Simplify: (3 1/2) ÷ (2 3/5) × (1 1/4) ÷ (7/13)

(show your work)

(3 1/2) ÷ (2 3/5) × (1 1/4) ÷ (7/13)

Change the mixed fractions to improper fractions:

(7/2) ÷ (13/5) × (5/4) ÷ (7/13)

Invert the fractions that are divided and change the
division to a multiplication

(7/2) × (5/13) × (5/4) × (13/7)

or

 7      5     5     13
——— × ———— × ——— × ————
 2     13     4      7

Cancel the 7 numerator in the first fraction
and the 7 denominator in the last fraction:
 
 1
 7      5     5     13
——— × ———— × ——— × ————
 2     13     4      7
                     1

Cancel the 13 denominator in the second fraction
and the 13 numerator in the last fraction:

 1                  1 
 7      5     5     13
——— × ———— × ——— × ————
 2     13     4      7
       1             1

So you have

 1     5     5     1
——— × ——— × ——— × ———
 2     1     4     1

Multiply the numerators 1×5×5×1 = 25
Multiply the denominators 2×1×4×1 = 8

You get

 25
————
  8

Finally we can change that to a mixed number

3 1/8

Edwin
AnlytcPhil@aol.com