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Q: Does adding the same nonzero number to the numerator and denominator of a fraction produce an equivalent fraction?

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Multiply numerator and denominator by the same number - any nonzero number - and you get an equivalent fraction.There are infinite answers, but here are a few:14/18, 21/27, 32/36

Any fraction that has a zero as the numerator equals zero. Any fraction that does not have a zero in the numerator would be a nonzero fraction.

Because doing so is equivalent to multiplying or dividing by x/x, which can be cancelled down to 1.

No, multiplying does. 2/4 does not equal 4/6 2/4 equals 4/8

because of mathematical equivalence: it doesn't change the result

Equal ratio

Because the ratio between the two numbers is not changed when you multiply both by the same non-zero number.

Natural numbers are a special kind of Rational numbers. Rational numbers can be expressed as a fraction. (Positive) fractions with the same (nonzero) numerator and denominator are natural numbers, for example 9/9 = 1.

Because division by zero is not defined and if the denominator were zero, we would be dividing by zero.

Any nonzero fractions where the numerator and denominator are the same number, are equal to 1. For example, 2/2 is equal to 1, or 3/3, 4/4, and so on.

This kind of number is called "irrational", meaning (to a mathematician!) "not a ratio."

Like denominator is the same denominator as the nonzero numbers.

No.Natural numbers by definition are whole: integers. However, if the numerator cannot be divided evenly by the denominator, or even if the numerator is less than the denominator, then it is impossible for such a ratio to result in an integer. Such ratios cannot simplify into natural numbers. (Note: This assumes that 0 is not a natural number--there is a disagreement over its membership. If 0 is considered a natural number, than any ratio with a 0 in the numerator but anything else in the denominator results in 0. A ratio with a nonzero numerator and a zero denominator is undefined. A 0/0 ratio is considered an indeterminate form and goes into calculus).

A fraction written with an integer numerator placed over a (nonzero) integer denominator is called a vulgar fraction. Vulgar fractions are also known as common fractions or simple fractions. Examples are 2/5 and 7/3. In those examples, the numerators are 2 and 7, the denominators are 5 and 3, all of which are integers. Simple/common/vulgar fractions are distinguished from compound fractions, from complex fractions, from mixed numerals, from decimal fractions, and from irrational fractions. Examples of fractions that are not common fractions are: * 0.75 -- decimal fraction * (3/4) / 2 -- complex fraction * (3/4) / (2/3) -- complex fraction * (1 1/2) / 2 -- complex fraction with mixed numeral in numerator * 3/4 of 5/7 -- compound fraction * 75% --- which equals 75/100, but written as a percent, it has neither a numerator nor a denominator * pi/4 -- irrational fraction. The distinction between common fractions and fractions that are not common is NOT the same as the distinction between proper fractions and improper fractions (which is explained below, but which is not needed to understand what a common fraction is). Common fractions can be either proper or improper. ------ If the absolute value of the numerator (the number on top) is less than the absolute value of the denominator (the number on the bottom) the fraction is called a PROPER fraction.. Examples are 2/3 and and -2/5. If the absolute value of the numerator is greater than the absolute value of the denominator (the number on the bottom) the fraction is called IMPROPER. Examples are 3/2 and and -5/2. Improper fractions can be converted to a mixed numeral, that is, an integer plus a fraction. For example 7/3 is equal to 2 1/3.

All fractions having the form n / (2 * n) where n is a nonzero integer are equivalent to the fraction 1/2. This can actually be generalized to the form x / (2 * x) where x is a nonzero number (e.g. real number, complex number).

Yes

You can't divide by zero. 3/4 is 3 divided by 4 or 0.75. 7/4 is 7 divided by 4 or 1.75

No, you cannot write any irrational number as a fraction.

When you multiply a nonzero fraction by its reciprocal you get 1. Take this example.Lets say you have a fraction called (a/b). The reciprocal of that fraction would be (b/a). If you multiply the two you'd get (a/b)*(b/a)=(ab/ab). Anything divided by itself is 1.

That is how equivalent fractions are made. When fractions are multiplied together, the numerators are multiplied together and the denominators are multiplied together. When the numerator and denominator of a fraction are both multiplied by the same non-zero number, the effect is of multiplying the original fraction by the non-zero number over the non-zero number, but any number over itself is 1, thus it is the same as multiplying by 1: let a/b be a fraction and let n be the non-zero number, then: (a x n)/(b x n) = a/b x n/n = a/b x 1 since any number divided by itself is 1. Dividing by the same non-zero number is the same effect. However, in this case, it is a slightly different proof: For this, it needs to be remembered that a fraction a/b is the same as a ÷ b. And to divide by a fraction, the divisor is inverted (numerator and denominator swap places) and then multiplied. let a/b be a fraction and n be the non-zero number, then: (a ÷ n)/(b ÷ n) = (a ÷ n) ÷ (b ÷ n) = a/n ÷ b/n = a/n x n/b = (a x n)/(n x b) = (a x n)/(b x n) (since multiplication is commutative) = a/b x n/n = a/b x 1 (as before).

Decimal

Any nonzero number will go into 1.0

mixed number

It is a mixed number.

It is 1