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What do you call the ratio of corresponding side lengths are proportional?
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∙ 7y ago
You call it similarity.
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∙ 7y ago
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What do you call a comparison of numbers or variables that can be written in fraction form?
These are the rational numbers.
What is an equation that sets two fractions equal to each other called?
I would call an equation of this type a ratio and proportion.
What is a two term ratio?
We may speak of two term and three or more term ratios. There is a big difference. Two term ratios may be identified with fractions. That identification may justify (I am not a historian and try to refrain from making remarks on the history of ideas in mathematics) calling unsigned and then signed fractions, rational numbers.In the discussion of maps, scale factor (the relation between actual distance and distance on the map) may be expressed as a ratio or fraction.Two term ratios may be called binary ratios.What is a two term ratio?We read and declare A:B as the ratio A to B. We say one ratio A:B is the same as another ratio C:D when and only when the cross products AD = BC. Equality of two-term ratiosWe write A:B :: C:D when and only when AD = CD and read A:B :: C:D as the ratio A:C and C:D are equal. We could use the equal sign = in place of the old fashioned four dot symbol ::. Convention: The ratio notation A:B appears when and only when the scaling properties of the first and second term are important.Two Term Ratios and FractionsNow the equality condition for ratios AD = BC holds when and only whenAD BD=BCBDwhich in turn holds when and when onlyAB=CDSo two ratios A:B and C:D are equal or equivalent when and only when the corresponding fractions (or compound fractions)ABandCDare equal or equivalent. So equality of two term ratios A:B and C:D may be cast as a comparision of fractionsABandCDDue to this correspondence, fractions where the numerators and denominators are both whole numbers are also called ratios.Rational numbers may be thought of as fractions whose numerators and denominators are provided by integers instead of whole numbers.Identification of Fractions and Binary (two-term) RatiosIn many places around the world, the fractionABis called a ratio, and no difference is emphasized between the concept of a ratio A:B and the concept of a fraction. Even I will call a fraction a ratio, or vice-versa. Reasoning involving equivalent ratios written as A:B can also be done with equivalent fractions written asABProportionality of Numerators and Denominators Or the first and second term in a ratioDirect Proportionality: A number or quantity Z is directly proportional to another quantity X in several circumstances when and only when the quotient Z ÷ X = Z/X has a constant value k,.or equivalently, there is a constant k such that Z = k X. That is in each instance where we find or measure the value of X, the value of Z will be kX.Fractions and Ratios scale in the same way. Therefore A:B = M:N when and only whenMN=ABare equal when and only when the first term M of the ratio M:NM=[AB]N=kNis proportional to the second term N in the ratio M:NMore on the Identification:Earlier writers identify a ratio m: n (read m to n) of a pair of numbers with the fraction mnThat makes sense when considering m parts of equal value out of n parts of equal value. With this identification two ratios a:b and c:d are equal when and only when the corresponding fractions are equivalentab=cd(1)or have equal values. Here a and d are called the extremes of the ratio;Therefore a:b = c:d implies c:d = a:b. Therefore a:b = c:d implies b:a = c:d (extremes swapped with means) and d:c = b:a as reciprocals of both sides in (1) must be equal.Algebraic forward and backward views of the latter equation implies the following when two ratios a:b and c:d are equal.ad=cb(2)clear denominators in (1) by multiplying by bd. So product of extremes a and d equals the product of meansac=bd(3)introduce denominators in (3) by dividing by cd. Soa:c = b:d. Swapping the means preserves equality.db=ca(3)introduce denominators in (2) by dividing by ba. Sod:c = b:a Swapping the extremes preserves equality.More on Scaling Ratios or raising termsFrom the equivalent fraction raising terms property thatAB=nAnBwe observe A: B = nA : nB when ever the first and second terms in a ratio A:B are multiplied by the same whole number n.Compound fractions have a similar property:AB=qAqBwhenever q is a fraction (or real number). So A: B = qA : qB when ever the first and second terms in a ratio A:B are multiplied by the same fraction or real number q.Differences between fractions A/B and ratios A:BWe can add, subtract, multiply and divide fractions written asA BBut these arithmetic operations are not (to the best of my knowledge) defined for the ratios written as A:B.We may also identify a fraction written asABwith a percentage or real numberRatios of a part to the whole -YESImagine a collection of q = m + n objects divided into disjoint subsets of m and n objects, respectively. Here the identification of the ratio m:q with the fraction mqcorrectly gives the part as a fraction of the whole.Ratios of complementary parts - Problematic, Food for thoughtImagine a collection of q = m + n objects divided into disjoint subsets of m and n objects, respectively. Here the identification of the ratio m:n with the fraction mnis problematic. The ratio may be identified, if we must, with the compound fractionmm+nmm+nAll this is to suggest that a distinction or nuance exists between the ratio written as m:n and the fraction m/n. The question is how. The ratio notation does not distinguish between the ratio of a part to a whole and the ratio of complimentary parts.
What do you call triangles with the same shape but different size?
Two figures are called congruent if they are the same shape and the same size. Two figures are called similar if they are the same shape, but different sizes. ... That means that there is a scale factor number that you multiply each number in the first shape by to get the corresponding side length in the other shape.
How does quadrupling the lengths of a rectangle affect its area?
Suppose a rectangle has a base x and a side y. The equation for the area A of a rectangle is A=x*y. Quadrupling both side and base means both are now 4x and 4y. Now, the new area, which I shall call A' will be described by the formula A'=4x*4y, which turns into A'=16xy. In the end, the new area is equal to sixteen times the original area. Try it with any possible combination of numbers, should always give sixteen times the original area, as long as you are only quadrupling the original lengths.
What do you call polygons that have equal angles and proportional side lengths?
a double triangle
Are all equilateral triangles are similar?
DFN: we call a triangle equilateral if all sides of the triangle are the same length DFN:we call two triangles similar if corresponding angles are equal, and corresponding sides are proportional. First show that all corresponding sides are proportional: Consider a equilateral triangle with side lengths 1, all other equal lateral triangles sides can be expressed as S*(1), where S is some scalar. Hence all equilateral triangles sides are proportional to each other. Next, show that all corresponding angles are equal: The angle between two sides of a triangle is related to the length of the sides. These relationships are called sin, cos, and tan. Knowing that the cos(x), where x is one of the angles in the triangle, is the adjacent divided by the hypotenuse we see that cos(x)=(1/2)c/a, since a = c (because its equal lateral) we are left with cos(x)=(1/2) which means x = 60 degrees. this can be applied to all three angles, which shows that all three angles are 60 degrees. / \ / | \ a / | \ b /__ |__\ c We have now shown that all equal lateral triangles are similar because they all have proportional sides, and they all have equal angles.
What did the plan call for?
It called for the states to have proportional representation.
What do you call the numbers in a ratio?
the numbers in a ratio called TERMS
What do you call the angles outside the transversal?
Corresponding or alternate exterior.
What do you call light divided into wave lengths?
You probably mean "Spectrum".
What do you call a Triangle that had 3 different lengths of sizes?
scalene triangle.
What do you call a shape with five sides with different lengths?
An irregular pentagon.
What do you call Ratios that name the same amount?
you call it an equivalent ratio
What do you call a fraction?
it can be called a ratio also.
What are corresponding and alternate angles?
Parallel lines can have a line crossing both of them. They call that the transversal. Corresponding angles are on the same side of the transversal. Alternate are on opposite sides of the transversal.
When ratios have the same units we call that ratio?
A proportion.
