Why do you start with the greater number when adding on a number line

Answers

Answer 1

Final answer:

We start with the larger number when adding on a number line due to the commutative property in mathematics, which means the order in numbers is not important in addition. Our counting system also plays a role since it's based on increases of ten, making it easier to use the larger number as a starting point. Number lines must be scaled accurately to represent the numbers involved.

Explanation:

The reason we start with the larger number when adding on a number line is because it acts as a starting point and the smaller number is treated as the distance to travel along the line. This practice is based on the concept of commutative property in mathematics, which states that the order in which the numbers are added does not affect the sum. So, if you're adding 2 + 3 or 3 + 2, the result is the same.

Our counting system is based on increases of ten, also known as powers-of-ten notation. Each place in our numbering system is ten times greater than the place to its right. This makes it convenient to use the larger number as a starting point since it positions us further along the number line.

When using a number line for addition, it's key to remember that the line must be properly scaled to accurately depict the numbers involved. Regardless of whether you start with a smaller or larger number, the line should be scaled in a way that represents all your data and makes it easy to identify trends.

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Related Questions

tim knows the volume and base area of a wooden chest that is in the shape of a rectangular prism. If the volume is 524 cubic unit and the base area is 15 square unit, what is the height of the chest?

Answers

The height of the rectangular prism chest is approximately 34.93 units, calculated using the volume and base area formulas for rectangular prisms.

To find the height of the rectangular prism chest, we can use the formula for the volume of a rectangular prism, which is given by the product of its length, width, and height. Let's denote the height of the chest as h the length as l , and the width as w.

Given that the volume of the chest is 524 cubic units and the base area (length times width) is 15 square units, we have two equations:

1. [tex]$ l \times w $ (base area) $ = 15 $[/tex] square units,

2. [tex]$ l \times w \times h $ (volume) \( = 524[/tex]) cubic units.

From the first equation, we can solve for one variable in terms of the other. Let's solve for l in terms of w :

[tex]\[ l = \frac{15}{w} \][/tex]

Now substitute this expression for l into the second equation:

[tex]\[ \frac{15}{w} \times w \times h = 524 \][/tex]

Simplify:

15h = 524

Solve for h:

[tex]\[ h = \frac{524}{15} \][/tex]

h ≈ 34.93

So, the height of the chest is approximately 34.93 units.

Explain step by step =) Harry rides his bike 25 3/8 miles. Karen rides her bike 25 2/5 miles. Who rides farther?

Answers

To answer this question we need to use subtraction.
we need to make the denominators the same.
In order to make them the same we need to find the least common multiple, of 8 and 5.
The least common multiple(the smallest shared value of the two numbers) is 40.

Next we divide our old denominator 5 by 40, which gives us 8, we multiply 8 by the numerator 2, which gives us 16. So now we have 16/20. We have to do the same to the other side. 8÷40 = 5. 5 x 3 = 15. Now we have 15/20.

Now we have a brand new equation, 16/40 - 15/40. The answer is 1/40.
In a fraction the answer is 1/40, so Karen rides her bike further.

In decimal form the answer is 0.025.

I hope this helps!

We can see Karren rode farther

[tex]25[/tex] [tex]\frac{2}{5}[/tex] with a common denominator is:

[tex]5+3=8[/tex] [tex]2+3=5[/tex]

[tex]\frac{2}{5}+\frac{3}{3}=\frac{5}{8}[/tex]

so we know that Karren rode [tex]25\frac{5}{8}[/tex] miles which is more than Harrys [tex]25\frac{3}{8}[/tex]

n + 9 < −6 plz help me

Answers

n+9-9<-6-9
n<-15

n<-15 Is your answer.

Subtract 9 from each side

N + (9 - 9) < -6 - 9

N < -15

What is the Negative Scale Factor?

Answers

A negative scale factor is a scale factor but it makes the enlargement appear opposite to the original shape and also upside down, I will include an example

Hope this helps :)

What is the value of x? 10x−15=−5x−20
a -1
b -1/3
c 1/3
d 1

Answers

10x-15 = -5x-20 add 5x to both sides
15x-15=-20 add 15 to both sides
15x= -5 divide by 15 on both sides
x= -1/3

Brainliest is always appreciated

kishauna rode her bike for 35 minutes each on Monday Wednesday and Saturday and 55 minutes each on Tuesday and Thursday. write an expression that shows the total amount of the time she spent riding her bike. than evaluate the expression

Answers

Since Kishauna rode her bike for 35 minutes on 3 days you are going to multiply 35 time 3 which equals 105.

