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About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. 2 6.5) 7 (1 2 13.5) Add 7 and 6.5. The rational number, 6.75, lies between 7 and 6.5. 015 6 1 2 1 3 1 6 2 3 The process above of finding another number between any two given numbers can be continued indefinitely. This suggests the.density property You can use the density property to solve real-world problems.

Here are some examples of decimal word problems. We will illustrate how block diagrams can be used to help you to visualize the decimal word problems in terms of the information given and the data that needs to be found. Block diagrams or bar modeling are used in Singapore Math and tape diagrams are used in Common Core Math.

Example:
The length of a ribbon is 1.28 m. The length of a rope is 2.74 m longer than the ribbon. What is the length of the rope?

Solution:

1.28 + 2.74 = 4.02

The length of the rope is 4.02 m.

Example:
The mass of a jar of sugar is 1.9 kg. What is the total mass of 4 such jars of sugar?

Solution:

1.9 × 4 = 7.6

The total mass of 4 such jars of sugar is 7.6 kg.

Example:
A pail holds 5.2 l of water. A bottle holds 3.9 l less water than the pail. What is the volume of water in the bottle?

Solution:

5.2 – 3.9 = 1.3

The volume of water in the bottle is 1.3 l.

Example:
Susan has 4 times as much money as her sister. If Susan has $10, how much money does her sister have?

Solution:

$10 ÷ 4 = $2.50

Susan’s sister has $2.50.

Decimal Word Problems: Addition, Subtraction, Multiplication, Division

Examples:

1. Maneesha purchased a box of pencils for $1.28 and gave the cashier $10.00. How much change should she get back?
   
2. If you buy an ebook for $29.62 and download 5 songs for $1.29 each, what is the total amount you have spent?
   
3. Emilio’s batting average in his first year playing baseball was 0.089. In his second year, he improved to an average of 0.29. His third year, he improved even more to an average of 0.329. What is Emilio’s average over the three years? What is the difference between the first and third year averages?
   
4. Shanelle purchased 4 pencils for $0.28 each. If she had a $5 bill, how much money did she have left after purchasing the pencils?
   
5. A train took 1.2 hours to go 73.8 miles from Cary to Fayetteville. Find the rate of the train.
   
6. I have a pile of DVD’s. Each DVD has a height of 0.3 cm. If the pile is 75 cm tall, how many DVD’s are there in the pile?

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Word Problems With Decimals

Solve word problems involving addition, subtraction, multiplication and division of decimal numbers.

Examples:

1. Matt deposits a check for $234.95 into his checking account. He now has a total of $1,479.87 in the account. How much was the account before the deposit?
   
2. Stan compares his checkbook record with his monthly bank statement that says he has $876.47. Stan sees that checks for $32.85, $97.10 and $158.78 have not been cashed yet. How much money does Stan really have available?
   
3. An ad for a computer system lists the price as $899.95. There is an instant rebate of $55.55 and a mail-in rebate of $66.66. What is the final price of the system after both rebates?
   
4. At work, Amy receives $22.25 per hour for up to 40 hours per week. Any time beyond that is paid at a rate of $37.80 per hour. If she receives $1,173.50 in her paycheck, how much time did she work that week?
   
5. The total receipts for a basketball game is $1,400 for 788 tickets sold. Adults pay $2.50 and students pay $1.25. How many tickets of each kind were sold?

Decimals Word Problem Using Block Model

Solving a 2-part decimals word problem using block modeling.

Example:
David took a walk around a park twice. He took 12.4 minutes to walk the first round. In the second round, he took 3.2 fewer minutes than he did the first round. How long did David take to complete his walk altogether?

2.6 Solve Problems Involving Decimalsmr. Mac's Page Key

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How to solve decimal word problems using tape diagrams?

2.6 Solve Problems Involving Decimalsmr. Mac's Page Numbering

The following video shows an example of a decimal word problem.

Example:
Manny tracked the amount of food he ate from Monday to Friday. He ate 16.3 pounds of food. On Monday, he ate 3.2 pounds and on Tuesday, he ate 2.9 pounds. He ate an equal amount on the other three days. How much did he eat on those days?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Quadratic 'Max/Min' Word Problems (page 3 of 3)

Sections: Projectile motion, General word problems, Max/min problems

When you get to calculus, you will see some of these max/min exercises again. At that point, they'll want you to differentiate to find the maximums and minimums; at this point, you'll find the vertex, since the vertex will be the maximum or minimum of the related graphed parabola. But they're the same exercise and you'll get the same answers then as you will now.

• You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?

The fencing-length information gives me perimeter. If the length of the enclosed area is L and the width is w, then the perimeter is 2L + 2w = 500, so L = 250 – w. By solving the perimeter equation for one of the variables, I can substitute into the area formula and get an equation with only one variable:

A = Lw = (250 – w)w = 250w – w² = –w² + 250w

To find the maximum, I have to find the vertex (h, k).

h = ^–b/_2a = –(250)/2(–1) = –250/–2 = 125

In my area equation, I plug in 'width' values and get out 'area' values. So the h-value in the vertex is the maximizing width, and the k-value will be the maximal area:

k = A(125) = –(125)² + 250(125) = –15 625 + 31 250 = 15 625

The problem didn't ask me 'what is the value of the variable w?', but 'what are the dimensions?' I have w = 125. Then the length is L = 250 – w = 250 – 125 = 125.

