Question

Hi, could you help me with this substitution question?
I'd really appreciate if you added workings out as I'm terribly confused.
Thanks,

Answer 1

Answer:

$-\dfrac{69}{14}$

Step-by-step explanation:

Substitute the given values of the variables into the given expression:

$\implies \dfrac{60 \left(\dfrac{1}{3}\right)\left(-\dfrac{1}{5}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}$

When multiplying fractions, simply multiply the numerators and the denominators:

$\implies \dfrac{60 \left(\dfrac{1 \cdot -1 \cdot 1}{3\cdot 5 \cdot 4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}$

$\implies \dfrac{60 \left(-\dfrac{1}{60}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}$

$\implies \dfrac{\left(-1\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}$

When adding or subtracting fractions, make the denominators the same:

$\implies \dfrac{\left(-1\right)\left(\dfrac{20}{60}-\dfrac{12}{60}+\dfrac{15}{60}\right)}{\left(\dfrac{5}{15}-\dfrac{3}{15}\right)\left(\dfrac{4}{12}+\dfrac{3}{12}\right)}$

Now add the numerators and put that over the denominator:

$\implies \dfrac{\left(-1\right)\left(\dfrac{20-12+15}{60}\right)}{\left(\dfrac{5-3}{15}\right)\left(\dfrac{4+3}{12}\right)}$

$\implies \dfrac{\left(-1\right)\left(\dfrac{23}{60}\right)}{\left(\dfrac{2}{15}\right)\left(\dfrac{7}{12}\right)}$

Again, multiply the fractions:

$\implies \dfrac{\left(-1 \cdot \dfrac{23}{60}\right)}{\left(\dfrac{2 \cdot 7}{15 \cdot 12}\right)}$

$\implies \dfrac{-\dfrac{23}{60}}{\dfrac{14}{180}}$

To divide the fractions, turn the second fraction upside down, then multiply it by the first fraction:

$\implies -\dfrac{23}{60} \cdot \dfrac{180}{14}$

$\implies -\dfrac{4140}{840}$

Finally, simplify:

$\implies -\dfrac{4140 \div 60}{840 \div 60}$

$\implies -\dfrac{69}{14}$