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## Addition of Numbers Using A Number Line

The addition on the number line helps us to visually perform the addition operation on small numbers. A number line is a visual representation of numbers on a straight line where the value of the numbers increases as we move from left to right. Arithmetic operations like addition, subtraction, multiplication, and division can be performed on a number line. In this article, you will learn about number lines and their concepts. How to add and subtract a number line will be explained in this article, and some solved examples and practice problems will also be shown for your help.

Number Line

### Addition of Numbers Using A Number Line

Addition on number line is as simple as counting positive numbers by moving towards the right-hand side of a number line. It helps us to visually understand the addition operation using small numbers.

By utilising small numbers, the sum on the number line makes the addition operation easier to understand visually. Moving to the right makes it simple to count positive numbers.

• So to add the negative number, move to the left.

• To add the positive number, move to the right.

### Addition of a Positive Number to a Positive Number

The addition of a positive number to a positive number means that both numbers will be positive. Here we will mainly look at adding a positive number to a positive number. Let’s understand it through an example:

Solution: Let us look into the steps below to understand addition on a number line.

Step 1: Consider the first number (1) as the starting point on the number line. To add 1 + 2, mark 1 on the number line.

Step 2: Now, from the first number, jump by the number of units equivalent to the second number towards the right. This is because the values on a number increase as we move towards the right-hand side. In this case, we are adding 1 + 2. Therefore, we will move 2 steps to the right. This will bring us to number 3. So, 1 + 2 = 3

### Addition of a Negative Number to a Positive Number

Here we will mainly look at the addition of a negative number to a positive number:

To add a negative number to a positive number, we always move to the left on the number line. Let us take an example to understand this.

Ans: Here, we take 3 as the starting number and move 4 units towards the left on the number line, which gives the result as -1.

Addition of a Positive Number to a Negative Number

### Addition of a Positive Number to a Negative Number

We always move to the right on the number line to add a positive number to a negative number. Let us take an example to understand this.

Example: Add -6 + (3) = -3

Ans: Here, we take -6 as the starting number and move 3 units towards the right on the number line, which gives the result as –3.

Addition of a Positive Number to a Negative Number

### Addition of a Negative Number to a Negative Number

To add a negative number to a negative number, we always move to the left on the number line. Let us take an example to understand this.

Example: Add -6 + (-3) = -9

Ans: Here, we take -6 as the starting number and move 3 units towards the left on the number line which gives the result as –9.

Addition of a Negative Number to a Negative Number

### Solved Examples

Here the addition of numbers using number line-related examples are described, which are as follows:

Q 1. Addition (-4) with 3.

Ans: In this case, we start with -4 and move 3 units to the right on the number line, yielding the result -1.

Use an addition of numbers using the number line method,

Addition of -4 with 3 on Number Line

Q 2. Addition 4 with 3.

Ans: In this case, we start with 4 and move 3 units to the right on the number line, yielding the result 7.

Use an addition of numbers using the number line method,

Addition of 4 with 3 on Number Line

### Practice Problems

Solve these additions by using the number line:

Q 1. \$4+(-5)=\$

Q 2. \$-2+2=\$

Q 3. \$-3+7=\$

Q 4. \$2+(-5)=\$

1. -1

2. 0

3. 4

4. -3

### Benefits of Using a Number Line

In this section, we will talk about the importance of using a number line in daily life. The benefits of using a number line are:

• It helps teach children the concept of place value by comparing digits and ordering them according to their value;

• It helps children count by arranging numbers from least to greatest;

• It can be used for mental math, such as adding and subtracting;

• It can help students understand how fractions work by representing them with parts of a whole.

### Summary

The number line is a simple and easy way to show the relationship between numbers. It is used in mathematics, science, and finance. In daily life, number lines teach children to read numbers. A number line is a mathematical tool that can help people understand how numbers work. A number line is a straight line in mathematics with numbers spread at equal intervals or segments along its length. The article on number lines explains how a number line can be stretched indefinitely in any direction and how it is typically depicted horizontally.

## Adding on a Number Line

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### Adding on a Number Line

Number lines are a helpful tool when you need to add multiple numbers. But, what is Number Line Addition? An addition number line is a straight line with numbers spaced apart equally. What is Addition on a Number Line? When we use a number line for addition, that means we are modeling addition on a number line. Using a number line model for addition, helps us keep track of what we are adding easily. In the next section you will learn how to use a number line for addition.

### How to Show Addition on a Number Line

Showing addition on a number line is very simple if you follow the steps on how to add numbers on the number line. Here are the steps on how to do addition with number line:

Step # What to do
1 Find the starting number or the amount we have on the number line.
2 Count the number we are adding, moving to the right.
3 Write the number you land on in the total, this is the answer.

If you’re still wondering how to use a number line for addition, the next section will show how to add 2 numbers using a number line.

