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kari74 [83]
3 years ago
10

when two fractions refer to the same whole and have the same denominators, explain why you can compare only the numerators

Mathematics
2 answers:
nata0808 [166]3 years ago
7 0
When two fractions with the same denominators are used to refer the same whole numbers have have the same denominator, you compare only the numerator because the denominators are already equal and the only sufficient part to confirm that the fractions are equal is if the denominators are equal. This is because the only way two fractions with the same denominator can be equal to each other is if they both have equal numerators.
ZanzabumX [31]3 years ago
5 0

Answer:

Because the denominator of the whole is exactly the same denominator of the fractions.

Step-by-step explanation:

Let:

a, b,c,d,e,f,K

Arbitrary constants, where:

K=\frac{e}{f}

\{a, b,c,d,e,f,K\} \in Z

Let's rewrite the problem this way:

K=\frac{a}{b} \pm \frac{c}{d}

Where:

\frac{a}{b} \pm \frac{c}{d}=\frac{ad\pm bc}{bd}

If the fractions have the same denominator, that is:

b=d

Then:

\frac{a}{b} \pm \frac{c}{d}=\frac{ad\pm bc}{bd}=\frac{ad\pm dc}{d^2}

Factor:

\frac{d(a\pm c)}{d(d)} =\frac{a\pm c}{d}

Thus:

K=\frac{e}{f} = \frac{a\pm c}{d}

As you can see from the equation, you can conclude directly from it that:

f=d

In another words, when two fractions refer to the same whole and have the same denominators, the denominator of the whole is exactly the same denominator of the fractions. That's the reason why you can compare only the numerators.

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A 14 inch pizza (diameter is 14) was cut in to 8 pieces. What is the angle measure of each slice? *
Luda [366]

Answer:

The angle for each slice is 45 degrees.

Step-by-step explanation:

In order to calculate the angle of each slice, we first need to calculate the total area of the pizza, because we will use that to find the area of each slice and as a result it's angle. To calculate the area of the pizza we must use:

pizza area = pi*r²

r = d / 2 = 14 /2 = 7 inches

pizza area = pi*(7)² = 153.86 square inches

Since the pizza was divided in 8 pieces, the area of each piece is given by the area of the pizza divided by the number of slices. We have:

slice area = pizza area  / 8 = 153.86 / 8 =19.2325 square inches

Each slice is a circle sector, therefore it's area is given by:

slice area = (angle*pi*r²)/360

Therefore we can solve for angle:

19.2325 = (angle*pi*7²)/360

angle*pi*49 = 6923.7

angle = 6923.7 / pi*49 = 45 degrees

The angle for each slice is 45 degrees.

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3 years ago
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mario62 [17]

I think the answer is B! I hope that helps!!!!!

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4 0
3 years ago
11. Identify the properties below.<br> a. 5 + 6 = 6 + 5<br> b. 7 + (3 + 9) = (7 + 9) + 3
jenyasd209 [6]
A is commutative property
B is associative property
Explanation:
5 0
3 years ago
Suppose two radii of a circle determine a 45° angle, and the length of both radii is 64 yards. What is the arc length formed by
Ilia_Sergeevich [38]

The arc length formed by the 2 radio is 15.24 yards

Step-by-step explanation:

Angle between the 2 radio = 45°

Radius = 64 yards

Arc length = (45/360) (2π) (64)

= (1/8) (2π) (64

= 16π

= 16(3.14)

=15.24 yards

The arc length formed by the 2 radio is 15.24 yards

8 0
3 years ago
Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa
Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 8.7% and standard deviation 20.2%.

This means that \mu = 8.7, \sigma = 20.2

40 years:

This means that n = 40, s = \frac{20.2}{\sqrt{40}}

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = 1.35

Z = 1.35 has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

Z = \frac{X - \mu}{s}

Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = -0.22

Z = -0.22 has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0
2 years ago
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