## Decimals

 3.1 Multiply and Divide Decimals

Situation 1

 STEP 1 STEP 2 $$\space\space\space\space\small{\color{red}1}\\ \space\space\space1\,\space.\space5\space l\\ \underline{\times\space\space\space\space\space2\space\space}\\ \underline{\space\space\space3\,\space.\space0\space l}\\$$ \begin{aligned}\color{red}{\space0\space.\space3\space7\space5\space l} \\8\space\overline{)3\space.\space0\space0\space0\space l} \\\underline{-\space0}\space\space\space\space\space\space\quad\space\space\space \\3\space\space\space0\quad\quad \\\underline{-\space2\space\space\space4}\space\quad\space\space\space \\ \space6\space0\quad\space\\\underline{-\space\space5\space6}\space\space\space\space\space \\\space4\space0\space\space \\\underline{-\space4\space0}\space\space \\\color{green}{0\space\space} \end{aligned}

Situation 2

$$36.27\times5.9\div13=$$

 STEP 1 STEP 2 $$\quad\space\small{\color{red}3}\space\small{\color{red}1}\space\space\space\small{\color{red}3}\space\space\\ \quad\space\small{\color{red}5}\space\small{\color{red}2}\space\space\space\small{\color{red}6}\space\\ \space\space\space\space\quad\space3\space6\space.2\,\space7\\ \underline{\times\space\space\quad\space\quad\space\space5\space.9}\\ \small{\color{red}1}\quad\quad\quad\quad\\ \space\space\space\space\space\space3\space2\space6\space\space4\space\space3\\ \underline{+1\space8\space1\space3\space\space5\space\space0}\\\underline{\space\space\space2\space1\space3.9\space\space9\space\space3}\\$$ \begin{aligned}\color{red}{\space1\space6\space.\space4\space6\space1} \\13\space\overline{)2\space1\space3\space.\space9\space9\space3} \\\underline{-\space1\space3}\space\quad\quad\quad \\8\space3\quad\space\space\quad \\\underline{-\space7\space8}\quad\quad\space\space \\ \space5\space9\quad\space\space\space\\\underline{-\space\space5\space2}\quad\space\space\space \\\space7\space9\quad \\\underline{-\space7\space8}\quad\\\ \space1\space3\space\\\underline{-\space1\space3}\space\\\color{green}{0\space} \end{aligned}

 3.2 Solve the Problems

Situation 1

The diagram shows 25 packets of sugar in a container. Each packet has equal mass. Calculate the mass, in kg, of 15 packets of sugar. The total mass is 0.125 kg.

Solution:

 STEP 1 STEP 2 \begin{aligned}\color{red}{\space0\space.\space0\space0\space5\space kg} \\25\space\overline{)0\space.\space1\space2\space5\space kg} \\\underline{-\space0}\space\quad\space\quad\quad\space \\0\space\space\space1\quad\quad\space\space \\\underline{-\space\space\space\space0}\space\quad\quad\space \\ \space1\space2\quad\space\space\space\\\underline{-\space\space\space0}\space\quad\space\space\\\space1\space2\space5\space \\\underline{-\space1\space2\space5}\space\\\color{green}{0\space} \end{aligned} $$\quad\quad\quad\space\small{\color{red}2}\\ \space\space\space\space\space\space0\space.\space0\space0\space5\space kg\\ \underline{\times\quad\space\space\quad\space1\space5\space\space\space\space}\\ \space\space\space\space\space\space0\space\space\space\space0\space2\space5\\ \underline{+\space0\space0\space\space\space0\space5\space0\space\space\space\space}\\ \underline{\quad\space\space0\space.\space0\space7\space5\space kg}\\$$

Situation 2

The length of the windowpane in Amin’s room is 1.2 m and its width is 1.14 m. The window consists of two windowpanes of the same size. The right part of the windowpane has broken and needs to be replaced. Calculate the area, in m2, of the broken windowpane.

Solution:

$$1.2\ m\times1.14\ m\div2=$$

 STEP 1 STEP 2 \begin{aligned}\space\space\space\space\space\space\space1\space.\space1\space\space4\space m\\ \underline{\times\space\space\space\space\space\space\space\space\space1\space.2\space m}\\ \space\space2\space\space\space\space2\space\space8\space\space\space\space\\ \underline{+\space\space1\space1\space\space\space\space4\space\space0\quad}\\ \underline{\space\space\space\space\space1.3\space\space\space6\space\space8\space m^2} \end{aligned}\\ \begin{aligned}\color{red}{\space0\space.\space6\space8\space4\space m^2} \\2\space\overline{)1\space.\space3\space6\space8\space m^2} \\\underline{-\space0}\space\quad\space\quad\quad\space \\1\space\space\space3\quad\quad\space\space \\\underline{-\space1\space\space\space2}\space\quad\quad\space \\ \space1\space6\quad\space\space\space\\\underline{-\space1\space6}\space\quad\space\space\\\space0\space8\space\space\space\space \\\underline{-\space\space8}\space\space\space\space\\\color{green}{0\space\space\space\space} \end{aligned}

