Question

The sum of two numbers is 5/9.if one of the numbers is 1/3 find the other

Answer 1

Answer:

2/9

Step-by-step explanation:

The sum of two numbers is 5/9 can be expressed as:

$\displaystyle \large{x+y=\dfrac{5}{9}}$

One of the numbers is 1/3. Find the other - this means that either x or y is 1/3 but that doesn’t matter as we can either let x = 1/3 or y = 1/3 via property:

$\displaystyle \large{x+y = y+x}$

Hence, let x = 1/3:

$\displaystyle \large{\dfrac{1}{3}+y=\dfrac{5}{9}}$

Solve for y - subtract both sides by 1/3:

$\displaystyle \large{\dfrac{1}{3}-\dfrac{1}{3}+y=\dfrac{5}{9}-\dfrac{1}{3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1}{3}}$

We know that we can only evaluate the fractions if both have same denominator so what we have to do is to multiply 1/3 by 3 for both top and bottom:

$\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1\cdot 3}{3\cdot 3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{3}{9}}\\\displaystyle \large{y=\dfrac{2}{9}}$

Therefore, the other number is 2/9

Answer 2

Answer:

The other number is 2/9

Step-by-step explanation:

"a" is the other number

The equation:

$a+\frac{1}{3} =\frac{5}{9}$

Then

$a=\frac{5}{9} -\frac{1}{3} =\frac{15-9}{27} =\frac{6}{27}$

simplifying the fraction:

$a = \frac{2}{9}$

Hope this helps