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Calculations 計算

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この記事は約23分で読めます。

spoken calculations

2+2=4

Two and two is four.  (informal)
Two plus two equals/is four.  (formal)

7-4=3

Four from seven is/leaves three.  (informal)
Seven take away four is/leaves three.  (informal)
Seven minus four equals/is three.  (formal)

3×4=12

Three fours are twelve.  (informal)
Three times four is twelve.  (informal)
Three multiplied by four equals/is twelve.  (formal)

to calculate on paper

146
×281
29200
11680
146
41026

setting:
A hundred and forty-six times two hundred and eighty-one.

beginning:
Put down two noughts/zeros. Tow sixes are twelve; put down two and carry one; two fours are eight and one are nine; two ones are two.

next line:
Put down one nought/zero. eight sixes are forty-eight; put down eight and carry four; eight fours are thirty-two and four is thirty-six; put down six and carry three; eight ones are eight and three is eleven.

next line:
One times 146 is 146.

addition:
Six and nought/zero and nought/zero is six; eight and four and nought/zero is twelve; put down two and carry one; six and two are eight and one is nine and one is ten; put down nought/zero carry one; nine and one are ten and one is eleven; put down one and carry one; two and one are three and one are four.

total:
Forty-one thousand and twenty-six.

9÷3=3

Three(s) into nine goes three (times).  (informal, especially BrE)
Nine divided by three equals/is three. (formal)

$$\frac{2}{7} \div \frac{2}{3} = \frac{3}{7}$$

Two sevenths divided by two thirds equals/is three sevenths.

10 ÷ 3 = 3 r 1

Oh, there’s a remainder!

Ten divided by three equals/is three with a remainder of one.

power and root  累乗と根

$$x^n$$

x to the nth power

$$x^{-n}$$

x to the minus nth power

$$5^2$$

five squared
five to the second power

$$7^3$$

seven cubed
seven to the third power

$$a^2 + b^3 = c^4$$

A squared plus b cubed equals c to the fourth power.

$$\sqrt[n]{x}$$

the nth root of x

$$\sqrt{7}$$

the square root of seven
the second root of seven
root seven
radical seven

$$\sqrt[3]{25}$$

the cube root of twenty-five
the third root of twenty-five

$$\sqrt[5]{432}$$

the fifth root of four hundred thirty-two

Multiplication / Times tables 九九

Please tell me the four times table.

Let’s begin our multiplication table of four.

The four times table starts; “Four times zero is zero, four times one is one, …”

1 Times Table

0 X 1 = 0Zero times one is zero.
1 X 1 = 1One times one is one.
2 X 1 = 2Two times one is two.
3 X 1 = 3Three times one is three.
4 X 1 = 4Four times one is four.
5 X 1 = 5Five times one is five.
6 X 1 = 6Six times one is six.
7 X 1 = 7Seven times one is seven.
8 X 1 = 8Eight times one is eight.
9 X 1 = 9Nine times one is nine.
10 X 1 = 10Ten times one is ten.
11 X 1 = 11Eleven times one is eleven.
12 X 1 = 12Twelve times one is twelve.

2 Times Table

0 X 2 = 2Zero times two is zero.
1 X 2 = 2One times two is two.
2 X 2 = 4Two times two is four.
3 X 2 = 6Three times two is six.
4 X 2 = 8Four times two is eight.
5 X 2 = 10Five times two is ten.
6 X 2 = 12Six times two is twelve.
7 X 2 = 14Seven times two is forteen.
8 X 2 = 16Eight times two is sixteen.
9 X 2 = 18Nine times two is eighteen.
10 X 2 = 20Ten times two is twenty.
11 X 2 = 22Eleven times two is twenty-two.
12 X 2 = 24Twelve times two is twenty-four.

3 Times Table

0 X 3 = 0Zero times three is zero.
1 X 3 = 3One times three is three.
2 X 3 = 6Two times three is six.
3 X 3 = 9Three times three is nine.
4 X 3 = 12Four times three is twelve.
5 X 3 = 15Five times three is fifteen.
6 X 3 = 18Six times three is eighteen.
7 X 3 = 21Seven times three is twenty-one.
8 X 3 = 24Eight times three is twenty-four.
9 X 3 = 27Nine times three is twenty-seven.
10 X 3 = 30Ten times three is thirty.
11 X 3 = 33Eleven times three is thirty-three.
12 X 3 = 36Twelve times three is thirty-six.

4 Times Table

0 X 4 = 0Zero times four is zero.
1 X 4 = 4One times four is four.
2 X 4 = 8Two times four is eight.
3 X 4 = 12Three times four is twelve.
4 X 4 = 16Four times four is sixteen.
5 X 4 = 20Five times four is twenty.
6 X 4 = 24Six times four is twenty-four.
7 X 4 = 28Seven times four is twenty-eight.
8 X 4 = 32Eight times four is thirty-two.
9 X 4 = 36Nine times four is thirty-six.
10 X 4 = 40Ten times four is forty.
11 X 4 = 44Eleven times four is forty-four.
12 X 4 = 48Twelve times four is forty-eight.

