2/3+(3k)/4 = 71/12 — step-by-step solution

Let's solve in

ℝ

\frac{2}{3} + \frac{3 k}{4} = \frac{71}{12}

ⓘ We subtract

\frac{2}{3}

from both sides

\frac{3 k}{4} = \frac{71}{12} - \frac{2}{3}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

12

, the least common multiple of

12

and

3

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{71}{12} - \frac{2}{3}

\frac{71}{12} + \frac{-2 \cdot 4}{3 \cdot 4}

\frac{71 - 2 \cdot 4}{12}

\frac{3 k}{4} = \frac{71 - 2 \cdot 4}{12}

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 4

8

\frac{3 k}{4} = \frac{71 - 8}{12}

ⓘ The numerator and the denominator are computed before the division:

71 - 8

63

\frac{3 k}{4} = \frac{63}{12}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{63}{12}

\frac{21 \cdot 3}{4 \cdot 3}

\frac{21}{4}

\frac{3 k}{4} = \frac{21}{4}

ⓘ We multiply both sides by

4

3 k = 4 \cdot \frac{21}{4}

ⓘ Both sides are divided by

3

k = \frac{4 \cdot \frac{21}{4}}{3}

ⓘ Multiplying a fraction by a number multiplies its numerator:

4 \cdot \frac{21}{4}

\frac{4 \cdot 21}{4}

\frac{84}{4}

k = \frac{\frac{84}{4}}{3}

ⓘ Dividing a fraction by

3

is multiplying its denominator by

3

\frac{\frac{84}{4}}{3}

\frac{84}{4 \cdot 3}

■A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{84}{4 \cdot 3}

\frac{21}{3}

k = \frac{21}{3}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{21}{3}

7

▶Solution obtained:

k = 7