LOCATING NUMBERS ON A NUMBER LINE

Comparing Numbers Using Number Line

Problem 1 :

Locate the numbers 3 and 6 on a number line and compare them.

Solution :

Let us locate the two numbers 3 and 6 on a number line and mark them.

Here, 6 comes to the right of 3.

Therefore 6 is greater than 3.

And 3 comes to the left of 6.

Therefore 3 is smaller than 6.

Problem 2 :

Locate the numbers 6 and 9 on a number line and compare them.

Solution :

Let us locate the two whole numbers 6 and 9 on a number line and mark them.

Here, 9 comes to the right of 6.

Therefore 9 is greater than 6.

And 6 comes to the left of 9.

Therefore 6 is smaller than 9.

Ordering Numbers Using Number Line

Problem 3 :

Locate the numbers 12, 5, 9, 6, 1, 3 on a number line and order them from least to greatest.

Solution :

Let us locate the numbers 12, 5, 9, 6, 1, 3 on a number line and mark them.

From the above number line, write the numbers from left to right to list them in order from least to greatest.

Thus, we get

1, 3, 5, 6, 9, 12

Solving World Problems Using Number Line

Problem 4 :

In 2010, Sacramento, California, received 23 inches in annual precipitation. In 2011, the city received 17 inches in annual precipitation. In which year was there more precipitation ?

Solution :

Locate the two numbers 23 and 17 on a number line and mark them.

23 is to the right of 17 on the number line.

This means that 23 is greater than 17.

We can write the above situation in terms of inequality as 23 > 17.

17 is to the left of 23 on the number line.

This means that 17 is less than 23.

We can write the above situation in terms of inequality as 17 < 23.

There was more precipitation in 2010.

Problem 5 :

John recorded the following golf scores during his first week at a golf academy. In golf, a lower score beats a higher score.

Graph John’s scores on the number line, and then list the numbers in order from least to greatest.

Solution :

Step 1 :

Graph the scores on the number line.

Step 2 :

Read from left to right to list the scores in order from least to greatest.

The scores listed from least to greatest are

0, 1, 3, 5, 6, 9, 12

Plot each set of fractions on a number line:

-3/5, 1/5, 7/5, 18/5

-5/2, -4/3, 1/6, 2/3, 7/2

Find the fractions represented by the points A, B, C and D on the number lines :

Problem 6 :

Solution :

In between 0 and 1, we have 3 equal spaces. Each will be 1/3

• Position of B = 1/3
• Position of D = 2/3
• Position of C = 4/3
• Position of A = 5/3

Problem 7 :

Solution :

In between 0 and 1, we have 6 equal spaces. Each will be 1/6

• Position of D = 1/6
• Position of B = 3/6 or 1/2
• Position of C = 1 1/6 or 7/6
• Position of A = 1  4/6 or 10/6

Problem 8 :

Solution :

In between 0 and 1, we have 4 equal spaces. Each will be 1/4

• Position of A = 2/4 or 1/2
• Position of B = 5/4 or 1  1/4
• Position of D = 7/4 or 1  3/4
• Position of C = 9/4 or 1  5/4

Problem 9 :

Solution :

In between 0 and 1, we have 7 equal spaces. Each will be 1/7

• Position of A = 2/7
• Position of C = 6/7
• Position of D = 8/7 or 1  1/7
• Position of B = 10/7 or 1  3/7

Problem 10 :

Place each of the following decimals on the number line

If necessary, draw a number line to help answer these  questions :

Problem 11 :

Find the opposite of :

a) 7    b) -3    c) 0    d) 2.8    e) -3.17   f) -0.6731

Solution :

a) Opposite of 7 is -7

b) Opposite of -3 is 3

c)  Opposite of 0 is 0

d) Opposite of 2.8 is -2.8

e)Opposite of -3.17 is 3.7

f) Opposite of -0.6731 is 0.6731

Problem 12 :

Increase:

a) 3 by 5    b) 0 by 4    c) -2 by 3    d) -4 by 4

e) -7 by 3

Solution :

a) 3 + 5 = 8

b) 0 + 4 = 4

c) -2 + 3 = 1

d) -4 + 4 = 0

e) -7 + 3 = -4

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