5 Times Table

0 X 5 = 0Zero times five is zero.
1 X 4 = 5One times five is five.
2 X 5 = 10Two times five is ten.
3 X 5 = 15Three times five is fifteen.
4 X 5 = 20Four times five is twenty.
5 X 5 = 25Five times five is twenty-five.
6 X 5 = 30Six times five is thirty.
7 X 5 = 35Seven times five is thirty-five.
8 X 5 = 40Eight times five is forty.
9 X 5 = 45Nine times five is forty-five.
10 X 5 = 50Ten times five is fifty.
11 X 5 = 55Eleven times five is fifty-five.
12 X 5 = 60Twelve times five is sixty.

6 Times Table

0 X 6 = 0Zero times six is zero.
1 X 6 = 6One times six is six.
2 X 6 = 12Two times six is twelve.
3 X 6 = 18Three times six is eighteen.
4 X 6 = 24Four times six is twenty-four.
5 X 6 = 30Five times six is thirty.
6 X 6 = 36Six times six is thirty-six.
7 X 6 = 42Seven times six is forty-two.
8 X 6 = 48Eight times six is forty-eight.
9 X 6 = 54Nine times six is fifty-four.
10 X 6 = 60Ten times six is sixty.
11 X 6 = 66Eleven times six is sixty-six.
12 X 6 = 72Twelve times six is seventy-two.

7 Times Table

0 X 7 = 0Zero times seven is zero.
1 X 7 = 7One times seven is seven.
2 X 7 = 14Two times seven is forteen.
3 X 7 = 21Three times seven is twenty-one.
4 X 7 = 28Four times seven is twenty-eight.
5 X 7 = 35Five times seven is thirty-five.
6 X 7 = 42Six times seven is forty-two.
7 X 7 = 49Seven times seven is forty-nine.
8 X 7 = 56Eight times seven is fifty-six.
9 X 7 = 63Nine times seven is sixty-three.
10 X 7 = 70Ten times seven is seventy.
11 X 7 = 77Eleven times seven is seventy-seven.
12 X 7 = 84Twelve times seven is eighty-four.

8 Times Table

0 X 8 = 0Zero times eight is zero.
1 X 8 = 8One times eight is eight.
2 X 8 = 16Two times eight is sixteen.
3 X 8 = 24Three times eight is twenty-four.
4 X 8 = 32Four times eight is thirty-two.
5 X 8 = 40Five times eight is forty.
6 X 8 = 48Six times eight is forty-eight.
7 X 8 = 56Seven times eight is fifty-six.
8 X 8 = 64Eight times eight is sixty-four.
9 X 8 = 72Nine times eight is seventy-two.
10 X 8 = 80Ten times eight is eighty.
11 X 8 = 88Eleven times eight is eighty-eight.
12 X 8 = 96Twelve times eight is ninety-six.

9 Times Table

0 X 9 = 0Zero times nine is zero.
1 X 9 = 9One times nine is nine.
2 X 9 = 18Two times nine is eighteen.
3 X 9 = 27Three times nine is twenty-seven.
4 X 9 = 36Four times nine is thirty-six.
5 X 9 = 45Five times nine is forty-five.
6 X 9 = 54Six times nine is fifty-four.
7 X 9 = 63Seven times nine is sixty-three.
8 X 9 = 72Eight times nine is seventy-two.
9 X 9 = 81Nine times nine is eighty-one.
10 X 9 = 90Ten times nine is ninety.
11 X 9 = 99Eleven times nine is ninety-nine.
12 X 9 = 108Twelve times nine is one hundred oh eight.

10 Times Table

0 X 10 = 0Zero times ten is zero.
1 X 10 = 10One times ten is ten.
2 X 10 = 20Two times ten is twenty.
3 X 10 = 30Three times ten is thirty.
4 X 10 = 40Four times ten is forty.
5 X 10 = 50Five times ten is fifty.
6 X 10 = 60Six times ten is sixty.
7 X 10 = 70Seven times ten is seventy.
8 X 10 = 80Eight times ten is eighty.
9 X 10 = 90Nine times ten is ninety.
10 X 10 = 100Ten times ten is one hundred.
11 X 10 = 110Eleven times ten is one hundred and ten.
12 X 10= 120Twelve times ten is one hundred and twenty.

11 Times Table

0 X 11 = 0Zero times eleven is zero.
1 X 11 = 11One times eleven is eleven.
2 X 11 = 22Two times eleven is twenty-two.
3 X 11 = 33Three times eleven is thirty-three.
4 X 11 = 44Four times eleven is forty-four.
5 X 11 = 55Five times eleven is fifty-five.
6 X 11 = 66Six times eleven is sixty-six.
7 X 11 = 77Seven times eleven is seventy-seven.
8 X 11 = 88Eight times eleven is eighty-eight.
9 X 11 = 99Nine times eleven is ninety-nine.
10 X 11 = 110Ten times eleven is one hundred and ten.
11 X 11 = 121Eleven times eleven is one hundred and twenty-one.
12 X 11= 132Twelve times eleven is one hundred and thirty-two.

