Chapter 4.3, Problem 64E

(Simplest Form)

To determine

To find which fraction in not equivalent.

Answer to Problem 64E

Option D. Fraction is not equivalent $\frac{39}{52}\ne \frac{31}{42}$

Explanation of Solution

Given information: $\frac{39}{52}$

Formula Used: Factorisation

Calculation:

  $\frac{39}{52}$

Now, Simplify by breaking numerator and denominator into multiplication of prime numbers

  $\frac{39}{52}=\frac{3\times 13}{2\times 2\times 13}$

Now, divide the numerator by denominator to make fraction in simplest form.

  $\frac{3\times 13}{2\times 2\times 13}=\frac{3}{2\times 2}$

Hence, fraction in simplest form

  $\frac{39}{52}=\frac{3}{4}$

(A)

To determine

To find fraction in simplest form and equivalent.

Answer to Problem 64E

Fraction is equivalent $\frac{39}{52}=\frac{36}{48}$

Explanation of Solution

Given information: $\frac{36}{48}$

Formula Used: Factorisation

Calculation:

  $\frac{36}{48}$

Now, Simplify by breaking numerator and denominator into multiplication of prime numbers

  $\frac{36}{48}=\frac{2\times 2\times 3\times 3}{2\times 2\times 2\times 2\times 3}$

Now, divide the numerator by denominator to make fraction in simplest form.

  $\frac{2\times 2\times 3\times 3}{2\times 2\times 2\times 2\times 3}=\frac{3}{2\times 2}$

Hence, fraction in simplest form

  $\frac{36}{48}=\frac{3}{4}$

(B)

To determine

To find fraction in simplest form and equivalent.

Answer to Problem 64E

Fraction is equivalent $\frac{39}{52}=\frac{3}{4}$

Explanation of Solution

Given information: $\frac{3}{4}$

Formula Used: Factorisation

Calculation:

  $\frac{3}{4}$

Now, Simplify by breaking numerator and denominator into multiplication of prime numbers

  $\frac{3}{4}=\frac{3\times 1}{4\times 1}$

Hence, fraction in simplest form

  $\frac{36}{48}=\frac{3}{4}$

(C)

To determine

To find fraction in simplest form and equivalent.

Answer to Problem 64E

Fraction is equivalent $\frac{39}{52}=\frac{78}{104}$

Explanation of Solution

Given information: $\frac{78}{104}$

Formula Used: Factorisation

Calculation:

  $\frac{78}{104}$

Now, Simplify by breaking numerator and denominator into multiplication of prime numbers

  $\frac{78}{104}=\frac{2\times 3\times 13}{2\times 2\times 2\times 13}$

Now, divide the numerator by denominator to make fraction in simplest form.

  $\frac{2\times 3\times 13}{2\times 2\times 2\times 13}=\frac{3}{2\times 2}$

Hence, fraction in simplest form

  $\frac{78}{104}=\frac{3}{4}$

(D)

To determine

To find fraction in simplest form and equivalent.

Answer to Problem 64E

Fraction isnot equivalent $\frac{39}{52}\ne \frac{31}{42}$

Explanation of Solution

Given information: $\frac{31}{42}$

Formula Used: Factorisation

Calculation:

  $\frac{31}{42}$

Now, Simplify by breaking numerator and denominator into multiplication of prime numbers

  $\frac{31}{42}=\frac{31}{2\times 3\times 7}$

Now, divide the numerator by denominator to make fraction in simplest form gives same result as 31 is prime number.

Hence,

  $\frac{31}{42}$ is already a simplest form.

So,

Fraction isnot equivalent $\frac{39}{52}\ne \frac{31}{42}$