What is 25 2/3 - 15 1/3 =

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

7 0

Answer:

10 1/3

Step-by-step explanation:

Convert mixed numbers into improper fractions (whole number × denominator + numerator)

25 2/3 and 15 1/3

25 × 3 + 2 = 75 + 2 = 77

Put the number over the same denominator

77/3

15 × 3 + 1 = 45 + 1 = 46

Put the number over the same denominator

46/3

77/3 - 46/3

They have common denominators so we can simply subtract the numerator values

77 - 46/3

31/3

To convert it back to a whole number, find how many times 3 fits into 31 evenly

It fits 10 times evenly with 1 remainding which looks like:

10 1/3

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1/1×3 + 1/3×5 + ... + 1/47×49 HELP PLZ

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Answer:

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Step-by-step explanation:

Let's add the terms and see if there's a pattern

$\dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}=\dfrac{5+1}{1\times 3\times 5}=\dfrac{2}{5}\quad\text{sum of 2 terms}\\\\\dfrac{2}{5}+\dfrac{1}{5\times 7}=\dfrac{14+1}{5\times7}=\dfrac{3}{7}\quad\text{sum of 3 terms}$

Suppose we say the sum of n terms is (n/(2n+1)), the next term in the series will be 1/((2n+1)(2n+3)) and adding that to the presumed sum gives ...

$\dfrac{n}{2n+1}+\dfrac{1}{(2n+1)(2n+3)}=\dfrac{n(2n+3)+1}{(2n+1)(2n+3)}=\dfrac{2n^2+3n+1}{(2n+1)(2n+3)}\\\\=\dfrac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\dfrac{n+1}{2n+3}\text{ matches }\dfrac{(n+1)}{2(n+1)+1}$