### Number Line Addition – Example

Here, we need to add four and five using addition using the number line. Let’s use the steps on how to do addition with number line:

• Step 1: Find the starting number or the amount we have on the number line
• Step 2: Count the number we are adding, moving to the right
• Step 3: Write the number you land on in the total, this is the answer

### Number Line Addition – Summary

How do you do addition on a number line? Remember, showing addition on a number line is very simple if you follow the steps on how to add numbers on the number line:

• Step 1: Find the starting number or the amount we have on the number line.
• Step 2: Count the number we are adding, moving to the RIGHT.
• Step 3: Write the number you land on in the total, this is the answer.

These steps tell you how to represent addition on a number line, or how to use a number line for addition. Have you practiced yet? On this website you can practice adding on a number line and find number line addition worksheets along with other activities, and exercises.

### Using Number Lines to Add exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Using Number Lines to Add.

• #### How many bananas do they have altogether?

Hints

Start at 2 and count 5 jumps on the number line. The number you end on is the answer.

Solution

Mr. Squeaks and Imani have seven bananas!

• Mr. Squeaks had two bananas, so we find 2 on the number line.
• We then count 5 jumps forwards because Imani brought five bananas.
• We will end on 7, so the answer is seven bananas.
• You could have also found 5 on the number line and counted 2 jumps forwards.
• We would still end on 7 this way too.
• #### How many strawberries do they have?

Hints

Remember, you are trying to solve 9 + 6.

Find 9 on the number line and count 6 jumps forwards.

Solution

Mr. Squeaks had 9 strawberries and Imani brought 6 more, so we are solving 9 + 6.

• First, find 9 on the number line.
• Next, jump forward 6 spaces, this time highlighting each jump in yellow.
• We end on 15 so that is our answer. Highlight it in green.
• Mr. Squeaks and Imani had fifteen strawberries altogether.
• Also, you can also start at 6 and count 9 jumps forward.
• You would still land on 15.
• However, it is often easier to start with the larger number.
• #### Can you add the fruit to find the total number of ingredients in each smoothie?

Hints

How many pieces of each fruit are there? For example, here we would be adding 2 + 2.

You can then use a number line to find the total like this.

2 + 2 = 4

Solution

This number line shows us how to find the total amount of fruit in the mango and peach smoothie.

• We would start by finding 7 on the number line as this is the larger number.
• We could then count 2 jumps forwards.
• We land on 9.
• So, there are 9 pieces of fruit in this smoothie.
• We could have also started at 2 and counted 7 jumps forward. We would still land on 9.

For the blueberry and banana smoothie

• We would start by finding 13 on the number line as this is the larger number.
• We could then count 5 jumps forward.
• We land on 18.
• So, there are 18 pieces of fruit in this smoothie.
• We could have also started at 5 and counted 13 jumps forward. We would still land on 18.

For the pineapple and cherry smoothie

• We would start by finding 11 on the number line as this is the larger number.
• We could then count 2 jumps forward.
• We land on 13.
• So, there are 13 pieces of fruit in this smoothie.
• We could have also started at 2 and counted 11 jumps forwards. We would still land on 13.

For the strawberry and raspberry smoothie

• We would start by finding 9 on the number line as this is the larger number.
• We could then count 5 jumps forward.
• We land on 14.
• So, there are 14 pieces of fruit in this smoothie.
• We could have also started at 5 and counted 9 jumps forwards. We would still land on 14.
• #### Can you help Mr. Squeaks and Imani with their recipes?

Hints

If you were adding 5 + 4, you would find the number 5 and then count 4 jumps forward to reach the answer, 9.

Start at the larger number and count on the smaller number.

Solution

• For smoothie number one, we were adding 15 + 3 to find the total ingredients.
• First we find 15 on the number line.
• We then count 3 jumps forwards.
• We will land on 18, so that is our answer.

___________________________________________________

• To find the total ingredients for smoothie number two, we needed to add 7 + 6 to get a total of 13.
• To find the total ingredients for smoothie number three, we needed to add 8 + 9 to get a total of 17.
• To find the total ingredients for smoothie number four, we needed to add 12 + 7 to get a total of 19.
• To find the total ingredients for smoothie number five, we needed to add 11 + 9 to get a total of 20.

_______________________________________________________

Remember:

• It doesn’t matter which number we start with when we are adding, but it is often a good idea to start with the larger number so you do fewer jumps.
• #### How many berries do they have?

Hints

How many blueberries did Mr. Squeaks have? This is your starting number. We are starting with this number because it is the biggest number.

How many raspberries did Imani bring? This is the number you are adding on.

Use the jumps on the number line to help you to find the total number of berries.

Solution

They have eleven berries altogether.

• Mr. Squeaks had 8 blueberries.
• Imani brought 3 raspberries.
• Using a number line to help us we start at 8 and count on 3 more.
• We end on 11, so that is our answer.
• This problem could also be solved by starting at 3 and counting 8 jumps forwards.
• We would still land on 11 if we did it this way.
• #### Can you help Mr.

Squeaks with his challenge?

Hints

Can you use your knowledge of doubles? For example, what pair of numbers do you know that equal 10?

Solution

Here are the different ways to make 10, 15 and 20 from this problem.

