(1) The division of two numbers is also called the ratio of two numbers.
(2) "Bi:" is a comparative symbol, pronounced "Bi". The number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison. The quotient obtained by dividing the former term by the latter term is called the ratio.
(3) Compared with division, the former term of ratio is equivalent to dividend, the latter term is equivalent to divisor, and the ratio is equivalent to quotient.
(4) The ratio is usually expressed in fractions, decimals or even integers.
(5) The latter term of the ratio cannot be zero.
(6) According to the relationship between fraction and division, we can know that the former term of ratio is equivalent to numerator, the latter term is equivalent to denominator, and the ratio is equivalent to fractional value.
2. Basic properties of ratio: The first and second items of ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged, which is called the basic properties of ratio.
3. Find the ratio and simplify the ratio:
The method of finding the ratio: divide the former term of the ratio by the latter term, and the result is that a numerical value can be an integer, a decimal or a fraction.
According to the basic properties of the ratio, the ratio can be reduced to the simplest integer ratio. Its result must be the simplest ratio, that is, the first term and the last term are prime numbers.
4. Proportional distribution:
In agricultural production and daily life, it is often necessary to allocate a quantity according to a certain proportion. This distribution method is usually called proportional distribution.
Methods: First, find out the scores of each part in the total, and then find out what the scores of the total are.
5. Meaning of proportion: Two expressions with equal proportion are called proportion.
The four numbers that make up a proportion are called proportional terms.
The two items at both ends are called external items, and the two items in the middle are called internal items.
6. Basic properties 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.
7, the difference between ratio and proportion
The ratio of (1) indicates the division of two quantities, which has two terms (i.e. the former and the latter); Proportion refers to two formulas with equal proportions, which have four items (namely, two internal items and two external items).
(2) The ratio has basic properties, which is the basis of simplifying the ratio; Proportion also has a basic nature, which is the foundation of solution ratio.
8. Proportional quantity: two related quantities, one change and the other change. If the ratio (that is, quotient) of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship.
X/y=k (certain) is represented by letters.
9. Inverse proportional quantity: two related quantities, one change and the other change. 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.
X×y=k in the letter (sure).
10, a method for judging whether two quantities are directly proportional or inversely proportional:
The key is to see that the quotient of two relative numbers in these two related quantities must still be a product, and if the quotient is certain, it is proportional; If the product is constant, it is inversely proportional.
1 1. scale: the ratio of the distance on a picture to the actual distance is called the scale of this picture.
12, classification of scale
(1) Digital scale and line scale (2) Reduced scale and enlarged scale
13, distance on the map:
Map distance/actual distance = scale
Actual distance × scale = map distance
Distance on the map/scale = actual distance
14, application steps of scale drawing:
(1) Write the name of the graph,
(2) determine the scale;
(3) Calculate the distance on the map according to the scale;
(4) Drawings (unit length of drawings)
(5) Mark the actual distance and write down the place names.
(6) mark the scale
15. Magnification and reduction of graphics: same shape, different sizes.
16, solve the problem by proportion:
According to the invariants in the problem, find out two related quantities, correctly judge the proportional relationship between the two related quantities, and list the corresponding equations according to the positive and negative proportional relationship and solve them.
17. Common quantitative relations: (directly proportional or inversely proportional)
Unit price × quantity = total price
Single output × quantity = total output
Speed × time = distance
Efficiency × working hours = total amount of work
18、
Given the distance on the map and the actual distance, we can find the scale.
Given the scale and distance on the map, you can find the actual distance.
Given the scale and the actual distance, you can find the distance on the map.
When calculating, the units of drawing distance and real distance must be unified.
19, the total number of hectares sown is fixed. Is the number of hectares sown per day inversely proportional to the number of days to be used?
Answer: the number of hectares sown every day × days = the total number of hectares sown.
It is known that the total number of hectares sown is fixed, that is, the product of the number of hectares sown every day and the number of days to be used is fixed, so the number of hectares sown every day is inversely proportional to the number of days to be used.