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Authoritative PPT Summary
"Mathematics in Beer Production" PPT courseware 3
1. Review and sorting out
What do you know about ratios and proportions?
Review the organizing requirements:
1. Work in groups to review and organize the knowledge of comparison and proportion in an organized manner;
2. Express the sorting results in any way you like, such as tables, flow charts, tree diagrams, etc.
Ratio and Proportion
significance
The division of two numbers is also called the ratio of two numbers. An expression that expresses the equality of two ratios is called a proportion.
0.6: 0.8 = 0.75 2: 3 = 6: 9
The first and last terms of a ratio are multiplied or divided by the same number (except 0) and the ratio remains unchanged.
In proportion, the product of two external terms is equal to the product of two internal terms.
Finding ratios and simplifying ratios
Find the ratio. According to the meaning of the ratio, divide the former term by the latter term.
The result is a number, which can be a whole number, decimal, or fraction.
Simplification ratio
According to the basic properties of ratio, multiply or divide both the first and last terms of the ratio by the same number (except zero).
The result is a ratio, and it is the simplest integer ratio.
give it a try
Determine whether the two quantities in each of the following groups are proportional? If proportional, what proportional relationship is there?
①The area of one face of the cube and its surface area
proportional to
②The size of the fraction is certain, its numerator and denominator
proportional to
③The area of a triangle is certain, its base and height
inversely proportional
④The speed is constant, the distance and time traveled are
proportional to
2. Discussion and exchange
What is the connection between the basic properties of ratios, the basic properties of fractions, and the property of constant quotients?
0.2 : 0.3=(0.2×10) :(0.3×10)=2 :3
2.5÷1.5=(2.5×2)÷(1.5×2)=5:3
Basic properties of ratio
If the first and last terms of a ratio are multiplied or divided by the same number (except 0) at the same time, the ratio remains unchanged.
Basic properties of fractions
If the denominator and numerator of a fraction are multiplied or divided by the same number (except 0) at the same time, the magnitude of the fraction remains unchanged.
Invariable properties of quotient
In division, the dividend and divisor are multiplied or divided by the same number (except 0) at the same time, and the quotient remains unchanged.
The contents of the properties of constant quotients, the basic properties of ratios and the basic properties of fractions are essentially the same.
3. Application and reflection
1. Talk and discuss.
Normally, the ratio of head length to height of a 12-year-old child is about 2:15.
Normally, the head length of a 12-year-old child is 2/15 of the height.
The ratio of protein to fat content in soybeans is 2:1.
Normally, the height of a 12-year-old child is 7.5 times the length of his head.
The mass ratio of cement, sand and gravel in a kind of concrete is 2:3:5.
The ratio of the speed of artificial earth satellites to spacecraft is 40:57.
Can you give any other examples of this?
Use ratio to express the relationship between quantities concisely and clearly.
How do you feel when comparing these representation methods?
2. Fill in the blanks.
(1) Put 20 grams of sugar into 100 grams of water. The ratio of sugar to sugar water is ( ).
(2) Convert 1 kilogram: 20 grams into the simplest integer ratio is ( ), and their ratio is ( ).
(3) If A×8=B×3, then A:B=(): ()
(4) Select 4 numbers from the even numbers within 20 to form a ratio ( ).
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