Positive and Negative Numbers on a Number Line

The Number Line and Ordering

​

Rounding Whole Numbers​

7th Grade Math -Lesson 2

Number Line and Ordering

7th Grade Lesson 2

​A number line can be used to help us arrange numbers in order. Each number corresponds to a unique point on the number line. The zero point of a number line is called the origin. The numbers to the right of the origin are called positive numbers, and they are all greater than zero. Every positive number has an opposite that is an equal distance to the left of the origin. The numbers to the left of the origin are called negative numbers. The negative numbers all have values that are less than zero.

7th Grade | Lesson 2

Number Lines and Ordering

​On the number line above, the tick marks show the location of integers. The set of integers includes all of the counting numbers and their opposites, as well as the number zero.

(. . . , -3, -2, -1, 0, 1, 2, 3, . . .)​

Negative numbers are written with a negative sign. For -3, we say "negative three." ​Positive numbers may be written with or without a positive sign. Both +3 and 3 are positive and equal to each other.

7th Grade | Lesson 2

Number Lines and Ordering

​As we move either right or left, the numbers either increase or decrease depending on their distance from zero. The further right we move, the greater the numbers get. The further left we move the value decreases.

​

When we place a point on a number line to mark the location of a number, we call the point the graph of the number. The associated with the point on the number line is called the coordinate of the point.​ Any group of numbers can be arranged in order from least to greatest.

Fill in the Blanks

Arrange the following numbers in order from least to greatest:

465, 654, -546, 456, 564

7th Grade | Lesson 2

Number Lines and Ordering

​Negative numbers are always less than positive numbers, so -546 is the least number. Since all of the positive numbers have three digits, the number with the least value among these is the one with the digit of least value in the hundreds' place. We have two numbers that begin with 4:

465 and 456

Now we look at the second digits (the tens' place) and see that 456 is the lesser of the two numbers because 5 is less than 6. Therefore, the two positive numbers with the least value are

456 and 465​

7th Grade | Lesson 2

Number Lines and Ordering

​This leaves us with the numbers 654 and 564. Since 5 is less than 6, 564 is less than 654. Therefore, the correct answer is

​

-546, 456, 465, 564, 654​

​

When these numbers are graphed, they will appear on the number line in this order. ​

7th Grade | Lesson 2

Rounding Whole Numbers

​Rounding Whole Numbers

​We often use the rounded form of a number. We round because some numbers, such as multiples of 10 or 100, are easier to say and to think about than others, and in many real-life situations approximations are as useful as more exact values. If the distance to the bus stop is 109 yards, the distance might be stated as about 100 yards.

Rather than draw a number line, we can use a circle and an arrow to help us round numbers. If we round 24,372 to the nearest thousand if three steps, we would do the following:

​

1.) Circle the digit in the place we are rounding and mark the digit to the right.

​

2.) If the digit to the right is less than five, we do not change the circled digit. If the digit to the right is 5 or greater, we increase the circled by one.

​

3.) Change all of the digits to the right to zeros.

7th Grade | Lesson 2

Rounding Whole Numbers

Fill in the Blanks

Round 1,234 to the nearest thousand.

Fill in the Blanks

Round 914,471,752 to the nearest ten thousand.

Fill in the Blanks

Round 83,625,502 to the nearest thousand.

Fill in the Blanks

Round 1,234 to the nearest hundred.

Fill in the Blanks

Round 471,326 to the nearest ten thousand.

Fill in the Blanks

Round 471,326 to the nearest hundred thousand.

Fill in the Blanks

Round 471,326,502 to the nearest ten thousand.

Fill in the Blanks

Arrange the following numbers from least to greatest.

-1, 4, -7, 0, 7, 5

Fill in the Blanks

Arrange the following numbers from least to greatest.

736, -637, 367, 376, 673