Simplify: (4)/(3)-(1)/(2)n=(5)/(8)

Write Equation: Write down the equation. (4/3) - (1/2)n = (5/8) We need to solve for n.Find Common Denominator: Find a common denominator for the fractions to combine them. The common denominator for 3, 2, and 8 is 24. Convert each fraction to have a denominator of 24. (4/3) becomes (32/24), (1/2) becomes (12/24)n, and (5/8) becomes (15/24).Rewrite with New Denominators: Rewrite the equation with the new denominators. (32/24) - (12/24)n = (15/24)Compare Numerators: Since all terms have the same denominator, we can compare the numerators directly. 32 - 12n = 15Isolate Term with n: Subtract 32 from both sides to isolate the term with n. 32 - 12n - 32 = 15 - 32 -12n = -17Divide to Solve for n: Divide both sides by -12 to solve for n. n = -17 / -12Simplify Fraction: Simplify the fraction. n = 17/12

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Simplify:

\frac{4}{3}-\frac{1}{2} n=\frac{5}{8}

Write Equation: Write down the equation. $\newline$ $(\frac{4}{3}) - (\frac{1}{2})n = (\frac{5}{8})$ $\newline$ We need to solve for $n$ .
Find Common Denominator: Find a common denominator for the fractions to combine them. $\newline$ The common denominator for $3$ , $2$ , and $8$ is $24$ . $\newline$ Convert each fraction to have a denominator of $24$ . $\newline$ $(\frac{4}{3})$ becomes $(\frac{32}{24})$ , $(\frac{1}{2})$ becomes $(\frac{12}{24})$ , and $(\frac{5}{8})$ becomes $2$ $0$ .
Rewrite with New Denominators: Rewrite the equation with the new denominators. $\newline$ $(\frac{32}{24}) - (\frac{12}{24})n = (\frac{15}{24})$
Compare Numerators: Since all terms have the same denominator, we can compare the numerators directly. $32 - 12n = 15$
Isolate Term with n: Subtract $32$ from both sides to isolate the term with $n$ . $\newline$ $32 - 12n - 32 = 15 - 32$ $\newline$ $-12n = -17$
Divide to Solve for $n$ : Divide both sides by $-12$ to solve for $n$ . $n = \frac{-17}{-12}$
Simplify Fraction: Simplify the fraction. $n = \frac{17}{12}$