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Practice set b

Perform each operation. Simplify when possible.

Add 4 gal 3 qt to 1 gal 2 qt.

6 gal 1 qt

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Add 9 hr 48 min to 4 hr 26 min.

14 hr 14 min

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Subtract 2 ft 5 in. from 8 ft 7 in.

6 ft 2in.

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Subtract 15 km 460 m from 27 km 800 m.

12 km 340 m

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Subtract 8 min 35 sec from 12 min 10 sec.

3 min 35 sec

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Add 4 yd 2 ft 7 in. to 9 yd 2 ft 8 in.

14 yd 2 ft 3 in

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Subtract 11 min 55 sec from 25 min 8 sec.

13 min 13 sec

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Multiplying a denominate number by a whole number

Let's examine the repeated sum

4 ft 9 in. + 4 ft 9 in. + 4 ft 9 in. 3 times = 12 ft 27 in.

Recalling that multiplication is a description of repeated addition, by the distribu­tive property we have

3 ( 4 ft 9 in . ) = 3 ( 4 ft + 9 in. ) = 3 4 ft + 3 9 in. = 12 ft + 27 in. Now, 27 in. = 2 ft 3 in. = 12 ft + 2 ft + 3 in. = 14 ft + 3 in. = 14 ft 3 in.

From these observations, we can suggest the following rule.

Multiplying a denominate number by a whole number

To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to this product.

Sample set c

Perform the following multiplications. Simplify if necessary.

6 2 ft 4 in. = 6 2 ft + 6 4 in. = 12 ft + 24 in.

Since 3 ft = 1 yd size 12{"3 ft"=" 1 yd"} {} and 12   in . = 1 ft size 12{"12"" in" "." ="1 ft"} {} ,

12 ft + 24 in. = 4 yd + 2 ft = 4 yd 2 ft

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8 5 hr 21 min 55 sec = 8 5 hr + 8 21 min + 8 55 sec = 40 hr + 168 min + 440sec = 40 hr + 168 min + 7 min + 20 sec = 40 hr + 175 min + 20 sec = 40 hr + 2 hr + 55 min + 20 sec = 42 hr + 55 min + 20 sec = 24hr + 18hr + 55 min + 20 sec = 1 da + 18 hr + 55 min + 20 sec = 1 da 18 hr 55 min 20 sec

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Practice set c

Perform the following multiplications. Simplify.

2 10 min size 12{2 cdot left ("10 min" right )} {}

20 min

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5 3 qt size 12{5 cdot left ("3 qt" right )} {}

15 qt = 3 gal 3 qt size 12{"15 qt"="3 gal 3 qt"} {}

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4 5 ft 8 in . size 12{4 cdot left (5" ft 8 in" "." right )} {}

20 ft 32 in . = 7 yd 1 ft 8 in . size 12{"20 ft 32 in" "." =" 7 yd 1 ft 8 in" "." } {}

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10 2 hr 15 min 40 sec size 12{"10" cdot left (2" hr 15 min 40 sec" right )} {}

20 hr 150 min 400 sec = 22 hr 36 min 40 sec size 12{"20 hr 150 min 400 sec"="22 hr 36 min 40 sec"} {}

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Dividing a denominate number by a whole number

Dividing a denominate number by a whole number

To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit. Affix the unit to this quotient. Carry any remainder to the next unit.

Sample set d

Perform the following divisions. Simplify if necessary.

12 min 40 sec ÷ 4 size 12{ left ("12 min 40 sec" right ) div 4} {}

Long division. 12 min and 40 sec divided by 4. 4 goes into 12 minutes 3 times, making a quotient of 3 minutes with no remainder. 4 goes into 40 seconds 10 times, making a quotient of 10 seconds with no remainder. The total quotient is 3 min 10 sec.

