Question

$$1\frac{1}{2}\div1\frac{1}{4}-2\frac{1}{2}\times\frac{1}{4}; \frac{1}{3}\times\frac{1}{2}+\frac{1}{6}\times\frac{1}{2}$$

Answer

2-21/2*1/4;1/3*1/2+1/12

Solution


Invert and multiply.
\[\begin{aligned}&\frac{11}{2}\times \frac{4}{11}-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}\end{aligned}\]
Cancel \(11\).
\[\begin{aligned}&\frac{1}{2}\times 4-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}\end{aligned}\]
Simplify  \(\frac{1}{2}\times 4\)  to  \(\frac{4}{2}\).
\[\begin{aligned}&\frac{4}{2}-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}\end{aligned}\]
Simplify  \(\frac{4}{2}\)  to  \(2\).
\[\begin{aligned}&2-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1}{6}\times \frac{1}{2}\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&2-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1\times 1}{6\times 2}\end{aligned}\]
Simplify  \(1\times 1\)  to  \(1\).
\[\begin{aligned}&2-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1}{6\times 2}\end{aligned}\]
Simplify  \(6\times 2\)  to  \(12\).
\[\begin{aligned}&2-\frac{21}{2}\times \frac{1}{4}\\&\frac{1}{3}\times \frac{1}{2}+\frac{1}{12}\end{aligned}\]