underestimate overestimate

Sometimes it makes
more sense to underestimate.

Sometimes an overestimate is more
reasonable.

Solve the problem using the flowchart.

Lisa wants to buy a shirt that costs $9.95 and a sweater that costs $18.25. She has  $13.20 that she has saved and $25.40 from baby-sitting. Does she have enough money?

Start

Use the flowchart below to choose and apply estimation methods.

 

Underestimate,
round down.

To be sure that Lisa has enough money, underestimate.  You want your estimate to be less than what Lisa actually has. Round down the money she has. $13.20  $10.00 $24.25 $20.00 $10 + $20  = $30.00

 

Overestimate,
round up.

Overestimate the cost of the shirt and sweater. This way your estimate will be more than the actual cost. Round up the cost of the shirt and sweater. $9.95  $10.00 $18.25  $19.00  $10 + $19  = $29.00 Since Lisa has about $30 and the shirt and sweater cost about $29, she has enough money.

Read all the information to determine whether to underestimate or overestimate. Then find the facts you need. To Underestimate, round down. To Overestimate, round up.

Determine the number based on the ratio.

If A:B = 5:13 What is A if B is 26 = ?

If A:B = 8:3 What is A if B is 15= ?

If A:B = 4:11 What is A if B is 33= ?

If A:B = 7:13 What is B if A is 14 =?

If A:B = 2:7 What is A if B is 42=?

If A:B = 3:5 What is B if A is 24=?

If A:B = 2:7 What is A if B is 35 =?

If A:B = 7:1 What is A if B is 8=?

Determine the number based on the ratio.

If A:B = 7:1 What is B if A is 42 =  ?

If A:B = 5:13 What is B if A is 15 = ?

If A:B = 8:2 What is A if B is 8 = ?

If A:B = 6:3 What is B if A is 48= ?

If A:B = 1:11 What is B if A is 5= ?

If A:B = 3:13 What is A if B is 78= ?

Ratios

Ratios

Ratios tell how one number is related to another number.

A ratio may be written as A:B or A/B or by the phrase "A to B".

A ratio of 1:5 says that the second number is five times as large as the first.

The following steps will allow determination of a number when one number and the ratio between the numbers is given.

Example: Determine the value of B if A=6 and the ratio of A:B = 2:5

* Determine how many times the number A is divisible by the corresponding portion of the ratio. (6/2=3)
* Multiply this number by the portion of the ratio representing B (3*5=15)
* Therefore if the ratio of A:B is 2:5 and A=6 then B=15

Math Word Problems I: Addition - Fun with Toys

Math Word Problems I: Addition - Fun with Toys

1. Debbie made a necklace for her doll using 41 green beads and 41 red beads. How many beads does the necklace have? Answer
82


2. Stacy has two dolls. The first doll costs $ 36 and the second costs $ 41. How many dollars do the two dolls cost?Answer
77


3. Warren empties 66 marbles from a small box into a big box that already contains 393 marbles. How many marbles are now there in the big box?Answer
459


4. Peterarranges 54 blocks in four stacks. He then arranges 75 blocks in six stacks. How many blocks did he arrange in the ten stacks?Answer
129


5. Michael likes toy vehicles. He has 31 trucks and 47 cars. How many toy vehicles does he have?Answer
78

Decimal Word problems

Example 1:	If 58 out of 100 students in a school are boys, then write a decimal for the part of the school that consists of boys.
Analysis:	We can write a fraction and a decimal for the part of the school that consists of boys.
	fraction decimal 0.58
Answer:	0.58

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Example 2:	A computer processes information in nanoseconds. A nanosecond is one billionth of a second. Write this number as a decimal.
Analysis:	We can write a one billionth as a fraction and then as a decimal.
	fraction decimal  0.000000001
Answer:	A nanosecond, one billionth of a second, is written as 0.000000001 in decimal form.

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Example 3:	Five swimmers are entered into a competition. Four of the swimmers have had their turns. Their scores are 9.8 s, 9.75 s, 9.79 s, and 9.81 s. What score must the last swimmer get in order to win the competition?
Analysis:	We must order these decimals from least to greatest. Then we must determine how the least compares with the winning score.
Step 1:	9 . 8 0    9 . 7 5    9 . 7 9    9 . 8 1
Step 2:	The least decimal is 9.75. Now we must determine how 9.75 compares with the winning score.
Answer:	The last swimmer must get a score less than 9.75 s in order to win.

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Example 4:	To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm. Will a tire that is 1.4691 cm in diameter work? Explain why or why not.
Analysis:	We must compare and order these decimals to help us solve this problem. Specifically, we need to determine if the third decimal is between the first two.
Step 1:	Let's start by writing one decimal beneath the other in their original order. We will place an arrow next to 1.4691 so that we can track its value.
	1 . 4 6 5 0 1 . 4 7 2 0 1 . 4 6 9 1
Step 2:	Now let's order these decimals from least to greatest.
	1 . 4 6 5 0    1 . 4 6 9 1 1 . 4 7 2 0
Step 3:	Now we must determine if the third decimal (indicated by the arrow) is between the first two.
Answer:	A tire that is 1.4691 cm in diameter will work since 1.4691 is between 1.465 and 1.472.

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Example 5:	Ellen wanted to buy the following items: A DVD player for $49.95, a DVD holder for $19.95 and a personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90 with her?
Analysis:	The phrase enough money tells us that we need to estimate the sum of the three items. We will estimate the sum by rounding each decimal to the nearest one. We must then compare our estimated sum with $90 to see if she has enough money to buy these items.
Answer:	No, because rounding each decimal to the nearest one, we get an estimate of $92, and Ellen only has $90 with her.

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Example 6:	In Example 5, did we overestimate or underestimate? Explain your answer.
Analysis:	To determine if the estimate in Example 5 is an overestimate or an underestimate, we must compare her estimate with the actual sum.
Answer:	In Example 5, the estimate of $92 is an overestimate since it is greater than $91.85, the amount of money Ellen needs to buy these items.

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Example 7:	What is the combined thickness of these five shims: 0.008, 0.125, 0.15, 0.185, and 0.005 cm?
Analysis:	The phrase combined thickness tells us that we need to add these five decimals to get their sum.
Answer:	The combined thickness of these five shims is 0.473 cm.

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Example 8:	Melissa purchased $39.46 in groceries at a store. The cashier gave her $1.46 in change from a $50 bill. Melissa gave the cashier an angry look. What did the cashier do wrong?
Analysis:	We need to estimate the difference to see if the cashier made a mistake.
	$50.00 - $40.00 = $10.00
Estimate:	$1.46 is much smaller than the estimated difference of $10.00. So the cashier must have given Melissa the wrong change.

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Example 9:	In Example 8, how much change should Melissa get from the cashier? The cashier gave her $1.46
Analysis:	We need to find the difference of $50 and $39.46.
Answer:	$50.00 - $39.46 = $10.54

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Example 10:	If a 10-foot piece of electrical tape has 0.037 feet cut from it, then what is the new length of the tape?.46
Analysis:	We need to subtract: 10 - 0.037 and express the answer with proper units.
Answer:	10 ft. - 0.037 ft. = 9.963 ft.

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Summary:

In this lesson we learned how to solve word problems involving decimals. We used the following skills to solve these problems: reading and writing decimals, comparing and ordering decimals, estimating decimal sums and differences, and adding and subtracting decimals.