And since she rode her bike 55 minutes on 2 other days you are going to multiply 55 times 2 and get 110.

Now you add 105 + 110 and your answer is 215.

The expression and the evaluation are that represents the total amount of time should be

[tex]= 35\times 3 + 55\times 2\\\\= 105 + 110[/tex]

and 215 minutes.

Given that,

The bike should run for 35 minutes each on Monday Wednesday and Saturday.And, the 55 minutes each on Tuesday and Thursday.

Based on the above information, the calculation is as follows:

[tex]= 35\times 3 + 55\times 2\\\\= 105 + 110[/tex]

= 215 minutes

Therefore we can conclude that the expression that represents the total amount of time should be 215 minutes.

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if x - 3y = -9 and 5x - 2y = 7, what is the value of x?

Answers

the answer is x=16/13

Boxes of sticky finger s popsicles are 4.50. The supermarket is offering a 30%off coupon. What is the price with the coupon?

Answers

if it is 30% off, then ur actually paying 70%
70% of 4.50....turn percent to decimal...." of " means multiply
0.70(4.50) = 3.15 <==

another way...
4.50 - 0.30(4.50) = 4.50 - 1.35 = 3.15 <==

either way, u will get the same answer :)

The answer is $3.15.

a fair 20 sided dice is rolled 1000 times. how many times would you expect to roll a 6?
(Include working out too plz)
thxx

Answers

Well the probability of rolling a six on it would be 1/20.

So, if you're rolling it 1,000 times, 1,000 x 1/20 = 50.

You would roll a six approximately 50 times.

Solve.
(2x+24)(4x+36)

Answers

You just need to foil. 2x times 4x times 2x times 36 times 24 times 4x times 24times 36. then solve.

Hey there! Hello!

For this problem, you need to use the distributive property to expand the variables into one equation. In my attachment, I'll show you how to do this.

If you need to then factor out the equation back into two binomials, you could either do it the way I show you, or you could just factor out the GFC's of both binomials, 2 and 4, to get 8. Either way, it's good to know how to do these steps. If the "re-factoring" step isn't necessary for your question, the second line down in the lower portion of my work.

I hope this helped you out! Feel free to ask me any additional questions if you have any. :-)

What is the final price of a 240 bike with a 3.5% tax

Answers

240*0.035=?
You take the original price and mulitiply it by .035 and you get your answer.

Assuming you mean $240 and not $2.40:

C - cost
P- Price
T- tax

P = C + C*T

P = 240 + (240)(0.035)
"=248.4"

a rectangle with a length of x+5 has a perimeter of 4x+14. 1. write the expression for the width of yhe rectangle in terms of x. 2. suppose the perimeter of the rectangle is 42 inches. what are the length and width of the rectangle?

Answers

I hope this helps you

2 (width+x+5)=4x+14

width+x+5=2x+7

width=x+2

what is the estimate of 119÷23.3

Answers

Your answer would be 5.10... Hope this helps :)

help me this egg farm produces 2400 eggs on monday. you can pack them in crates of 144 eggs each. how many eggs would be needed to fill that last crate

Answers

That's easy, just divide 2400 by 144 then take the remainder(r) and calculate the following equation: 144-r.
Hope that helped :)

Hi
If you had to do an estimate with numbers: 32kg and 7 kg

What would be your total?

Need ASAP now, thanks

Answers

all you do is add them together
32+7
let me know if you need farther help

your total would be 32 turns into 30 and 7 turns into 10 so 30 +10=40kg

Elyse is cutting strips of paper for a scrapbook page. Each strip is 1.5 centimeters wide. How wide will 10 strips of paper be?

Answers

1.5 x 10 = 15 so 10 stripes would be 15 centimeteres wide

For a STEM competition, Julienne constructed a model rocket. The rocket can reach an average height of 545 feet. Find the differences between the average heigh and the actual heights reached. Then write then as positive and negative rational numbers. Order the differences from least to greatest.
Actual heights
534.2
556.4
554.0
535.3

Answers

535.3 is the answer because? ?????????

