How do you evaluate #4\frac { 1} { 3} \div 1\frac { 2} { 3} imes 2\frac { 3} { 4} \div \frac { 1} { 4}#?

Question

How do you evaluate #4\frac { 1} { 3} \div 1\frac { 2} { 3} 	imes 2\frac { 3} { 4} \div \frac { 1} { 4}#?

Isaiah Anthony · Accepted Answer

Use the order of operations and change all of the terms to improper fractions so they can be divided and multiplied.

PEMDAS Think if you get hurt in PE call an MD ASap There are no Parenthesis or Exponents so the first step can be skipped. Remember an MD a doctor is only one person so Multiplication and Division must be done at the same time working from left to right Start with #(4 1/3) /( 1 2/3)# Change both to improper fractions and divide using the complex fraction theorem. # 4 1/3 = 13/3" "and" " 1 2/3 = 5/3 # so #(4 1/3) /( 1 2/3) = ( 13/3)/ ( 5/3)# Now multiply both the top and the bottom by the inverse # 3/5# # ( 13/3 xx 3/5)/(5/3 xx 3/5) = 13/3 xx 3/5 # The bottom fraction is equal to 1: #rarr 5/3 xx 3/5 = 1 # # 13/cancel3 xx cancel3/5 = 13/5# Next multiply #13/5 xx 2 3/4" "# change #2 3/4 to 11/4 # # 13/ 5 xx 11/ 4 = (13 xx 11)/ (5 xx 4 )# Next divide by #1/4 # # { (13 xx 11)/(5 xx 4)}/ ( 1/4) # Multiply both the top and the bottom by the inverse : #4/1# # { ( 13 xx 11) / ( 5 xx 4) xx 4/1}/ (1/4 xx 4/1)# The bottom fraction and the factors of 4 divide out leaving # ( 13 xx 11)/5# = #143/5# = #28 3/5# There are no addition or subtraction operations ( ASap) so the problem is done

Eli Assouline · Answer

#4 1/3-:1 2/3xx2 3/4-:1/4=color(blue)(143/5)=color(teal)(28 3/5#

Given:

#4 1/3-:1 2/3xx2 3/4-:1/4#

Multiply and divide according to the order of operations, starting from the left.

Convert #4 1/3# and #1 2/3# to improper fractions by multiplying the denominator by the whole number and adding the numerator, placing the result over the same denominator.

#(3xx4+1)/3-:(3xx1+2)/3xx2 3/4-:1/4#

#13/3-:5/3xx2 3/4-:1/4#

Invert #5/3# and multiply.

#13/3xx3/5xx2 3/4-:1/4#

#39/15xx2 3/4-:1/4#

Convert #2 3/4# to an improper fraction.

#39/15xx(4xx2+3)/4-:1/4#

#39/15xx11/4-:1/4#

Simplify #39/15xx11/4# to #429/60#.

#429/60-:1/4#

Invert #1/4# and multiply.

#429/60xx4/1=#

#1716/60#

Simplify #1716/60# by dividing the numerator and denominator by #12#.

#(1716-:12)/(60-:12)=#

#143/5#

Convert to a mixed number by dividing #143# by #5# by long division. The whole number quotient is the whole number of the mixed number and the remainder is the new numerator, and the divisor #5# is the denominator.

#143-:5="28 remainder 3"#

#143/5=28 3/5#

Isaiah Anthony · Answer

#28 3/5#

This is one term with four factors that can be calculated in one step. The two operations, division and multiplication, are equally significant and can be performed in any order as long as each factor maintains its own operation.

#4 1/3 div 1 2/3 xx 2 3/4 div 1/4" "larr#change to improper fractions

#=13/3 color(blue)(div 5/3) xx 11/4 color(red)(div 1/4)" "larr a b/c = (c xx a +b)/c#

Multiply by the reciprocal to divide.

#=13/3color(blue)(xx3/5) xx 11/4 color(red)(xx4/1)#

#=13/cancel3 xxcancel3/5xx11/cancel4xxcancel4/1" "larr# cancel like factors

#= 143/5" "larr# multiply straight across

#= 28 3/5" "larr# change to mixed number as was given

Abigail Allen · Answer

undefined To evaluate the expression $4\frac{1}{3} \div 1\frac{2}{3} \times 2\frac{3}{4} \div \frac{1}{4}$:

1. Convert mixed numbers to improper fractions:
   $4\frac{1}{3}$ as an improper fraction is $\frac{13}{3}$.
   $1\frac{2}{3}$ as an improper fraction is $\frac{5}{3}$.
   $2\frac{3}{4}$ as an improper fraction is $\frac{11}{4}$.

2. Perform the division and multiplication operations from left to right:
   $\frac{13}{3} \div \frac{5}{3} = \frac{13}{3} \times \frac{3}{5} = \frac{13}{5}$
   $\frac{13}{5} \times \frac{11}{4} = \frac{143}{20}$
   $\frac{143}{20} \div \frac{1}{4} = \frac{143}{20} \times 4 = \frac{143 \times 4}{20} = \frac{572}{20} = 28.6$

So, $4\frac{1}{3} \div 1\frac{2}{3} \times 2\frac{3}{4} \div \frac{1}{4} = 28.6$.

How do you evaluate #4\frac { 1} { 3} \div 1\frac { 2} { 3} \times 2\frac { 3} { 4} \div \frac { 1} { 4}#?