Question

Can someone please simplify 3 1/3 divided by 2 2/5 please

Answer 1

Simplify the following:

(3 + 1/3)/(2 + 2/5)

Put 2 + 2/5 over the common denominator 5. 2 + 2/5 = (5×2)/5 + 2/5:

(3 + 1/3)/((5×2)/5 + 2/5)

5×2 = 10:

(3 + 1/3)/(10/5 + 2/5)

10/5 + 2/5 = (10 + 2)/5:

(3 + 1/3)/((10 + 2)/5)

10 + 2 = 12:

(3 + 1/3)/(12/5)

Put 3 + 1/3 over the common denominator 3. 3 + 1/3 = (3×3)/3 + 1/3:

((3×3)/3 + 1/3)/(12/5)

3×3 = 9:

(9/3 + 1/3)/(12/5)

9/3 + 1/3 = (9 + 1)/3:

((9 + 1)/3)/(12/5)

9 + 1 = 10:

(10/3)/(12/5)

Multiply the numerator by the reciprocal of the denominator, (10/3)/(12/5) = 10/3×5/12:

(10×5)/(3×12)

The gcd of 10 and 12 is 2, so (10×5)/(3×12) = ((2×5) 5)/(3 (2×6)) = 2/2×(5×5)/(3×6) = (5×5)/(3×6):

(5×5)/(3×6)

3×6 = 18:

(5×5)/18

5×5 = 25:

Answer: 25/18