For example:

• To find the answer for 12 + 8:
• We could find 12 on the number line.
• We could then jump forward 8 spaces.
• We will land on 20, so that is our answer.

Can you think of any other ways you could make 10, 15 or 20?

More videos for the topic

Number Pairs to 10

Finding the Unknown Number (in Addition) — Let’s Practice!

Make a Number Line to Add — Let’s Practice!

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## Number series

﻿

Number series

﻿

1. Number series.
2. Properties of convergent series.

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### 1.

Number series.

The number series is the sum of an infinite sequence of numbers u1, u2, u3, …un

The numbers u1 , u2 , u3 , … un, … are called members of the series, and the member un is the common or nth member of the series.
If a series has a limit of the sequence of its partial sums, then it is called convergent.

lim Sn = S
n → ∞

The number S is called the sum of the series. i.e.:

If there is no finite limit of the sequence of partial sums, then the series is said to be divergent.

The number series is usually given as a function of the natural argument un = f(n) where n = 1,2,3… .

Example: f(n) = (n+2) / n² is the common term of the series.

Example of a number series with a common term f(n) = (n+2) / n²

#### Tutor: Vasiliev Alexey Aleksandrovich

Subjects: mathematics, physics, computer science, economics, programming.

2000 rubles / 120 min — preparation for the USE and GIA for schoolchildren. 3000 rub / 120 min — individually (basic level). 2000 rub / 120 min — students.

### 2. Properties of convergent series.

1. If the series a1 + a2 + a3 + … + an + … converges and has the sum S, then the series ƛa1 + ƛa2 + ƛa3 + … + ƛan + … also converges and has the sum ƛS.
2. If the series a1 + a2 + a3 + … + an + … and b1 + b2 + b3 + … + bn + … converge and their sums are equal to S1 and S2, then the series obtained term by term addition, i.e. (a1 + b1) + (a2 + b2) + (a3 + b3) + … + (an + bn) + … also converges and its sum is S1 + S2.
3. The convergence of the series will not change if a finite number of terms are added or dropped.

Example.

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## Lecture No. 11. Number series.

### Question 11.1. Endless number series. Convergence. The sum of the number series.

Definition
11.1.
Endless
number series is called formal
infinite sum of numbers

End
definitions.

Numerical
series can also be written in abbreviated
form

.
Numbers

are called members of the series. Value

called n th
a member of the series and is a function
natural parameter

.

Definition
11.2.
If all
terms of the series have the same sign, then
series is called constant. IN
otherwise the row is called
alternating. In particular, if
the signs of the members of the series alternate, then the series
is called sign-ordered.

End
definitions.

Definition
11.3.
Amount
first n
members of the series is called n th
partial amount

.

End
definitions.

Definition 11.3. Numeric
a series is called convergent if
there is a finite limit of its partial
amounts. This limit is called
the sum of the numbers. If not exists
finite limit of partial sums, then
the series is called divergent.

End
definitions.

If

is the sum of a convergent series, then we will
write

.

Example 11.1. Endless
geometric progression

Calculate
n
partial amount

,
then we get

So
way

— the condition of convergence of the geometric
progression,

— the condition for the divergence of the geometric
progressions.

End of example.

Example
11.2.
Calculate
series sum

.

Yes
How

,
then

.

from here

.

End
example.

### Question 11.2. Properties of convergent series.

Feature
11.1.
At
adding two convergent series, one gets
convergent series whose sum is equal to
the sum of the sums of these series.

.

Proof.
Denote n -e
partial sums of these series in terms of

respectively. Then

and passing to the limit, we get

.

End
proof.

Note
11.1.
At
turn out to be both convergent and
divergent row. If the members of the series
are of constant sign and of the same sign, then the sum
two divergent series there is a divergent
row.

Property
11.2.
At
subtracting two convergent series
a convergent series is obtained, the sum
which is equal to the difference between the sums of these series

.

Proof.
Denote n -e
partial sums of these series in terms of

respectively. Then

and, going to the limit, we get

.

End
proof.

remark
11.2.
At
subtracting two divergent constants
rows of the same character can turn out
both convergent and divergent series.

Property
11.3.
At
multiplying a convergent series by a number
a convergent series is obtained, the sum
which is equal to the product of the sum
of the original row to this number

.

Proof.
Denote n -e
partial sums of these series in terms of

And

respectively. Then

and passing to the limit, we get

.

End
proof.

Note
11.3.
At
multiplying a divergent series by a number
again a divergent series is obtained.

Property
11.4.
If
terms, then its convergence is not violated,
and the sum will decrease by the sum of the first k
members.

Proof.
The partial sums of these series are related
ratio

.

Then
passing to the limit, we get

,

or

.

End
proof.

Note
11.4.
From
proof of property 11.4 follows,
that if the series diverges, then after
dropping the first k
members of the series, the series will diverge.

Property
11.5.
(Required
convergence sign). If the series converges,
then its n th
term tends to zero with growth n
to infinity, that is

at

.

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