Simplify: \(\dfrac{5}{6}-\dfrac{7}{12}+\dfrac{3}{4}+2.8-0.4\)
3.4
To simplify a mixed expression of fractions and decimals, combine the fractions over their LCM first and then add the decimal terms.
Step 1 — The LCM of 6, 12 and 4 is 12: \(\dfrac{5}{6}-\dfrac{7}{12}+\dfrac{3}{4}=\dfrac{10}{12}-\dfrac{7}{12}+\dfrac{9}{12}=\dfrac{12}{12}=1\).
Step 2 — Decimal part: \(2.8-0.4=2.4\).
Step 3 — Total: \(1+2.4=3.4\).
Step 4 — 2.4 is only the decimal part (it misses the fraction sum of 1), 2.8 ignores both the fractions and the subtraction of 0.4, and 3.9 comes from an arithmetic slip in combining the fractions.
3.4 option is correct.
Important Questions from Simplification
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done?
