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GalinKa [24]
3 years ago
6

Sarah said that when you multiply two fractions that are both less than 1, you may sometimes get a product equal to or greater t

han 1.
is sarah's statement true why or why not? please use some fractions to prove or disprove sarah's statement
Mathematics
2 answers:
blsea [12.9K]3 years ago
6 0

Answer:

Sarah's statement is false.

Step-by-step explanation:

If a fraction is less than 1, it means that its numerator is less than its denominator.

So, if we multiply two fractions both are less than 1, then, numerators of both the fractions are less than their denominators.

Hence, in the resultant fraction, the numerator is less than the denominator and hence its value is less than 1.

sveticcg [70]3 years ago
5 0

Answer:

Sarah's statement is not true and it is explained with the help of  counter example.    

Step-by-step explanation:

Sarah gave a statement that the product of two fraction whose value is smaller than 1 gives a product of 1 or greater than 1.

No, this may not always be true. In fact product of two fractions whose value are less than 1 is always smaller than 1.

This can be explained with the help of a counter example:

1)

\displaystyle\frac{1}{2} < 1\\\\\displaystyle\frac{1}{2}\times \displaystyle\frac{1}{2} = \displaystyle\frac{1}{4} < 1

2)

\displaystyle\frac{3}{4}, \displaystyle\frac{2}{4} < 1\\\\\displaystyle\frac{3}{4}\times \displaystyle\frac{2}{4} = \displaystyle\frac{6}{16} < 1

3)

\displaystyle\frac{3}{4}, \displaystyle\frac{4}{7} < 1\\\\\displaystyle\frac{3}{4}\times \displaystyle\frac{4}{7} = \displaystyle\frac{3}{7} < 1

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Cory writes the polynomial x7 3x5 3x 1. Melissa writes the polynomial x7 5x 10. Is there a difference between the degree of the
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Degree of a polynomial gives the highest power of its terms. Yes there is a difference between the degrees of sum and difference of the polynomials.

<h3>What is degree of a polynomial?</h3>

Degree of a polynomial is the highest power that its terms pertain(for multi-variables, the power of term is addition of power of variables in that term).

Thus, in x^3 + 3x^2 + 5, the degree of the polynomial is 3 as the highest power in its terms is 3.

(power and exponent are same thing)

<h3>What are like terms?</h3>

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For example, x^3 and 3x^3  are like terms since variable is same, and it is raised to same power 3.

For example 4x^2 and x^3 are not like terms as the variables are same but powers aren't same.

The given polynomials are:

c(x) = x^7 + 3x^5 + 3x + 1\\\\p(x) = x^7 + 5x + 10

Their sum is

c(x) + p(x)  = x^7 + 3x^5 + 3x + 1 + x^7 + 5x + 10 = (1+1)x^7 + 3x^5 + (3+5)x + 11\\\\c(x) + p(x) = 2x^7 + 3x^5 + 8x + 11

(only like terms' coefficients can be added (or subtracted) for addition or subtraction of them )

The sum's degree is 7

Their difference is:

c(x) - p(x) = x^7 + 3x^5 + 3x + 1 - x^7 -5x - 10 = (1-1)x^7 + 3x^5  +(3-5)x -9\\\\c(x) - p(x) = 3x^5 - 2x - 9

Difference's degree is 5

Thus, both's degrees are not same.

Thus, Yes there is a difference between the degrees of sum and difference of the polynomials.

Learn more about subtraction of polynomials here:

brainly.com/question/9351663

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