I need help solving this complex fraction

Question

25/4 ÷ 1/5-4/25

Answer 1

25/4 ÷ 1/5-4/25

To write the fractions with common denominator, find the least common denominator

Multiple of 4: 4, 8, 12, 16, 20, 24, 28,

list the prime factors of each number.

prime factors of 4 = 2 x 2 = 2².

prime factors of 1 = 1 = 1¹

prime factors of 25 = 5 x 5 = 5².

LCM is the product of each factor the greatest number of times it occurs in any number.
LCM = 2² * 1¹ * 5² = 100

Write the fractions with common denominator 100

25/4 ÷ 1/5-4/25 = (25*25 / 4*25) ÷ (20*1/5*20) - (4*25/25*4)

625/100 ÷ 20/100 - 16/100

To simplify the expression follow the order of operations: (PEMDAS)

1. Evaluate the expressions inside Brackets/Parenthesis (P).
2. Evaluate Powers/Exponents (E).
3. Multiply and/or Divide in order from left to right (MD).
4. Add and/or Subtract in order from left to right (AS).

 

Since there are no parenthesis and exponents first operation is division

= 625/20 - 16/100

= 3125/100 - 16/100

Next operation is subtraction

= 3109/100 or 31.09

Write the improper facrtion as mixed number

= 31 09/100