Thus 12 min 40 sec ÷ 4 = 3 min 10 sec size 12{ left ("12 min 40 sec" right ) div 4=3" min 10 sec"} {}

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5 yd 2 ft 9 in . ÷ 3 size 12{ left ("5 yd 2 ft 9 in" "." right ) div 3} {}

Long division. 5 yd 2 ft 9 in divided by 3. 3 goes into 5 yards one time with a remainder of 2 yards. Bring down the 2 feet. 2 yards and 2 feet is eight feet. 3 goes into eight feet twice with a remainder of 2 feet. Bring down the 9 inches. 2 feet 9 in is equal to 22 inches. 3 goes into 33 inches exactly 11 times. The total quotient is 1 yd 2 ft 11 in. Convert to feet: 2 yd 2 ft = 8 ft . Convert to inches: 2 ft 9 in . = 33 in .

Thus 5 yd 2 ft 9 in . ÷ 3 = 1 yd 2 ft 11 in . size 12{ left ("5 yd 2 ft 9 in" "." right ) div 3=1" yd 2 ft 11 in" "." } {}

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Practice set d

Perform the following divisions. Simplify if necessary.

18 hr 36 min ÷ 9 size 12{ left ("18 hr 36 min" right ) div 9} {}

2 hr 4 min

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34 hr 8 min . ÷ 8 size 12{ left ("34 hr 8 min" "." right ) div 8} {}

4 hr 16 min

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13 yd 7 in . ÷ 5 size 12{ left ("13 yd 7 in" "." right ) div 5} {}

2 yd 1 ft 11 in

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47 gal 2 qt 1 pt ÷ 3 size 12{ left ("47 gal 2 qt 1 pt" right ) div 3} {}

15 gal 3 qt 1 pt

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Exercises

For the following 15 problems, simplify the denominate numbers­.

85 min

1 hour 25 minutes

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26 qt

6 gallons 2 quarts

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135 oz

8 pounds 7 ounces

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16,300 mL

16 liters 300 milliliters (or 1daL 6 L 3dL)

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For the following 15 problems, perform the indicated opera­tions and simplify the answers if possible.

Add 6 min 12 sec to 5 min 15 sec.

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Add 14 da 6 hr to 1 da 5 hr.

15 days 11 hours

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Add 9 gal 3 qt to 2 gal 3 qt.

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Add 16 lb 10 oz to 42 lb 15 oz.

59 pounds 9 ounces

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Subtract 3 gal 1 qt from 8 gal 3 qt.

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Subtract 3 ft 10 in. from 5 ft 8 in.

1 foot 10 inches

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Subtract 5 lb 9 oz from 12 lb 5 oz.

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Subtract 10 hr 10 min from 11 hr 28 min.

1 hour 18 minutes

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Add 3 fl oz 1 tbsp 2 tsp to 5 fl oz 1 tbsp 2 tsp.

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Add 4 da 7 hr 12 min to 1 da 8 hr 53 min.

5 days 16 hours 5 minutes

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Subtract 5 hr 21 sec from 11 hr 2 min 14 sec.

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Subtract 6 T 1,300 lb 10 oz from 8 T 400 lb 10 oz.

1 ton 1,100 pounds (or 1T 1,100 lb)

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Subtract 15 mi 10 in. from 27 mi 800 ft 7 in.

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Subtract 3 wk 5 da 50 min 12 sec from 5 wk 6 da 20 min 5 sec.

2 weeks 23 hours 29 minutes 53 seconds

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Subtract 3 gal 3 qt 1 pt 1 oz from 10 gal 2 qt 2 oz.

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Exercises for review

( [link] ) Find the value: 5 8 2 + 39 64 size 12{ left ( { {5} over {8} } right ) rSup { size 8{2} } + { {"39"} over {"64"} } } {} .

1

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( [link] ) Find the sum: 8 + 6 3 5 size 12{8+6 { {3} over {5} } } {} .

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( [link] ) Convert 2 . 05 1 11 size 12{2 "." "05" { {1} over {"11"} } } {} to a fraction.

2 14 275 size 12{2 { {"14"} over {"275"} } } {}

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( [link] ) An acid solution is composed of 3 parts acid to 7 parts water. How many parts of acid are there in a solution that contains 126 parts water?

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( [link] ) Convert 126 kg to grams.

126,000 g

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Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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