(1)/(5)+4h=(1)/(3) What is the value of h in the equation?

Isolate variable h: First, we need to isolate the variable h on one side of the equation. To do this, we will subtract (1/5) from both sides of the equation to get 4h by itself. (1/5) + 4h - (1/5) = (1/3) - (1/5)Calculate right side: Now, we calculate the right side of the equation by finding a common denominator for (1/3) and (1/5), which is 15. Then we subtract the fractions. (1/3) - (1/5) = (5/15) - (3/15) = (2/15)Equation simplification: The equation now looks like this: 4h = (2/15)Divide by 4: To find the value of h, we divide both sides of the equation by 4. h = (2/15) / 4Multiply by reciprocal: Dividing by 4 is the same as multiplying by the reciprocal of 4, which is 1/4. So we multiply (2/15) by (1/4). h = (2/15) * (1/4)Multiply numerators and denominators: Now we multiply the numerators and the denominators separately. h = (2 * 1) / (15 * 4) h = 2 / 60Simplify fraction: Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. h = (2/60) / (2/2) h = 1 / 30

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Math Problems

Algebra 1

Add and subtract rational numbers

Full solution

\frac{1}{5}+4 h=\frac{1}{3}

\newline

What is the value of

h

in the equation?

Isolate variable h: First, we need to isolate the variable h on one side of the equation. To do this, we will subtract $(1/5)$ from both sides of the equation to get $4h$ by itself. $\newline$ $(1/5) + 4h - (1/5) = (1/3) - (1/5)$
Calculate right side: Now, we calculate the right side of the equation by finding a common denominator for $(\frac{1}{3})$ and $(\frac{1}{5})$ , which is $15$ . Then we subtract the fractions. $\newline$ $(\frac{1}{3}) - (\frac{1}{5}) = (\frac{5}{15}) - (\frac{3}{15}) = (\frac{2}{15})$
Equation simplification: The equation now looks like this: $4h = \left(\frac{2}{15}\right)$
Divide by $4$ : To find the value of $h$ , we divide both sides of the equation by $4$ . $h = \frac{\frac{2}{15}}{4}$
Multiply by reciprocal: Dividing by $4$ is the same as multiplying by the reciprocal of $4$ , which is $\frac{1}{4}$ . So we multiply $\left(\frac{2}{15}\right)$ by $\left(\frac{1}{4}\right)$ . $\newline$ $h = \left(\frac{2}{15}\right) \times \left(\frac{1}{4}\right)$
Multiply numerators and denominators: Now we multiply the numerators and the denominators separately. $\newline$ $h = (2 \times 1) / (15 \times 4)$ $\newline$ $h = 2 / 60$
Simplify fraction: Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $h = \frac{\frac{2}{60}}{\frac{2}{2}}$ $\newline$ $h = \frac{1}{30}$