How do you simplify #(5/6)/(1 1/4)#?

Question

Benjamin Altschul · Accepted Answer

Use the complex fraction theorem

# (5/6)/ ( 1 1/4) = (5/6)/(5/4) " "larr( 1 1/4 = 4/4 + 1/4 = 5/4)# Using the multiplicative inverse and the multiplication property of equality multiply both the top fraction and the bottom fraction by the reciprocal of the bottom fraction # 4/5 # # (5/6 xx 4/5)/ (5/4 xx 4/5 )" "larr" " 5/4 xx 4/5 = 1" "# leaving # 5/6 xx 4/5 # #= 20/30# #= 2/3#

Noah Archer · Answer

#(5/6)/(1 1/4)=2/3# Let us first convert mixed fraction #1 1/4# into improper fraction #1 1/4=1+1/4=4/4+1/4=5/4# Now dividing by a fraction #a/b# is equivalent to multiplying by its reciprocal #b/a# Hence #(5/6)/(1 1/4)# = #(5/6)/(5/4)# = #5/6xx4/5# = #cancel5/(cancel6^3)xx(cancel4^2)/cancel5# = #2/3#

Noah Archer · Answer

#2/3#

To divide and multiply, you need to work with common fractions, so change any mixed number into an improper fraction.

#1 1/4 = (4xx1 +1)/4 = 5/4#

There is a useful technique for dividing fractions given in this form:

#(color(green)(a/b))/(color(magenta)(c/d)) = color(green)(a/b) div color(magenta)(c/d) = a/b color(magenta)(xx d/c) = (ad)/(bc)#

#:.(color(red)(5)/color(blue)(6))/(color(blue)(5)/color(red)(4)) = color(red)(5xx4)/(color(blue)(6xx5))" "larr# now simplify

#(cancel5xxcancel4^2)/(cancel6^3xxcancel5) = 2/3#

Autumn Arnold · Answer

undefined To simplify (5/6)/(1 1/4), first convert the mixed number 1 1/4 to an improper fraction, which is 5/4. Then, rewrite the expression as (5/6) ÷ (5/4). To divide fractions, multiply the first fraction by the reciprocal of the second. Therefore, it becomes (5/6) * (4/5). Cancel out common factors between the numerators and denominators. After simplification, you get 1/6.