Use the order of operations to simplify this expression. express your answer in simplest form. 1/4 +1/2 ÷ 3/8

You do the division first which actually is really multiplication because you can't divide fractions. So anyway you apply the fraction rule which states that a/b÷c/d=a/b×d/c you flip second part of fraction like this

original problem: 1/4+1/2÷3/8

change division into
multiplication now so: 1/4+1/2×3/8

remember you have
to follow order of
operations (pemdas) do
multiplication first(remember
to flip the fraction
on the end so : 1/2×8/3

then multiply across: 1x8=8
2x3=6 so answer is 8/6
(cancel out common factors of 8 and 6 which is 2)
so 8÷2/6÷2=4/3

now take the first part
of problem which is 1/4
and add it to answer you
got which is 4/3 so it looks like : 1/4+4/3

solve by adding fractions
by finding lcm of changing
bottom numbers 3 and 4 so the fractions have the same denominator: lcm=12

lcm changes the problem
now you have to multiply
the numerator of each to
whatever you need to get
the bottom answer so
for 1/4 the denominator is 4
so 4x3 gives you 12 multiply numerator by 3also which gives you: 3/12
And for the second fraction
4/3 you look at denominator 3
And you know 3x4=12 multiply the 4 by the numerator also and that gives you: 16/12

now add them: 3/12+16/12= 19/12

simplify: 19/12=
19÷12= 1 7/12

hope this helped and didn't confuse you more

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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