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How is a plus b over a minus b equals c plus d over c minus d?
(a + b)/(a - b) = (c + d)/(c - d) cross multiply(a + b)(c - d) = (a - b)(c + d)ac - ad + bc - bd = ac + ad - bc - bd-ad + bc = -bc + ad-ad - ad = - bc - bc-2ad = -2bcad = bc that is the product of the means equals the product of the extremesa/b = b/c
What do you do after cross multiplying when comparing fractions with unlike denominators?
Suppose the two fractions are a/b and c/d ad that b, d > 0. Then cross multiplication gives ad and bc. If ad > bc then a/b > c/d, If ad = bc then a/b = c/d, and If ad < bc then a/b < c/d
Can you always find another fraction in between ant two fractions why?
Yes. The simple answer is that rational fractions are infinitely dense. A longer proof follows:Suppose you have two fractions a/b and c/d where a, b, c and d are integers and b, d are positive integers.Without loss of generality, assume a/b < c/d.The inequality implies that ad < bc so that bc-ad>0 . . . . . . . . . . . . . . . . . . . (I)Consider (ad + bc)/(2bd)Then (ad+bc)/2bd - a/b = (ad+bc)/2bd - 2ad/2bd = (bc-ad)/2bdBy definition, b and d are positive so bd is positive and by result (I), the numerator is positive.That is to say, (ad+bc)/2bd - a/b > 0 or (ad+bc)/2bd > a/b.Similarly, by considering c/d - (ad+bc)/2bd is can be shown that c/d > (ad+bc)/2bd.Combining these results,a/b < (ad+bc)/2bd < c/d.
How do you tell a proportion is true?
You appear to be referring to the fact that if a/b = c/d then ad = bc. You know this is true because of the axioms of equality (If you do the same thing to both sides of an equation, then equality is maintained). a/b = c/d multiply by d ad/b = c multiply by b ad = bc If you wish to prove a specific proportion is true, you can test it with the equation ad = bc
What are 2 ways you can tell that two ratios can form a proportion?
1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).
How is a plus b over a minus b equals c plus d over c minus d?
(a + b)/(a - b) = (c + d)/(c - d) cross multiply(a + b)(c - d) = (a - b)(c + d)ac - ad + bc - bd = ac + ad - bc - bd-ad + bc = -bc + ad-ad - ad = - bc - bc-2ad = -2bcad = bc that is the product of the means equals the product of the extremesa/b = b/c
What do you do after cross multiplying when comparing fractions with unlike denominators?
Suppose the two fractions are a/b and c/d ad that b, d > 0. Then cross multiplication gives ad and bc. If ad > bc then a/b > c/d, If ad = bc then a/b = c/d, and If ad < bc then a/b < c/d
Can you always find another fraction in between ant two fractions why?
Yes. The simple answer is that rational fractions are infinitely dense. A longer proof follows:Suppose you have two fractions a/b and c/d where a, b, c and d are integers and b, d are positive integers.Without loss of generality, assume a/b < c/d.The inequality implies that ad < bc so that bc-ad>0 . . . . . . . . . . . . . . . . . . . (I)Consider (ad + bc)/(2bd)Then (ad+bc)/2bd - a/b = (ad+bc)/2bd - 2ad/2bd = (bc-ad)/2bdBy definition, b and d are positive so bd is positive and by result (I), the numerator is positive.That is to say, (ad+bc)/2bd - a/b > 0 or (ad+bc)/2bd > a/b.Similarly, by considering c/d - (ad+bc)/2bd is can be shown that c/d > (ad+bc)/2bd.Combining these results,a/b < (ad+bc)/2bd < c/d.
What were the four Mesoamerican civilizations?
In approximate chronological order, they wereOlmecs (c. 1500 BC - 400BC)Mayans (Maya) (c. 2000 BC-1500 AD, tribal influence continues to present)Toltecs (c. 800-1000 AD)Aztecs (c. 1300-1600 AD)
If a over b equals c over d then is it possible that a plus b equals c plus d If not then give Mathematical Reason for that?
a/b=c/d =>ad=bc =>a =bc/d b =ad/c c =ad/b d =bc/a so if a+b=c+d is true => (bc/d)+(ad/c)=(ad/b)+(bc/a) => (bc2+ad2)/dc=(da2+cb2)/ab => ab(bc2+ad2)=dc(da2+cb2) and since ad=bc, => ab(adc+add) =dc(ada+adc) => abadc+abadd =dcada + dcadc => abadc-dcadc =dcada-abadd => (ab-dc)adc =(dc-ab)add ad cancels out => (ab-dc)c =(dc-ab)d => -(dc-ab)c =(dc-ab)d => -c = d so there's your answer :)
Is the ancient Persia BC or AD?
It is B C (Before Christ)
How do you tell a proportion is true?
You appear to be referring to the fact that if a/b = c/d then ad = bc. You know this is true because of the axioms of equality (If you do the same thing to both sides of an equation, then equality is maintained). a/b = c/d multiply by d ad/b = c multiply by b ad = bc If you wish to prove a specific proportion is true, you can test it with the equation ad = bc
What is ancient Egypt's capital city?
This is a list of Egyptian capitals in a chronological order.Thinis (before 2950 BC) the first capital of Upper and Lower EgyptMemphis: (2950 BC - 2180 BC)Herakleopolis: (2180 BC - 2060 BC)Thebes: (2135 BC - 1985 BC)Itjtawy: (1985 BC - 1785 BC)Thebes: (1785 BC - 1650 BC)Xois: (1715 BC - 1650 BC)Avaris: (1650 BC - 1580 BC)Thebes: (1650 BC - c. 1353 BC)Akhetaten: (c. 1353 BC - c. 1332 BC)Thebes: (c. 1332 BC - 1279 BC) Ramesses IIPi-Ramesses (1279 BC - 1078 BC)Tanis: (1078 BC - 945 BC)Bubastis: (945 BC - 715 BC)Tanis: (818 BC - 715 BC)Sais: (725 BC - 715 BC)Napata/Memphis (715 BC - 664 BC)Sais: (664 BC - 525 BC)Sais: (404 BC - 399 BC)Mendes: (399 BC - 380 BC)Sebennytos: (380 BC - 343 BC)Alexandria: (332 BC - 641 AD)Al-Fustat: (641 AD - 750 AD)Al-Askar: (750 - 868 AD)Al-Qatta'i: (868 - 905 AD)Al-Fustat: (905 - 969 AD)Al-Qahira (Cairo): the present capital (969 AD - Present)
What are 2 ways you can tell that two ratios can form a proportion?
1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).1. They are equivalent fractions.2. They cross-multiply to the same value (a/b = c/d if and only if ad = bc).
What is oldest kingdom in world?
Magadha dynasties (c. 1700 BC - 550 AD)
What the seven new wonders of the world?
The Seven Wonders of the ancient world were large, impressive ancient constructions, monuments built by many of the great early civilizations. They did not all exist in the same time period, and only one (the Great Pyramid) has survived to the present day.Great Pyramid of Giza (built c. 2570 BC)Hanging Gardens of Babylon (built c. 600 BC, gone by 100 BC)Statue of Zeus at Olympia (carved c. 435 BC, destroyed c. 400 AD)Temple of Artemis at Ephesus (550 BC to 262 AD)Mausoleum of Maussollos at Halicarnassus (351 BC, destroyed 1494 AD)Colossus of Rhodes (280 BC, lost to earthquake 226 BC)Lighthouse of Alexandria (280 BC to 1480 AD)
Factor ac plus ad plus bc plus bd?
a(c+d)+b(c+d)=(a+b)(c+d)