Answer: -11.4, -9, 9.7, and 10.8

Step by step explanation: You had to subtract the actual height from the average height and then order the sum of each answer from least to greatest. Hope this helped!

7x3.8 find the product mentally

Answers

the answer would be 26.6.

The answer of 7answer of 7×3.9 is 226.6

Please help...........

Answers

-3r-2r-8=-12r-14
-5r-8=-12r-14
12r-5r=8-14
7r=-6
7r/7=-6/7
r=-6/7

It is 14r-12r-8r-3r-2r

Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change. The sandwich cost $7.75 and sales tax was $0.47. What was the cost of her drink?

Answers

Okay, first you will have to subtract every thing together:
10 - 7.75 = 2.25
2.25 - 0.47 = 1.78
So the cost of her drink is $1.78
Hope This Helps!!
:)

Given

Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change.

The sandwich cost $7.75 and sales tax was $0.47.

Find out the cost of her drink

To proof

Let the cost of her drink be x.

As given in the question

Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change.

Elysse paid for her sandwich and drink = 10 - 0.63

= $ 9.37

sandwich cost $7.75 and sales tax was $0.47

Than the equation becomes

x = 9.37 - (7.75 + 0.47)

x = 9.37 - 8.22

x = $ 1.15

The cost of the drink is $ 1.15.

Hence proved

Help please!!!!!!!!!!

Answers

answer is d (the last one)

-7x + y = 13

each week,steven gets an allowance of $8 plus $3 for each chore he does. his younger sister jill gets an allowance of $6 plus $2 per chore. write an expression for how much their parents give steven and jill each week if they do the same number of chores.

Answers

the allowance expression would be 3x+8=2x+6

Final answer:

The expression representing the total weekly allowance Steven and Jill receive for doing the same number of chores is 14 + 5c, where c represents the number of chores done.

Explanation:

The question asks for an expression to represent the total allowance that Steven and Jill receive each week if they do the same number of chores. Steven gets a fixed allowance of $8 plus an additional $3 for each chore he completes, while Jill gets a fixed allowance of $6 plus $2 for each chore she completes.

Let's represent the number of chores they each do with the variable c. The expression for Steven's weekly allowance would be 8 + 3c, and the expression for Jill's weekly allowance would be 6 + 2c. To find the total combined allowance, we simply add the two expressions:

8 + 3c + 6 + 2c

Simplifying this expression, we combine like terms:

14 + 5c

This expression represents the total weekly allowance that their parents give to Steven and Jill together, if they do the same number of chores.

A ceramic tile is in the shape of a triangle. The angle measurements of this triangle are 30 degrees, 60 degrees, and 90 degrees. The leg across from the 30 degree angle is 6.25 cm long. How long is the hypotenuse of this triangle?

Answers

Ratio of 30-60-90 triangles in terms of side lengths is 1-[tex] \sqrt{3} [/tex]-2

So, the side across the 30-degree angle is 6.25.
Thus, the side across the 90-degree angle (hypotenuse) is 12.5.

A 30 60 90 triangle is a special triangle that has simple proportions for it's side lengths. The short leg to long leg ratio is 1:sqrt(3); the short leg to hypotenuse ratio is 1:2. If the length of the short leg (across from the 30 degree angel) is 6.25 cm long, then the length of the hypotenuse is twice that: 12.5 cm.

A rectangular garden sits next to a house. Three sides of the garden are fenced, and the fourth side is the house. The length of the garden is 9 meters. A total of 21.5 meters of fencing is used. If w stands for the width of the garden in meters, which equation can be used to find its width?

Answers

To find the width of the rectangular garden, use the equation 2w + 9 = 21.5, which leads to a width of 6.25 meters after solving step by step. The total fencing used is 21.5 meters for the three sides, with the fourth side being the house.

Finding the Width of the Rectangular Garden

Given that three sides of the rectangular garden are fenced and the fourth side is the house, let's break down the problem step by step:

The length of the garden is given as 9 meters.A total of 21.5 meters of fencing is used for the three sides.We need to find the width w of the garden.

