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7 4 = 1 3 4 9 2 = −4 1 2 8 3 = 2 2 3

[link] shows the number line with all the points plotted.

There is a number line shown that runs from negative 6 to positive 6. From left to right, the numbers marked are negative 5, negative 9/2, negative 4/5, 1/5, 4/5, 8/3, and 3. The number negative 9/2 is halfway between negative 5 and negative 4. The number negative 4/5 is slightly to the right of negative 1. The number 1/5 is slightly to the right of 0. The number 4/5 is slightly to the left of 1. The number 8/3 is between 2 and 3, but a little closer to 3.

Locate and label the following on a number line: 4 , 3 4 , 1 4 , −3 , 6 5 , 5 2 , and 7 3 .

Locate and plot the integers, 4 , −3 .

Locate the proper fraction 3 4 first. The fraction 3 4 is between 0 and 1. Divide the distance between 0 and 1 into four equal parts then, we plot 3 4 . Similarly plot 1 4 .

Now locate the improper fractions 6 5 , 5 2 , 7 3 . It is easier to plot them if we convert them to mixed numbers and then plot them as described above: 6 5 = 1 1 5 , 5 2 = −2 1 2 , 7 3 = 2 1 3 .

There is a number line shown that runs from negative 6 to positive 6. From left to right, the numbers marked are negative 3, negative 5/2, negative 1/4, 3/4, 6/5, 7/3, and 4. The number negative 5/2 is halfway between negative 3 and negative 2. The number negative 1/4 is slightly to the left of 0. The number 3/4 is slightly to the left of 1. The number 6/5 is slightly to the right of 1. The number 7/3 is between 2 and 3, but a little closer to 2.
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Locate and label the following on a number line: −1 , 1 3 , 6 5 , 7 4 , 9 2 , 5 , 8 3 .

There is a number line shown that runs from negative 4 to positive 5. From left to right, the numbers marked are negative 8/3, negative 7/4, negative 1, 1/3, 6/5, 9/2, and 5. The number negative 8/3 is between negative 3 and negative 2 but slightly closer to negative 3. The number negative 7/4 is slightly to the right of negative 2. The number 1/3 is slightly to the right of 0. The number 6/5 is slightly to the right of 1. The number 9/2 is halfway between 4 and 5.

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Locate and label the following on a number line: −2 , 2 3 , 7 5 , 7 4 , 7 2 , 3 , 7 3 .

There is a number line shown that runs from negative 4 to positive 5. From left to right, the numbers marked are negative 7/3, negative 2, negative 7/4, 2/3, 7/5, 3, and 7/2. The number negative 7/3 is between negative 3 and negative 2 but slightly closer to negative 2. The number negative 7/4 is slightly to the right of negative 2. The number 2/3 is slightly to the left of 1. The number 7/5 is between 1 and 2, but closer to 1. The number 7/2 is halfway between 3 and 4.

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In [link] , we’ll use the inequality symbols to order fractions. In previous chapters we used the number line to order numbers.

  • a<b a is less than b ” when a is to the left of b on the number line
  • a>b a is greater than b ” when a is to the right of b on the number line

As we move from left to right on a number line, the values increase.

Order each of the following pairs of numbers, using<or>. It may be helpful to refer [link] .

2 3 ___ −1 −3 1 2 ___ −3 3 4 ___ 1 4 −2 ___ 8 3

There is a number line shown that runs from negative 4 to positive 4. From left to right, the numbers marked are negative 3 and 1/2, negative 3, negative 8/3, negative 2, negative 1, negative 3/4, negative 2/3, and negative 1/4. The number negative 3 and 1/2 is between negative 4 and negative 3 The number negative 8/3 is between negative 3 and negative 2, but closer to negative 3. The numbers negative 3/4, negative 2/3, and negative 1/4 are all between negative 1 and 0.

Be careful when ordering negative numbers.


  1. 2 3 ___ −1 2 3 is to the right of −1 on the number line. 2 3 > −1


  2. −3 1 2 ___ −3 −3 1 2 is to the left of −3 on the number line. −3 1 2 < −3


  3. 3 4 ___ 1 4 3 4 is to the left of 1 4 on the number line. 3 4 < 1 4


  4. −2 ___ 8 3 −2 is to the right of 8 3 on the number line. −2 > 8 3
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Order each of the following pairs of numbers, using<or>:

1 3 ___ −1 −1 1 2 ___ −2 2 3 ___ 1 3 −3 ___ 7 3 .

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Order each of the following pairs of numbers, using<or>:

−1 ___ 2 3 −2 1 4 ___ −2 3 5 ___ 4 5 −4 ___ 10 3 .

< < > <

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Locate decimals on the number line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Locate 0.4 on the number line.

A proper fraction has value less than one. The decimal number 0.4 is equivalent to 4 10 , a proper fraction, so 0.4 is located between 0 and 1. On a number line, divide the interval between 0 and 1 into 10 equal parts. Now label the parts 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0. We write 0 as 0.0 and 1 and 1.0, so that the numbers are consistently in tenths. Finally, mark 0.4 on the number line. See [link] .

There is a number line shown that runs from 0.0 to 1. The only point given is 0.4, which is between 0.3 and 0.5.
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Locate on the number line: 0.6.