12 Times Table

0 X 12 = 0Zero times twelve is zero.
1 X 12 = 12One times twelve is twelve.
2 X 12 = 24Two times twelve is twenty-four.
3 X 12 = 36Three times twelve is thirty-six.
4 X 12 = 48Four times twelve is forty-eight.
5 X 12 = 60Five times twelve is sixty.
6 X 12 = 72Six times twelve is seventy-two.
7 X 12 = 84Seven times twelve is eighty-four.
8 X 12 = 96Eight times twelve is ninety-six.
9 X 12 = 108Nine times twelve is one hundred oh eight.
10 X 12 = 120Ten times twelve is one hundred and twenty.
11 X 12 = 132Eleven times twelve is one hundred and thirty-two.
12 X 12= 144Twelve times twelve is one hundred and forty-four.

Find the area of this figure. この図形の面積を求めよ

πr2  円の面積

The area of a circle is equal to pi times the radius squared.

円の面積は、π×半径の2乗

b × h  平行四辺形の面積

The area of a parallelogram is equal to its base (b) times the height (h).

平行四辺形の面積は、底辺×高さ

(b × h)÷2  三角形の面積

The area of a triangle is equal to its base (b) times the height (h) divided by two.

三角形の面積は、底辺×高さ÷2

{(a+b)×h}÷2  台形の面積

The area of a trapezoid is equal to the sum of both bases (a+b) times the height (h) divided by two.

台形の面積は、(上底+下底)×高さ÷2

Find the volume of this box. この箱の体積を求めよ

l3  立方体の体積

The volume of a cube is equal to the length of one of its sides cubed.

立方体の体積は、一辺の長さの3乗

(b×l×h)÷3  四角錐の体積

The volume of a pyramid is equal to the area of its base (b times l) times the height (h) divided by three.

四角錐の体積は、幅×奥行×高さ÷3

(4×π×r3)÷3  球の体積

The volume of a sphere is equal to four times pi times the radius cubed divided by three.

球の体積は、4×π×半径の3乗÷3

mathematical expressions  数式

4x + 2x = 6x

Four x plus two x equals six x.

y = – 6x2 + 8x + 3

Y equals  negative/minus six x squared plus eight x plus three.

(a + b)2 = a2 + 2ab + b2

[The quantity] A plus b squared equals a squared plus two (times) a (times) b plus b squared.

(a+b)(a-b)=a2 – b2

[The quantity] A plus b times [the quantity] a minus b equals a squared minus b squared.

y = (4x2 – 12x + 9)÷(2x – 3)

Y equals [the quantity] four x squared minus twelve x plus 9 divided by [the quantity] two x minus three.

a2 + b2 ≧ 2(a – b – 1)

A squared plus b squared is greater than or equal to two times [the quantity] a minus b minus one.

$$ \sqrt{4} + \sqrt{16} = 6$$

The square root of four plus the square root of sixteen equals six.

$$a^2 + b^3 = \sqrt[3]{c}$$

A squared plus b cubed equals the cube root of c.

$$y = f(x)$$

Y is[equals] a function of x.

3 : 7 = 6 : 14

Three is to seven as six is to fourteen.

$$\sum_{n=0}^\infty a_n$$

Summation from zero to infinity of a sub n.

シグマのn=0から無限のエーエヌ

$$\int_a^b f(x) dx$$

Integral of a function of x with respect to x from x equals a to x equals b.

インテグラルa, bエフエックスディエックス

relational operator 関係演算子

A ≠ B

A is not equal to B.
A does not equal B.
AはBと等しくない

A > B

A is greater than B.
AはBより大きい

A < B

A is less than B.
AはBより小さい

A ≧ B

A is greater than or equal to B.
AはBより大きいか等しい

A ≦ B

A is less than or equal to B.
AはBより小さいか等しい

\begin{eqnarray}
30未満 = \begin{cases}
under\,\,30 \\
below\,\,30 \\
less\,\,than\,\,30 \\
\end{cases}
\end{eqnarray}
\begin{eqnarray}
30以下 = \begin{cases}
not\,\,more\,\,than\,\,30 \\
30\,\,and\,\,(or)\,\,less \\
30\,\,and\,\,(or)\,\,under \\
30\,\,and\,\,(or)\,\,below \\
\end{cases}
\end{eqnarray}
\begin{eqnarray}
30より多く = \begin{cases}
more\,\,than\,\,30 \\
over\,\,30 \\
above\,\,30 \\
\end{cases}
\end{eqnarray}
\begin{eqnarray}
30以上 = \begin{cases}
not\,\,less\,\,than\,\,30 \\
30\,\,and\,\,(or)\,\,more \\
30\,\,and\,\,(or)\,\,above \\
30\,\,and\,\,(or)\,\,over \\
\end{cases}
\end{eqnarray}

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