How do you add #4\frac { 1} { 5} + 2\frac { 3} { 10}#?

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Answer 1 · 2017-07-15T18:59:16

See a solution process below:

First, convert each mixed number to an improper fraction:

#4 1/5 + 2 3/10 =>#

#(4 + 1/5) + (2 + 3/10) =>#

#([5/5 xx 4] + 1/5) + ([10/10 xx 2] + 3/10) =>#

#(20/5 + 1/5) + (20/10 + 3/10) =>#

#21/5 + 23/10#

We can next convert the fraction on the left to a common denominator:

#(2/2 xx 21/5) + 23/10 =>#

#42/10 + 23/10#

Then, we can add the numerators over the common denominator:

#(42 + 23)/10 =>#

#65/10#

Now, if necessary, we can convert the fraction to a mixed number:

#65/10 => (60 + 5)/10 => 60/10 + 5/10 => 6 + 1/2 => 6 1/2#

Answer 2 · 2017-07-15T19:20:06

#6 1/2#

You can add mixed numbers by adding the whole numbers and the fractions separately. This has the effect of giving us smaller numbers to work with.

#color(blue)(4) 1/5 +color(blue)(2) 3/10#

#= color(blue)(6) (?+?)/10" "larr# add whole numbers, find the LCM

#= 6 (2+3)/10" "larr# make equivalent fractions.

#=6 5/10#

#= 6 1/2#