Solve 45 28 * 2 3 / 15 7 g| 1 4 - 2 3 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{45}{28}\times\frac{2}{3}\div\frac{15}{7}g|\frac{1}{4}-\frac{2}{3}$$

Evaluate

$\frac{5g}{24}$

Solution Steps

Multiply $\frac{45}{28}$ times $\frac{2}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{45\times 2}{28\times 3}}{\frac{15}{7}}g|\frac{1}{4}-\frac{2}{3}|$$

Do the multiplications in the fraction $\frac{45\times 2}{28\times 3}$.

$$\frac{\frac{90}{84}}{\frac{15}{7}}g|\frac{1}{4}-\frac{2}{3}|$$

Reduce the fraction $\frac{90}{84}$ to lowest terms by extracting and canceling out $6$.

$$\frac{\frac{15}{14}}{\frac{15}{7}}g|\frac{1}{4}-\frac{2}{3}|$$

Divide $\frac{15}{14}$ by $\frac{15}{7}$ by multiplying $\frac{15}{14}$ by the reciprocal of $\frac{15}{7}$.

$$\frac{15}{14}\times \frac{7}{15}g|\frac{1}{4}-\frac{2}{3}|$$

Multiply $\frac{15}{14}$ times $\frac{7}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 7}{14\times 15}g|\frac{1}{4}-\frac{2}{3}|$$

Cancel out $15$ in both numerator and denominator.

$$\frac{7}{14}g|\frac{1}{4}-\frac{2}{3}|$$

Reduce the fraction $\frac{7}{14}$ to lowest terms by extracting and canceling out $7$.

$$\frac{1}{2}g|\frac{1}{4}-\frac{2}{3}|$$

Least common multiple of $4$ and $3$ is $12$. Convert $\frac{1}{4}$ and $\frac{2}{3}$ to fractions with denominator $12$.

$$\frac{1}{2}g|\frac{3}{12}-\frac{8}{12}|$$

Since $\frac{3}{12}$ and $\frac{8}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}g|\frac{3-8}{12}|$$

Subtract $8$ from $3$ to get $-5$.

$$\frac{1}{2}g|-\frac{5}{12}|$$

The absolute value of a real number $a$ is $a$ when $a\geq 0$, or $-a$ when $a<0$. The absolute value of $-\frac{5}{12}$ is $\frac{5}{12}$.

$$\frac{1}{2}g\times \frac{5}{12}$$

Multiply $\frac{1}{2}$ times $\frac{5}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{2\times 12}g$$

Do the multiplications in the fraction $\frac{1\times 5}{2\times 12}$.

$$\frac{5}{24}g$$

Differentiate w.r.t. g

$\frac{5}{24} = 0.20833333333333334$

Steps Using Definition of a Derivative

Multiply $\frac{45}{28}$ times $\frac{2}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{\frac{45\times 2}{28\times 3}}{\frac{15}{7}}g|\frac{1}{4}-\frac{2}{3}|)$$

Do the multiplications in the fraction $\frac{45\times 2}{28\times 3}$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{\frac{90}{84}}{\frac{15}{7}}g|\frac{1}{4}-\frac{2}{3}|)$$

Reduce the fraction $\frac{90}{84}$ to lowest terms by extracting and canceling out $6$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{\frac{15}{14}}{\frac{15}{7}}g|\frac{1}{4}-\frac{2}{3}|)$$

Divide $\frac{15}{14}$ by $\frac{15}{7}$ by multiplying $\frac{15}{14}$ by the reciprocal of $\frac{15}{7}$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{15}{14}\times \frac{7}{15}g|\frac{1}{4}-\frac{2}{3}|)$$

Multiply $\frac{15}{14}$ times $\frac{7}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{15\times 7}{14\times 15}g|\frac{1}{4}-\frac{2}{3}|)$$

Cancel out $15$ in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{7}{14}g|\frac{1}{4}-\frac{2}{3}|)$$

Reduce the fraction $\frac{7}{14}$ to lowest terms by extracting and canceling out $7$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{2}g|\frac{1}{4}-\frac{2}{3}|)$$

Least common multiple of $4$ and $3$ is $12$. Convert $\frac{1}{4}$ and $\frac{2}{3}$ to fractions with denominator $12$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{2}g|\frac{3}{12}-\frac{8}{12}|)$$

Since $\frac{3}{12}$ and $\frac{8}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{2}g|\frac{3-8}{12}|)$$

Subtract $8$ from $3$ to get $-5$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{2}g|-\frac{5}{12}|)$$

The absolute value of a real number $a$ is $a$ when $a\geq 0$, or $-a$ when $a<0$. The absolute value of $-\frac{5}{12}$ is $\frac{5}{12}$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{2}g\times \frac{5}{12})$$

Multiply $\frac{1}{2}$ times $\frac{5}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1\times 5}{2\times 12}g)$$

Do the multiplications in the fraction $\frac{1\times 5}{2\times 12}$.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{5}{24}g)$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{5}{24}g^{1-1}$$

Subtract $1$ from $1$.

$$\frac{5}{24}g^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{5}{24}\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{5}{24}$$