Answer to Question #218469 in Algebra for Nonkululeko

Question

1. Explain how part to part ratio occur in:

i. Geometry

ii. Algebra

iii. Probability

2. The ratio of the sides of a pentagon is 5:3:2:4:1 . The perimeter of the pentagon is 75cm. How long is the shortest side?

5+3+2+4+1, so x is?

a. 5/15 × 75/1 = 25cm

b. 2/15 × 75/1 = 10cm

c. 3/10 × 75/1 = 5cm

d. 1/5 × 75/1 = 5cm

Answer 1

Answer:

1. In mathematics, a ratio indicates how many times one number contains another.

In mathematics, a ratio indicates how many times one number contains another

The numbers in the ratio can be any quantity, such as the number of people or objects, or such as measurements of length, weight, time, and so on. In most contexts, both numbers are limited to positives.

Therefore, the relation can be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as a value denoted by this fraction. Calculation coefficients given (non-zero) natural numbers are rational numbers, and can sometimes be natural numbers. When two quantities are measured by the same unit, as is often the case, their ratio is equal to a dimensionless number.

In general, a comparison of the values ​​of the ratio of two subjects can be expressed as a fraction derived from the ratio. For example, in the ratio 2∶3 the number, size, volume or quantity of the first entity is 2/3 of that of the second subject.

If you multiply all the quantities involved in the ratio by the same number, this ratio remains valid.

The coefficients can be reduced (as fractions) by dividing each quantity by the common factors of all quantities. As for fractions, the simplest form is one in which the numbers in relation are the smallest possible integers.

When solving problems in geometry, if a ratio is given, the coefficient of proportionality is introduced - the number by which this ratio was reduced.

In probability theory, the ratio means the probability of an event.

2.$5x+3x+2x+4x+x=75;$

$15x=75;$

$x=5;$

$1\sdot 5=5cm;$

d. 1/15 × 75/1 = 5cm.