \times 7$

Identify the common prime factors between the numerator and the denominator. These will be used to find the GCD.
Common prime factors of 195 and 315 are $3$ and $5$ .

Calculate the GCD by multiplying the common prime factors.
$GCD = 3 \times 5 = 15$

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{195}{315} = \frac{195 \div 15}{315 \div 15}$

Perform the division for both the numerator and the denominator.
$\frac{195 \div 15}{315 \div 15} = \frac{13}{21}$

The fraction $\frac{195}{315}$ simplifies to $\frac{13}{21}$ .
This is the simplest form because 13 and 21 have no common factors other than 1.
The simplified fraction is $\frac{13}{21}$ .