• Decimals represent fractions with denominators \(10, 100, 1\,000\) and so on.

• When adding decimals in vertical form, make sure that the decimal points are aligned vertically.
• Then, add from the right to the left as in adding the whole numbers.

As example,

\(0.18+4.59=\underline{\hspace{1cm}}\)

\(\begin{array}{rr} \small{\color{green}{1}}\space\space\space\space \\0\space.\space1\space8 \\+\quad4\space.\space5\space9 \\\hline4\space.\space7\space7 \\\hline \end{array}\)

• When subtracting decimals in vertical form, make sure that the decimal points are aligned vertically.
• Subtract the numbers from the right to the left.

As example,

\(8.322-2.7=\underline{\hspace{1.5cm}}\)

\(\begin{array}{rr} \small{\color{red}{7}}\space\space\small{\color{green}{13}\space\space\space\space\space\space\space} \\\cancel{8}\space.\space\cancel{3}\space2\space2 \\-\quad\quad2\space.\space7\space0\space0 \\\hline5\space.\space6\space2\space2 \\\hline \end{array}\)

• Multiplication of a decimal by a whole number is adding up the repeating decimal.
• To find the product of a decimal and a whole number, multiply the digits in the same way as for whole numbers.
• The decimal point is placed as in the multiplied number.

As example,

\(6.4\times6=\underline{\hspace{1cm}}\)

\(\begin{array}{rr} \small{\color{red}{2}}\quad\space\space\space \\6\space.\space4 \\\times\quad\quad\quad6 \\\hline3\space8\space.\space4 \\\hline \end{array}\)

• Divide decimals as in whole numbers.
• The decimal point is placed as in the divided number.
• Note that the decimal point is aligned vertically to that in the dividend.

As example,

\(18.768\div6=\underline{\hspace{1.5cm}}\)

\(\begin{aligned}\color{red}{3\space.\space1\space2\space8} \\6\space\overline{)1\space8\space.\space7\space6\space8} \\\underline{-\space1\space8}\space\space\space\space\space\quad\space\space \\7\quad\space\space \\\underline{-\space6}\space\space\quad \\1\space6\space\space\space \\\underline{-\space1\space2}\space\space\space\\4\space8 \\\underline{-\space4\space8} \\0 \end{aligned}\)

• Decimals represent fractions with denominators \(10, 100, 1\,000\) and so on.

• When adding decimals in vertical form, make sure that the decimal points are aligned vertically.
• Then, add from the right to the left as in adding the whole numbers.

As example,

\(0.18+4.59=\underline{\hspace{1cm}}\)

\(\begin{array}{rr} \small{\color{green}{1}}\space\space\space\space \\0\space.\space1\space8 \\+\quad4\space.\space5\space9 \\\hline4\space.\space7\space7 \\\hline \end{array}\)

• When subtracting decimals in vertical form, make sure that the decimal points are aligned vertically.
• Subtract the numbers from the right to the left.

As example,

\(8.322-2.7=\underline{\hspace{1.5cm}}\)

\(\begin{array}{rr} \small{\color{red}{7}}\space\space\small{\color{green}{13}\space\space\space\space\space\space\space} \\\cancel{8}\space.\space\cancel{3}\space2\space2 \\-\quad\quad2\space.\space7\space0\space0 \\\hline5\space.\space6\space2\space2 \\\hline \end{array}\)

• Multiplication of a decimal by a whole number is adding up the repeating decimal.
• To find the product of a decimal and a whole number, multiply the digits in the same way as for whole numbers.
• The decimal point is placed as in the multiplied number.

As example,

\(6.4\times6=\underline{\hspace{1cm}}\)

\(\begin{array}{rr} \small{\color{red}{2}}\quad\space\space\space \\6\space.\space4 \\\times\quad\quad\quad6 \\\hline3\space8\space.\space4 \\\hline \end{array}\)

• Divide decimals as in whole numbers.
• The decimal point is placed as in the divided number.
• Note that the decimal point is aligned vertically to that in the dividend.

As example,

\(18.768\div6=\underline{\hspace{1.5cm}}\)

\(\begin{aligned}\color{red}{3\space.\space1\space2\space8} \\6\space\overline{)1\space8\space.\space7\space6\space8} \\\underline{-\space1\space8}\space\space\space\space\space\quad\space\space \\7\quad\space\space \\\underline{-\space6}\space\space\quad \\1\space6\space\space\space \\\underline{-\space1\space2}\space\space\space\\4\space8 \\\underline{-\space4\space8} \\0 \end{aligned}\)