Basic and mixed operations

Basic and Mixed Operations

1.2

Basic and Mixed Operations

BASIC OPERATIONS

ADDITION

The table shows the population of three districts in Seberang Perai in 2020.

DISTRICT IN SEBERANG PERAI	North	Middle	South
POPULATION	405 100	467 800	235 100

What is the total population of all three districts in Seberang Perai?

ANSWER:
\(405\,100\;+\;467\,800\;+\;235\,100=\)

\(\begin{array} {rr} \small{\color{red}{1}}\,\, \small{\color{red}{1}}\,\, \small{\color{red}{1}}\quad\quad\;\; \\\space\space4\space0\space5\;\space1\space0\space0 \\\space\space4\space6\space7\;\space8\space0\space0 \\+\quad\space2\space3\space5\;\space1\space0\space0 \\\hline\space1\;\space1\space0\space8\;\space0\space0\space0 \\\hline \end{array}\)

So, the total population of all three districts in Seberang Perai is \(1\ 108\ 000\).

SUBTRACTION

The pictures show three types of gadgets produced by a factory.

A	B
\(710\text{ million}\)	\(0.56\text{ million}\)
C
\(4\ 905\ 127\)

How many more gadgets does C have compared to B?

ANSWER:
\(4\,905\,127-0.56\ \text{million}=\)

STEP 1	STEP 2
\(\begin{aligned} 0.56\text{ million}&=0.56\;\times1\,000\,000 \\&=560\,000 \end{aligned}\)	\(\begin{array} {rr} \small{\color{red}{8}}\, \small{\color{red}{10}}\quad\quad\;\;\;\,\, \\\space\space4\;\space\cancel{9}\space\cancel{0}\space5\;\space1\space2\space7 \\-\quad\;\space5\space6\space0\;\space0\space0\space0 \\\hline\space\space4\;\space3\space4\space5\;\space1\space2\space7 \\\hline \end{array}\)

So, the number of gadgets C is more than \(4\ 345\ 127\) compared to the number of gadgets B.

MULTIPLICATION

A factory produces \(1\ 150\ 000\) bars of soap weekly. How many bars of soap are produced in \(8\) weeks?

ANSWER:
\(8\;\times\;1\,150\,000=\)
\(\begin{array} {rr} \small{\color{red}{1}}\quad\small{\color{red}{4}}\quad\quad\quad\quad\;\; \\\quad1\quad1\space5\space0\quad0\space0\space0 \\\times\quad\quad\quad\quad\quad\quad\quad8 \\\hline\quad9\quad2\space0\space0\quad0\space0\space0 \\\hline \end{array}\)

So, the number of soap produced in \(8\) weeks is \(9\ 200\ 000\) bars.

DIVISION

\(1\ 200\ 000\) pairs of gloves are to be packed equally into several plastic packages. Each plastic package has \(10\) pairs of gloves. How many plastic packages of gloves are produced? Give the answer in a whole number and in decimal of a million.

ANSWER:
\(1\,200\,000\;\div\;10=\)

STEP 1	STEP 2
\(\begin{aligned}\frac{1\;200\;00\cancel{0}}{1\cancel{0}} =120\;000\quad\quad\quad \end{aligned}\)	\(120\;000\div\;1\;000\;000=0.12\text{ million}\)

So, the number of plastic packages of gloves produced is \(120\ 000\) or \(0.12\text{ million}\).

MIXED OPERATIONS

ADDITION & SUBTRACTION

The table shows the number of orders and sale of face shields.

ORDERS IN 2019	\(0.4\text{ million}\)
SALES IN 2019	\(0.372\text{ million}\)
ORDERS IN 2020	\(5.25\text{ million}\)

Calculate the number of unsold face shields.

