1, ratio

Meaning of ratio: The division of two numbers is also called the ratio of two numbers.

The ratio represents the division of two numbers.

":"is a comparative symbol. In the ratio of two numbers, the number before the comparison sign is called the first term of the ratio, and the number after the comparison sign is called the last term of the ratio. The quotient obtained by dividing the former term by the latter term is called the ratio. The ratio is usually expressed in fractions, and can also be expressed in decimals or integers.

According to the relationship between fraction and division, the ratio of two numbers can also be written as a fraction. The former term of the ratio is equivalent to the dividend in the division formula, the latter term is equivalent to the divisor in the division formula, and the ratio is equivalent to the quotient in the division formula. The last item of the ratio cannot be 0.

The basic nature of the ratio:

(Ratio is related to division and fraction, so the basic properties of ratio are related to the invariance of quotient and the basic properties of fraction.

Invariant properties of quotient:

Divider and divisor are multiplied or divided by the same number (except 0) at the same time, and the quotient remains unchanged.

Basic attributes of a score:

The numerator and denominator of a fraction are multiplied or divided by the same number at the same time, and the value of the fraction remains unchanged. )

The two items before and after the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged. This is the basic nature of the so-called ratio.

Simplified ratio:

According to the basic properties of the ratio, the ratio can be reduced to the simplest integer ratio.

Whether it is fractional ratio, integer ratio or fractional ratio, we should change them into integer ratio and simplify them.

2. Proportion

Meaning of proportion: Two expressions with equal proportions are called proportions.

The four numbers that make up a proportion are called proportional terms. The two terms at both ends are called external terms of proportion, and the two terms in the middle are called internal terms of proportion.

The basic nature of proportion:

In proportion, the product of two external terms is equal to the product of two internal terms. This is the basic nature of the so-called proportion.

Solution ratio:

According to the basic nature of proportion, if any three items in the proportion are known, another unknown item in this proportion can be found. Finding the unknown term in the proportion is called the solution ratio.

3. Positive proportion and inverse proportion

The significance of positive proportion:

Two related quantities, one of which changes and the other changes with it. If the ratio of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and their relationship is called proportional relationship.

If the letters X and Y are used to represent two related quantities and K is used to represent their ratio (certain), the positive proportional relationship can be expressed by the following formula:

Y÷x=k (OK)

The meaning of inverse proportion:

Two related quantities, one quantity changes, and the other quantity changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship.

If the letters X and Y are used to represent two related quantities and K is used to represent their product (certain), the inverse ratio relationship can be expressed by the following formula:

Xy=k (ok)

4. Scale

When drawing a plan such as a map, it is necessary to reduce (or expand) the actual distance according to a certain proportion before drawing it on the drawing. At this time, it is necessary to determine the ratio of the distance on the map to the corresponding actual distance.

The ratio of the distance on a picture to the actual distance is called the scale of this picture.

Distance on the map: actual distance = scale (note: the units of distance on the map and actual distance must be unified)

Distance on the map = scale × actual distance

Actual distance = distance on map/scale.

There are two scales: numerical scale and line scale.