Answer: [tex]11\frac{1}{20}y-3\frac{5}{11}[/tex]
Step-by-step explanation:
[tex]8\frac{3}{10}y-(3\frac{5}{11}-2\frac{3}{4}y)[/tex]
Distribute the negative sign. This basically changes the signs inside the parenthesis.
[tex]8\frac{3}{10}y-3\frac{5}{11}+2\frac{3}{4}y[/tex]
Combine like terms. I'll group them so that you can easily see them.
[tex](8\frac{3}{10}y+2\frac{3}{4}y)-3\frac{5}{11}[/tex]
They're like terms because they have the same variable raised to the same power.
To add mixed numbers, add the whole numbers and then the fractions.
[tex](8+2+\frac{3}{10}+\frac{3}{4} )y-3\frac{5}{11}[/tex]
To be able to obtain the same denominator, multiply the first fraction by 4 and the second by 10.
[tex](10\frac{3}{10}*\frac{4}{4}+\frac{3}{4}*\frac{10}{10} )y-3\frac{5}{11}[/tex]
[tex](10\frac{12}{40}+\frac{30}{40} )y-3\frac{5}{11}[/tex]
When you have the same denominator, add numerators.
[tex](10\frac{12+30}{40})y-3\frac{5}{11}[/tex]
[tex](10\frac{42}{40})y-3\frac{5}{11}[/tex]
Simplify.
42/2=21
40/2=20
[tex](10\frac{21}{20})y-3\frac{5}{11}[/tex]
Because the fraction part is greater than 1, we must convert it to a mixed number. You can do this by dividing.
21/20=1
20
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1
The one next to the equal sign is the whole number, the one in the remainder part is the numerator and 20 the denominator.
[tex]1\frac{1}{20}[/tex]
Rewrite this and add the whole number with 10.
[tex](10+1\frac{1}{20})y -3\frac{5}{11}\\11\frac{1}{20}y-3\frac{5}{11}[/tex]