ANSWER:
\(0.4\text{ million}-0.372\text{ million}+5.25\text{ million}=\)

STEP 1

STEP 2

\(\begin{array} {rr} \small{\color{red}{9}}\quad\quad\quad\quad\;\;\;\;\;\\\small{\color{red}{3}}\, \small{\color{red}{10}}\, \small{\color{red}{10}}\quad\quad\quad\;\; \\\space\space0\space.\cancel{4}\cancel{0}\cancel{0}\;\;\text{million} \\-\quad\space\space0\space.\space3\space7\space2\;\;\text{million} \\\hline\quad\space\space0\space.\space0\space2\space8\;\;\text{million} \\\hline \end{array}\)

\(\begin{array} {rr} \\\space\space0\space.\space0\space2\space8\;\;\text{million} \\+\quad\space\space5\space.\space2\space5\space0\;\;\text{million} \\\hline\quad\space\space5\space.\space2\space7\space8\;\;\text{million} \\\hline \end{array}\)

So, the number of unsold face shields is \(5.278\text{ million}\).

MULTIPLICATION & DIVISION

A container has \(\frac{1}{8}\) million pieces of face masks.

\(\Longrightarrow\)

There are \(7\) similar containers.

\(\Longrightarrow\)

Distribute the face masks equally to \(5\) hospitals.

How many face masks are received by each hospital?

ANSWER:
\(\frac{1}{8}\;\text{million}\;\times\;7\;\div\;5=\)

TIPS: SOLVE THE OPERATIONS FROM LEFT TO RIGHT.

STEP 1	STEP 2	STEP 3
\(\frac{1}{8}\text{ million }\times\ 7=0.875\text{ million}\)	\(\;\;\;\;0\;.\;1\;7\;5\;\;\text{million} \\5\overline{\smash{)}\;0\;.\;8\;7\;5\,}\;\text{million} \\\,\underline{-\;0}\;\;\,\downarrow \\\;\;\;\,0\;\;\;\,8 \\\;\;\;\;\;\;\underline{-\;5}\downarrow \\\ \;\;\;\;\;\;\;\;\;3\;7 \\\;\;\;\;\;\;\underline{-\;3\;5}\downarrow \\\ \;\;\;\;\;\;\;\;\;\;\;\;2\;5 \\\;\;\;\;\;\;\;\;\;\underline{-\;2\;5} \\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\,0\)	\(0.175\text { million}\times1\,000\,000 =175\,000\)

So, the number of face masks received by each hospital is \(175\ 000\).

ADDITION & MULTIPLICATION

Farmasi Sejahtera just received \(0.46\) million bottles of vitamin pills. They still have \(12\) boxes of vitamin pills in the stock. Each box contains \(15\) bottles of vitamin pills. Calculate the current number of bottles of vitamin pills.

ANSWER:
\(0.46\text{ million}+\;12\times15=\)

TIPS: ORDER OF OPERATION - (\(\times\)) FIRST, THEN (\(+\)).

STEP 1	STEP 2	STEP 3
\(\begin{array} {rr} \small{\color{red}{1}}\quad\;\; \\\quad1\quad2 \\\times\quad1\quad5 \\\hline\quad6\quad0 \\+\quad1\quad2\quad0 \\\hline \quad1\quad8\quad0 \\\hline \end{array}\)	\(0.46\text{ million}\times1\,000\,000=460\,000\)	\(460\ 000\ +180=460\ 180\)

So, the current number of bottles of vitamin pills is \(460\ 180\) bottles.

BASIC OPERATIONS & MIXED OPERATIONS INVOLVING UNKNOWN

Clothes manufactured by Factory T.

TYPES OF SHIRT	TOTAL CLOTHES MANUFACTURED
Long-sleeved	\(0.6\text{ million}\)
Short-sleeved	\(x\)
Total	\(1.3\text{ million}\)

How many short-sleeved clothes are manufactured by Factory T?

ANSWER:
\(\begin{aligned} 0.6\text{ million}+{\color{red}{x}}\;&=1.3\ \text{million} \\{\color{red}{x}}\;&=1.3\;\text{million}-0.6\ \text{million} \\{\color{red}{x}}\;&=\;0.7\ \text{million} \end{aligned}\)

So, the number of short-sleeved clothes manufactured by Factory T is \(0.7\ \text{million}\).