Calculations 計算

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

2 Times Table

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

3 Times Table

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

4 Times Table

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

5 Times Table

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

6 Times Table

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

7 Times Table

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

8 Times Table

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

9 Times Table

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

10 Times Table

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

11 Times Table

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

12 Times Table

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