## Decimals

 3.1 Multiply and Divide Decimals

Situation 1

 STEP 1 STEP 2 $$\space\space\space\space\small{\color{red}1}\\ \space\space\space1\,\space.\space5\space l\\ \underline{\times\space\space\space\space\space2\space\space}\\ \underline{\space\space\space3\,\space.\space0\space l}\\$$ \begin{aligned}\color{red}{\space0\space.\space3\space7\space5\space l} \\8\space\overline{)3\space.\space0\space0\space0\space l} \\\underline{-\space0}\space\space\space\space\space\space\quad\space\space\space \\3\space\space\space0\quad\quad \\\underline{-\space2\space\space\space4}\space\quad\space\space\space \\ \space6\space0\quad\space\\\underline{-\space\space5\space6}\space\space\space\space\space \\\space4\space0\space\space \\\underline{-\space4\space0}\space\space \\\color{green}{0\space\space} \end{aligned}

Situation 2

$$36.27\times5.9\div13=$$

 STEP 1 STEP 2 $$\quad\space\small{\color{red}3}\space\small{\color{red}1}\space\space\space\small{\color{red}3}\space\space\\ \quad\space\small{\color{red}5}\space\small{\color{red}2}\space\space\space\small{\color{red}6}\space\\ \space\space\space\space\quad\space3\space6\space.2\,\space7\\ \underline{\times\space\space\quad\space\quad\space\space5\space.9}\\ \small{\color{red}1}\quad\quad\quad\quad\\ \space\space\space\space\space\space3\space2\space6\space\space4\space\space3\\ \underline{+1\space8\space1\space3\space\space5\space\space0}\\\underline{\space\space\space2\space1\space3.9\space\space9\space\space3}\\$$ \begin{aligned}\color{red}{\space1\space6\space.\space4\space6\space1} \\13\space\overline{)2\space1\space3\space.\space9\space9\space3} \\\underline{-\space1\space3}\space\quad\quad\quad \\8\space3\quad\space\space\quad \\\underline{-\space7\space8}\quad\quad\space\space \\ \space5\space9\quad\space\space\space\\\underline{-\space\space5\space2}\quad\space\space\space \\\space7\space9\quad \\\underline{-\space7\space8}\quad\\\ \space1\space3\space\\\underline{-\space1\space3}\space\\\color{green}{0\space} \end{aligned}

 3.2 Solve the Problems

Situation 1

The diagram shows 25 packets of sugar in a container. Each packet has equal mass. Calculate the mass, in kg, of 15 packets of sugar. The total mass is 0.125 kg.

Solution:

 STEP 1 STEP 2 \begin{aligned}\color{red}{\space0\space.\space0\space0\space5\space kg} \\25\space\overline{)0\space.\space1\space2\space5\space kg} \\\underline{-\space0}\space\quad\space\quad\quad\space \\0\space\space\space1\quad\quad\space\space \\\underline{-\space\space\space\space0}\space\quad\quad\space \\ \space1\space2\quad\space\space\space\\\underline{-\space\space\space0}\space\quad\space\space\\\space1\space2\space5\space \\\underline{-\space1\space2\space5}\space\\\color{green}{0\space} \end{aligned} $$\quad\quad\quad\space\small{\color{red}2}\\ \space\space\space\space\space\space0\space.\space0\space0\space5\space kg\\ \underline{\times\quad\space\space\quad\space1\space5\space\space\space\space}\\ \space\space\space\space\space\space0\space\space\space\space0\space2\space5\\ \underline{+\space0\space0\space\space\space0\space5\space0\space\space\space\space}\\ \underline{\quad\space\space0\space.\space0\space7\space5\space kg}\\$$

Situation 2

The length of the windowpane in Amin’s room is 1.2 m and its width is 1.14 m. The window consists of two windowpanes of the same size. The right part of the windowpane has broken and needs to be replaced. Calculate the area, in m2, of the broken windowpane.

Solution:

$$1.2\ m\times1.14\ m\div2=$$

 STEP 1 STEP 2 \begin{aligned}\space\space\space\space\space\space\space1\space.\space1\space\space4\space m\\ \underline{\times\space\space\space\space\space\space\space\space\space1\space.2\space m}\\ \space\space2\space\space\space\space2\space\space8\space\space\space\space\\ \underline{+\space\space1\space1\space\space\space\space4\space\space0\quad}\\ \underline{\space\space\space\space\space1.3\space\space\space6\space\space8\space m^2} \end{aligned}\\ \begin{aligned}\color{red}{\space0\space.\space6\space8\space4\space m^2} \\2\space\overline{)1\space.\space3\space6\space8\space m^2} \\\underline{-\space0}\space\quad\space\quad\quad\space \\1\space\space\space3\quad\quad\space\space \\\underline{-\space1\space\space\space2}\space\quad\quad\space \\ \space1\space6\quad\space\space\space\\\underline{-\space1\space6}\space\quad\space\space\\\space0\space8\space\space\space\space \\\underline{-\space\space8}\space\space\space\space\\\color{green}{0\space\space\space\space} \end{aligned}