## Skip counting by 2’s

Jenna is in front of a long flight of stairs. She decides to climb them by leaving one stair in between.

She leaves out the first step and steps on the second step and leaves out the third step and steps on the fourth one and so on.

So the number of steps she hops on are** 2, 4, 6, ……..**

We can see that **2** is added each time. These are the multiples of **2**.

**The values obtained by adding by 2 are called the multiples of 2.**

The consecutive multiples of **2** can be written by leaving a number in between.

Example: Write **2**, skip **2**, write **4**, skip **5**, write **6,** and so on.

## Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 …

## Multiples of 2 and even numbers

**The multiples of 2 are also called even numbers.**

The even numbers are the numbers that are divisible by **2**. The multiples of **2** are also divisible by **2** and hence all the multiples of **2** are also even numbers.

### How to identify the multiples of 2?

All the multiples of 2 are even numbers.

### How do we identify even numbers?

Even numbers are the number that ends with the digits **0, 2, 4, 6,** and **8**.

All the numbers, no matter how large they are, that end with the digits **0, 2, 4, 6, 8 **are even numbers and are also the multiples of **2**.

**Example:**

Identify the multiples of 2 from the following numbers.

To identify the multiples of two, start by observing the last digit of each of the numbers.

*The last digit of 360 is 0*

*The last digit of*

**568**is**8***The last digit of*

**22**is**2***The last digit of*

**7800**is**0**and so on.List out all the numbers that have **0, 2, 4, 6,** and **8** as their last digits or one’s digit. These are the numbers that are the multiples of** 2**.

**Here the multiples of 2 are 360, 568, 22, 7800**

## The nth multiple of 2.

**We know that**

- The first multiple of
**2**is**2** - The second multiple of
**2**is**2×2 = 4** - The third multiple of
**2**is**3×2 = 6** - The tenth multiple of
**2**is**10×2 = 20** - The
**nth**multiple of**2**is**2n**.

That is any number of multiples of **2** can be found by multiplying the term by **2**.

Example:

**Find the 20th multiple of 2.**

The **20th** multiple of **2** is **20×2 = 40**

### “Multiples” Challenge!

What is the position of the value **512** in the sequence of the multiples of **2**?

**Answer:**

We could find the value of any number of multiples of **2** by multiplying the number by **2**.

When the value is given and we need to find the position of the value in the multiples of **2**, we perform the opposite of the multiplication operation i.e divide.

To find the position of the number **512**, divide the number by **2**.

**512 ÷ 2 = 256**

**So the number 512 is the 256th multiple of 2.**

## Check what I know?

Write down the first 15 multiples of 2.

1×2=2

2×2=4

3×2=6

4×2=8

5×2=10

6×2=12

7×2=14

8×2=16

9×2=18

10×2=20

11×2=22

12×2=24

13×2=26

14×2=28

15×2=30

The first 15 multiples of 2 can be found by multiplying the numbers 1 to 15 by 2.

**The first 15 multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28,30**

**Find the two nearest multiples of 2 to the number 95.**

**The nearest multiples of 2 are 94 and 96.**

All the even numbers are multiples of 2. The even numbers and odd numbers occur alternatively. The number 95 is an odd number. Hence the numbers before and after 95 are even numbers and are also the multiple of 2.

**Find the difference between the 15th and the 9th multiples of 2.**

**The difference between the 15th multiple and the 9th multiple of 2 is 30-18=12.**

The multiples of 2 are found by using 2n. That is 15 th multiple of 2 is 2×15=30

The 9 th multiple of 2 is 2×9=18

**Max has pulled out all the socks from his laundry in a basket. He is trying to put the socks as pairs in his sock rack. If he has counted 58 socks in the** **basket, how many pair would he make from it?**

**Hence the number of pairs is 58÷2=29.**

A pair is two in number. A pair of socks have 2 pieces. Here Max has 58 socks in

the basket.

If he finds the pair of all the socks, that would make groups of 2.

**Find the number of multiples of 2 till the number 108.**

**There are 56 multiples including 108.**

The number of multiples of **2** till any number is given by **2n**.

Here the value of **2n** is **108**.

Then the value of n is **108 ÷ 2 = 56**.

Note that when we are asked for the multiples between two given numbers, the

numbers at the beginning and the end should not be included.

**Nina is making a necklace of beads. She has red beads and green beads. If****she uses one red bead and one green bead alternatively, what will be the****color of the 16th bead if she started with a red bead?**

We need the bead in the 16th place. As **16** is a multiple of **2**, the color of the

bead in the **16th** place will be the green bead.

Nina started the necklace with a red bead. I will be the first bead.

Since the red and green beads are alternated, the places that the red beads will

take are** 1,3,5,7,…….**

The green bead is the second in the string and the places that green beads will

take are **2, 4, 6, 8…..**

**A school has 1876 students. If there are an equal number of boys and girls****in the school. Find the number of boys.**

**There are 938 boys in the school.**

Given that the school has 1876 students. There are equal number of boys and

girls. This means half of the total students are boys.

The number of boys is 1876 divided by 2= 938

**In the given table, color or circle the multiples of 2 to bring out the message****inside.**

78 | 951 | 567 | 125 | 204 | 984 | 5027 | 641 | 845 | 687 |

13 | 101 | 789 | 258 | 535 | 123 | 350 | 347 | 9821 | 4867 |

225 | 441 | 679 | 364 | 169 | 35 | 42 | 231 | 1125 | 8001 |

857 | 287 | 483 | 951 | 853 | 751 | 7300 | 485 | 685 | 6401 |

179 | 189 | 297 | 287 | 345 | 365 | 410 | 75 | 9401 | 8527 |

385 | 511 | 633 | 111 | 61 | 1034 | 9651 | 547 | 87 | 233 |

487 | 909 | 199 | 667 | 118 | 953 | 39 | 957 | 159 | 451 |

2207 | 4627 | 59 | 8542 | 267 | 359 | 101 | 547 | 765 | 285 |

79 | 263 | 333 | 12 | 277 | 593 | 2607 | 1205 | 521 | 23 |

953 | 4511 | 445 | 8 | 288 | 100 | 221 | 6470 | 401 | 19 |

78 | 951 | 567 | 125 | 204 | 984 | 5027 | 641 | 845 | 687 |

13 | 101 | 789 | 258 | 535 | 123 | 350 | 347 | 9821 | 4867 |

225 | 441 | 679 | 364 | 169 | 35 | 42 | 231 | 1125 | 8001 |

857 | 287 | 483 | 951 | 853 | 751 | 7300 | 485 | 685 | 6401 |

179 | 189 | 297 | 287 | 345 | 365 | 410 | 75 | 9401 | 8527 |

385 | 511 | 633 | 111 | 61 | 1034 | 9651 | 547 | 87 | 233 |

487 | 909 | 199 | 667 | 118 | 953 | 39 | 957 | 159 | 451 |

2207 | 4627 | 59 | 8542 | 267 | 359 | 101 | 547 | 765 | 285 |

79 | 263 | 333 | 12 | 277 | 593 | 2607 | 1205 | 521 | 23 |

953 | 4511 | 445 | 8 | 288 | 100 | 221 | 6470 | 401 | 19 |

## Frequently Asked Questions

The even numbers are the numbers divisible by 2. For a number to be divisible by 2 it should be a multiple of 2. Hence all the even numbers are multiples of 2 and all multiples of 2 are even numbers.

The significance of the number 2 is it helps in finding the value of items in pairs. Like a pair of socks, a pair of gloves etc.

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