Unit 1: Natural numbers.

- How to read and write numbers in English.

When reading a single number, all the number labels should be singular, for example 10,400 is ten thousand four hundred and not ten thousands four hundreds.

Generally, in British English we usually connect large numbers with and, but in American English and is not used. Note that hundreds, thousands and millions are not connected to each other with and, though.

For example:

• 345 is three hundred and forty-five (three hundred forty five in American).
• 59,321 is fifty nine thousand, three hundred and twenty one. (not fifty nine thousand and three hundred…)

You can then describe large numbers with a series of different figures, grouping numbers in hundreds and tens, starting with the biggest number. So we describe hundreds/tens of millions, then thousands, then hundreds:

• 1,345,612 = one million, three hundred and forty five thousand, six hundred and twelve
• 153,200 = one hundred and fifty three thousand, two hundred

Practise reading these numbers out loud:

1. 4,567
2. 367
3. 98,745
4. 120,005
5. 5,000
6. 34,230
7. 873,120
8. 10,043
9. 7,340,200
10. 54,500
11. 24
12. 4,567,090
13. 67,000
14. 92,000,031
15. 1,000,010,000,023

- Comparing numbers.

These are the important signs to know:

=	If two values are equal, we use the "equals" sign	example: 2+2 = 4
≠	If two values are definitely not equal, we use the "not equal to" sign	example: 2+2 ≠ 9
<	But if one value is smaller than another, we can use a "less than" sign.	example: 3 < 5
>	And if one value is bigger than another, we can use a "greater than" sign	example: 9 > 6

- The addition and the subtraction.

Here you can find the basic concepts of the addition and the subtraction. 

Here you have a song that help you with the addition and the subtraction.

And here you have more about the addition and the subtraction.

 - The multiplication.

Multiplying is doing an addition of equal addends. 

In any multiplication the numbers that are multiplied are called factors and the result is called a  product.
 

factor		factor		product
7	×	6	=	42

The multiplication 7 x 6 = 42 is said as "7 times 6 equals 42"

- Powers and the square root.

A power is a product with the same factors.

For example, 5² = 5 × 5 = 25. We call this 5 squared equals 25.

We can raise to other powers. For example, 5³ = 5 × 5 × 5 = 125. We call this 5 cubed equals 125.

In the same way, 5⁴ = 5 × 5 × 5 × 5 = 625. We call this 5 to the fourth power equals 625.

When we raise a number to a power, we multiply the power copies of the number together. When we have power = 1, we get the number itself: 5¹ = 5. We have one copy of the number multiplied.

Remember how ordinal numbers are written:

Multiplying and dividing with powers

If we multiply two numbers both raised to powers together, we add the powers.

For example,

$$3^2\times 3^1 = 3^{2+1};= 3^3 = 27$$.

We are adding up the total number of 3s we will multiply.

In the same way,

$$4^2 \times 4^3 = 4^{2+3} = 4^5 = 1024$$.

It has to be the same number we raise to each power. We cannot multiply $4^2 × 3^3$ in this way.

If we divide two numbers both raised to powers, we subtract the powers.

For example,
$$3^6 / 3^4 = 3^{6-4} = 3^2 = 9.$$

- Exercises.

Here you have a list of activities in Spanish. Enjoy!

Uso adecuado de los paréntesis. Jerarquía de las operaciones. Operaciones con números naturales

Uso adecuado de los paréntesis. Jerarquía de las operaciones (I)

Uso adecuado de los paréntesis. Jerarquía de las operaciones (II)

Uso adecuado de los paréntesis. Jerarquía de las operaciones. Autoevaluación