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How do you place rational numbers in order from least to greatest on a number line?

Rewrite improper fractionsAn improper fraction is a fraction with a bigger numerator than denominator. These numbers can be difficult to compare. For example, numbers such as 26/7, 31/9, 12/5, 8/3 and 22/13 do not have an obvious highest or lowest term.\n\nRewrite improper fractions as mixed numbers or as numbers with decimals. To turn an improper fraction into a decimal, divide the numerator by the denominator. If the denominator is large or a prime number greater than five, use a calculator.\n\nFor example, divide the numbers 26/7, 31/9, 12/5, 8/3 and 22/13 to create 3.71, 3.44, 2.4, 2.67 an..

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What great mathematical discoveries did Albert Einstein make?

Einstein's 16 field equations describe the gravitational effects produced by mass within general relativity. They describe the general theory of relativity, which explains that time is not objective, but rather dependent on an observer. One prominent equation that arose from the theory of relativity is what's known as mass-energy equivalence, which says that the mass of any system is the measure of its energy content.

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What is a real-life example of a mathematical array?

Any group of identical or similar items in an arrangement of rows and columns is an array. The muffin tin has identical muffin cups. The chocolate box has an assortment of types of chocolates in its array; one chocolate may contain caramel and another cream, but they are similar because both are chocolates. Each desk in a classroom is identical, but each has a different student sitting in it.\nAn example of teaching multiplication with arrays is to say that a classroom's student desks form six columns and four rows of seats. Students can multiply the columns and rows to get the total numb..

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What are some examples of unit rate word problems?

A unit rate is a ratio that compares two unlike quantities and has a denominator of 1. For example, 60 miles per hour is a unit rate because it compares miles and hours and uses 1 hour as the denominator, as in 60 miles/1 hour. Usually, a unit rate word problem presents a ratio that doesn't have a denominator of 1 and requires the person solving the problem to simplify the ratio so that it does. A typical example involves speed and distances. This can be seen in the sample problem, "When Mario rides his bike to the next town, which is 30 miles from his house, it takes him 3 hours. How fas..

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What is a coin toss simulation?

Coin toss simulations help teach elementary probability using random computer generated events called Bernoulli trials, binary tests with two outcomes (0 and 1) where each event remains separate from the other. The number of events determines the frequency, and as the frequency grows the probability of a binary event approaches 50 percent for each possible outcome. A single coin toss will always have a 50 percent outcome for heads, but flipping a coin four times may show lower outcomes because getting tails three times in a row can happen. As the number of coin tosses increase, the odds begin ..

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How do logarithms apply in everyday life?

The utility of logarithmic functions extends beyond just chemistry and sound engineering. Logarithms can be applied to solve complex problems in almost any situation that also involves the use of exponential functions. For example, determining different aspects of the photographic quality of an image can be broken down into logarithmic pieces. This is possible because information about the photograph, such as the ratio of incident light to transmitted light, can be expressed in mathematical ways. These ratios and variables can then be manipulated with logarithms to extract information about th..

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What are the steps to raising a number to the third power?

An easy way to visualize raising a number to its third power, or having a number with an exponent of three, is by breaking the problem down into pieces. To raise the number two to its third power, simply multiply two by itself twice. So, because 2 x 2 = 4 and 4 x 2 = 8, raising two to the third power equals eight.

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Is zero a natural number?

The argument over whether to include zero rests on whether natural numbers are all positive whole numbers or all non-negative whole numbers. Generally, natural numbers are the counting numbers, which also calls to question if the starting point is zero or one. Dictionary.com says it includes the numbers used to count the members of a set. It includes zero, because there are zero members in an empty set.

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What is a generic rectangle?

A generic rectangle is essentially grid-and-lattice multiplication that breaks down the numbers into more manageable chunks and provides a way to keep track of the carries during calculations. Generic rectangles are also very similar to algebra tiles. An algebra tile is a manipulative that can be used for learning polynomial multiplication. For polynomials, generic rectangles provide a way to keep track of all those terms that come out of the distributive law.

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What is the real number that corresponds to a point on a line?

A point is chosen on the number line as representing the real number 0. This point is called the origin on the number line. Points on the number line to the left of 0 represent negative real numbers. Points on the number line to the right of 0 represent positive real numbers. The distance between any two points on the number line is the same.

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