There is a number line shown that runs from 0.0 to 1. The only point given is 0.6, which is between 0.5 and 0.7.

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Locate on the number line: 0.9.

There is a number line shown that runs from 0.0 to 1. The only point given is 0.9, which is between 0.8 and 1.

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Locate −0.74 on the number line.

The decimal −0.74 is equivalent to 74 100 , so it is located between 0 and −1 . On a number line, mark off and label the hundredths in the interval between 0 and −1 . See [link] .

There is a number line shown that runs from negative 1.00 to 0.00. The only point given is negative 0.74, which is between negative 0.8 and negative 0.7.
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Locate on the number line: −0.6 .

There is a number line shown that runs from negative 1.00 to 0.00. The only point given is negative 0.6, which is between negative 0.8 and negative 0.4.

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Locate on the number line: −0.7 .

There is a number line shown that runs from negative 1.00 to 0.00. The only point given is negative 0.7, which is between negative 0.8 and negative 0.6.

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Which is larger, 0.04 or 0.40? If you think of this as money, you know that $0.40 (forty cents) is greater than $0.04 (four cents). So,

0.40 > 0.04

Again, we can use the number line to order numbers.

  • a<b a is less than b ” when a is to the left of b on the number line
  • a>b a is greater than b ” when a is to the right of b on the number line

Where are 0.04 and 0.40 located on the number line? See [link] .

There is a number line shown that runs from negative 0.0 to 1.0. From left to right, there are points 0.04 and 0.4 marked. The point 0.04 is between 0.0 and 0.1. The point 0.4 is between 0.3 and 0.5.

We see that 0.40 is to the right of 0.04 on the number line. This is another way to demonstrate that 0.40>0.04.

How does 0.31 compare to 0.308? This doesn’t translate into money to make it easy to compare. But if we convert 0.31 and 0.308 into fractions, we can tell which is larger.

Questions & Answers

A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet
Mikaela Reply
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Sam Reply
Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers.
Mckenzie Reply
Nathan walked on an asphalt pathway for 12 miles. He walked the 12 miles back to his car on a gravel road through the forest. On the asphalt he walked 2 miles per hour faster than on the gravel. The walk on the gravel took one hour longer than the walk on the asphalt. How fast did he walk on the gravel?
Mckenzie
Nancy took a 3 hour drive. She went 50 miles before she got caught in a storm. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. What was her speed driving in the storm?
Reiley Reply
Mr Hernaez runs his car at a regular speed of 50 kph and Mr Ranola at 36 kph. They started at the same place at 5:30 am and took opposite directions. At what time were they 129 km apart?
hamzzi Reply
90 minutes
muhammad
Melody wants to sell bags of mixed candy at her lemonade stand. She will mix chocolate pieces that cost $4.89 per bag with peanut butter pieces that cost $3.79 per bag to get a total of twenty-five bags of mixed candy. Melody wants the bags of mixed candy to cost her $4.23 a bag to make. How many bags of chocolate pieces and how many bags of peanut butter pieces should she use?
Jake Reply
enrique borrowed $23,500 to buy a car he pays his uncle 2% interest on the $4,500 he borrowed from him and he pays the bank 11.5% interest on the rest. what average interest rate does he pay on the total $23,500
Nakiya Reply
13.5
Pervaiz
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
Bridget Reply
The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Find the payment for a month when Randy used 15 units of water.
Bridget
help me understand graphs
Marlene Reply
what kind of graphs?
bruce
function f(x) to find each value
Marlene
I am in algebra 1. Can anyone give me any ideas to help me learn this stuff. Teacher and tutor not helping much.
Marlene
Given f(x)=2x+2, find f(2) so you replace the x with the 2, f(2)=2(2)+2, which is f(2)=6
Melissa
if they say find f(5) then the answer would be f(5)=12
Melissa
I need you to help me Melissa. Wish I can show you my homework
Marlene
How is f(1) =0 I am really confused
Marlene
what's the formula given? f(x)=?
Melissa
It shows a graph that I wish I could send photo of to you on here
Marlene
Which problem specifically?
Melissa
which problem?
Melissa
I don't know any to be honest. But whatever you can help me with for I can practice will help
Marlene
I got it. sorry, was out and about. I'll look at it now.
Melissa
Thank you. I appreciate it because my teacher assumes I know this. My teacher before him never went over this and several other things.
Marlene
I just responded.
Melissa
Thank you
Marlene
-65r to the 4th power-50r cubed-15r squared+8r+23 ÷ 5r
WENDY Reply
State the question clearly please
Rich
write in this form a/b answer should be in the simplest form 5%
August Reply
convert to decimal 9/11
August
0.81818
Rich
5/100 = .05 but Rich is right that 9/11 = .81818
Melissa
Equation in the form of a pending point y+2=1/6(×-4)
Jose Reply
write in simplest form 3 4/2
August
definition of quadratic formula
Ahmed Reply
From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
Melissa
what is the answer of w-2.6=7.55
What Reply
10.15
Michael
w = 10.15 You add 2.6 to both sides and then solve for w (-2.6 zeros out on the left and leaves you with w= 7.55 + 2.6)
Korin
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?
Mckenzie Reply
x > $110,000
bruce
greater than $110,000
Michael
Practice Key Terms 6

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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