How do you simplify #4 1/4 div 2#?

Question

Riley Anderson · Accepted Answer

#4 1/4-:2=2 1/8#

While using fractions, we convert division into multiplication by taking the multiplicative inverse or reciprocal of the divisor.

As reciprocal of a fraction is nothing but numerator and denominator reversed, if we have to divide #a/b# by #c/d#, we just multiply #a/b# and #d/c#.

If one of the numbers is not a fraction, we write it as fraction. For example #p# as #p/1#.

Hence #4 1/4-:2#

= #(4xx4+1)/4-:2/#

= #17/4xx1/2=(17xx1)/(4xx2)=17/8#

= #(2xx8+1)/8=(2xx8)/8+1/8=2 1/8#

Emery Allen · Answer

#17/8#

Full explanation given as to how it all works.

Given:#" "4 1/4 -:2# ,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider the #4 1/4# Write as:#" "4+1/4# Multiply by 1 and you do not change the value, but 1 comes in many forms. So we can change the way it looks without changing the intrinsic value. Multiply the 4 by 1 but in the form of #color(magenta)(1=4/4)# #[4color(magenta)(xx4/4)]+1/4# #[16/4]+1/4" "=" "(16+1)/4# #"So "4 1/4" is the same as "17/4# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Putting it all together: #-> 17/4-:2# #color(magenta)("Shortcut method "->" Invert the 2 and multiply")# #color(blue)(17/4xx1/2 = 17/8) larr" shortcuts make calculation faster"# '............................................................................................. #color(magenta)("First principle method "->" turn the 2 into quarters")# Multiply the 2 by 1 but in the form of #color(green)(1=4/4)# #17/4-:[2color(green)(xx4/4)]# #17/4-:8/4# Fraction structure is #("count")/("size indicator")" "->" "("numerator")/("denominator")# #color(brown)("As both the size indicators are the same we can just divide counts")# #=> 17/4-:8/4" "=" "17-:8" "=" "color(blue)(17/8)#

Everly Taylor · Answer

undefined To simplify $ 4 \frac{1}{4} \div 2 $, first convert the mixed number $ 4 \frac{1}{4} $ to an improper fraction, which is $ \frac{17}{4} $. Then, divide $ \frac{17}{4} $ by 2. The division of fractions is done by multiplying the numerator of the first fraction by the reciprocal of the second fraction. So, $ \frac{17}{4} \div 2 = \frac{17}{4} \times \frac{1}{2} = \frac{17}{8} $. Therefore, $ 4 \frac{1}{4} \div 2 = \frac{17}{8} $.