The largest area will have dimensions of 125' by 125',
for a total area of 15 625 square feet.

Note that the largest rectangular area was a square. This is always true: for a given perimeter, the largest rectangular area will be that of a square. However, teachers are starting to notice that students have figured this out, so they're giving more complicated area-perimeter problems.

• You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure?
  

I'm dealing with something that looks like this: It doesn't really matter which side I label as the 'length' and which I label as the 'width', as long as I label clearly and work consistently.

With the labelling I've chosen, the fencing gives me a 'perimeter' of 2L + 3w = 1200. Solving for one of the variables, I get:

2L + 3w = 1200
L + 1.5w = 600
L = –1.5w + 600

Then the area is: Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved

A = Lw = (–1.5w + 600)w = –1.5w² + 600w

To maximize this area, I have to find the vertex. Since all I need are the dimensions (not the area), all I need from the vertex (h, k) is the value of h, since this will give me the maximal width.

h = ^–b/_2a = –(600)/2(–1.5) = –600/–3 = 200

Then the length will be L = –1.5(200) + 600 = –300 + 600 = 300.

The paddock should be 300' by 200', with the divider
running parallel to the 200-foot-long side.

2.6 Solve Problems Involving Decimalsmr. Mac's Page Numbers

Notice that, with the divider running down the middle of the paddock, you don't get a square as being the maximal shape. If they throw in cost considerations (like putting prettier but more expensive fencing on the side of the paddock facing the street), you'll get odd-sized results, too. Warning: Don't just assume that the maximal rectangular shape will always be a square.

In many quadratic max/min problems, you'll be given the formula you need to use. Don't try to figure out where they got it from. Just find the vertex. Then interpret the variables to figure out which number from the vertex you need, where, and with what units.

• Your factory produces lemon-scented widgets. You know that each unit is cheaper, the more you produce. But you also know that costs will eventually go up if you make too many widgets, due to the costs of storage of the overstock. The guy in accounting says that your cost for producing x thousands of units a day can be approximated by the formula C = 0.04x² – 8.504x + 25302. Find the daily production level that will minimize your costs.

As you might guess, it will be a lot easier to use the vertex formula to find the minimizing value for this quadratic than it would be to complete the square. So I'll use the vertex formula:

h = ^–b/_2a = –(–8.504)/2(0.04) = 8.504/0.08 = 106.3

Since the inputs to the formula they gave me are the production levels ('thousands of units'), I've found the number I need. The other number for the vertex would be the actual costs for making this amount of widgets, and the problem doesn't ask for that. I do need to remember, though, that x is in thousands of units, so my best level of production is not 106.3 units, but (106.3)(1 000) = 106 300 units.

I will minimize my costs if I produce 106 300 units a day.

Sometimes you'll get hit with a problem that seems much more complicated, especially when you have to invent the formula yourself.

• You run a canoe-rental business on a small river in Ohio. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge?

Let's say I have no idea how to set this problem up. Instead of going straight to an equation, I'll need to put in some real numbers, see what I do when I know what the values are, and then follow the pattern to get my formula. Here is my reasoning, neatly laid out in a table:

price hikes	price per rental	number of rentals	total income / revenue
none	$12.00	36	$12.00×36 = $432.00
1 price hike	$12.00 + 1(0.50)	36 – 1(2)	$12.50×34 = $425.00
2 price hikes	$12.00 + 2(0.50)	36 – 2(2)	$13.00×32 = $416.00
3 price hikes	$12.00 + 3(0.50)	36 – 3(2)	$13.50×30 = $405.00
xprice hikes	$12.00 + x(0.50)	36 – x(2)	(12 + 0.5x)(36 – 2x)

Then my formula for my revenues R after x fifty-cent price hikes is:

R(x) = (12 + 0.5x)(36 – 2x) = 432 – 6x – x² = –x² – 6x + 432

The maximum income will occur at the vertex of this quadratic's parabola, and the vertex is at
(–3, 441):

h = ^–b/_2a = –(–6)/2(–1) = 6/(–2) = –3
k = R(h) = –(–3)2 – 6(–3) + 432 = –9 + 18 + 432 = 450 – 9 = 441

That is, my income will be maximized (assuming the journal article is correct) if I lower my current price of $12 by three times of fifty cents, or by $1.50.

I should charge $10.50 per canoe.

Whenever you're not sure of your formula, try doing what I did above: write out what you would do if you knew what the numbers were, and see if you can turn that into a formula. But make sure you write things out completely, like I did, so you can see the pattern. Warning: Don't simplify too much in your head, or you could miss what your formula is supposed to be.

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