Since only three sides are fenced, the total length of the fencing is the sum of two widths and one length of the garden. Therefore, we can write this equation:

2w + 9 = 21.5

To find w, we solve the equation as follows:

Subtract the length from the total fencing: 2w = 21.5 - 9Calculate the difference: 2w = 12.5Divide by 2 to isolate w: w = 12.5 / 2Final result: w = 6.25 meters

Therefore, the width of the garden is 6.25 meters.

Julie has read 27 pages out of an 80 page book. What percent of the pages has she read

Answers

27 : 80 x 100 = 33.75%

To get percentage, divide 27 by 80. 27/80 = 0.3375 If you want to convert the decimal to percent, multiply the decimal value by 100:
0.3375 x 100 = 33.75 which can be written as 33.75%

what is 7.7 tons roundef to the nearest ton

Answers

8 tons. Hope that helps!

The answer would be 8.0 Tons!

A store offers a $900 to buy a computor the terms of the loan are 9% simple interest and equal monthly payments for three years what is the monthly payment

Answers

The monthly payment should be 20.25

Hey there! Hello!

For this problem, I'm going to assume that the 9% interest is a yearly rate. Please let me know if this assumption isn't correct, and we'll take it from there.

To calculate the full payment including the interest, all you need to do is multiply the $900 by 9%, or 0.09, to get $81. Since this is a yearly thing, we'll multiply 81 by 3 to represent 3 years, and we'll get $243. The total amount a customer will have to pay for the computer is $1,143, which is the interest plus the original price.

Now, for the monthly rate, you would need to divide that amount by 36, which is how many months are in three years. In order to pay the amount for the computer off in three years, a customer would have to pay $31.75 per month.

I hope this helped you out! Feel free to ask any additional questions if you have any. :-)

Gina saves quarters. She has $17.75 in quarters. How many quarters does she have? Show your solution in two ways. Use division to show one way. Use words, nnumbers, or models for the second way.

Answers

Gina wants to know how many quarters she has if she has seventeen dollars and seventy-five (17.75)cents in all quarters. To find he number of quarters, you need to divid seventeen dollars and seventy-five cents (17.75) by twenty five cents (0.25) to get her answer.

17.75/0.25=71

Final answer:

Using division and a visual method, it is calculated that Gina has 71 quarters, given she has a total of $17.75.

Explanation:

Gina has $17.75 and since each quarter is worth $0.25, we need to find out how many quarters make up this amount. First, using division we have 17.75 ÷ 0.25 = 71. Therefore, Gina has 71 quarters.

The second method is a more visual and explanatory one. Since each quarter is 25 cents, four quarters make up a dollar. Therefore, if we have $17, that directly translates to 17 x 4 = 68 quarters. We also have 75 cents left which correspond to another 3 quarters (75 ÷ 25 = 3). Adding these together gives us 68 + 3 = 71 quarters. So, either way, Gina has 71 quarters.

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is 7 x (6 x t) equivalent to (7 x 6) x t

Answers

Yes the associative property of multiplication allows this to be true

In other words, you can multiply in different groupings and still get the same result

Example: (2*3)*5 = 6*5 = 30 or 2*(3*5) = 2*15 = 30

7 x (6 x t)= 7 x 6t= 42t
(7 x 6) x t = 42 x t= 42t
yes they're equivalent

Evaluate for x = 2.

(12x + 8)
4
A) 4
B) 5
C) 6
D) 8

Answers

what you want to do here is plug 2 in for x. when a question asks you to evaluate a certain equation at a certain number, it's just asking you to plug the value in for your variable. i'm assuming that 12x + 8 is meant to be set over 4 as a fraction.

(12(2) + 8)/4 ... figure out the top first. 12*2 = 24, 24 + 8 = 32.

32/4 = 8, so your correct choice is D.

Final answer:

To evaluate the expression (12x + 8) / 4 for x = 2, you multiply 12 by 2, add 8, and then divide by 4. The final answer is 8, which corresponds to option D.

Explanation:

To evaluate the expression (12x + 8) / 4 for x = 2, you substitute the value of x into the expression and then simplify. First, multiply 12 by 2 to get 24, then add 8 to get 32. After that, divide 32 by 4 to get the final answer.

Here is the step-by-step calculation:

Substitute x with 2: (12*2 + 8) / 4.Multiply 12 by 2: (24 + 8) / 4.Add 24 and 8: 32 / 4.Divide 32 by 4: 8.

The correct answer is D) 8.

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