Master mathematical terms and find equivalence relations
Quantitative relationship in practical problems: general sum-difference relationship or multiple relationship, which is often expressed by terms such as "one * * * has", "greater than ……", "less than …" and "several times more than ……". When solving problems, you can find the equivalence relation by grasping these terms, and list the equations in narrative order.
For example, the school carried out tree planting activities, and 50 trees were planted in the fifth grade, 4 fewer than in the fourth grade. How many trees were planted in the fourth grade?
The key word of this question is "less than ……", from which we can find such an equivalence relation: 2 times the number of trees planted in the fourth grade minus 4 equals the number of trees planted in the fifth grade, thus listing the equation 2x-4=50.
Find the equivalence relation according to the common quantitative relation.
Common quantitative relationship: working efficiency × working time = total workload; Unit price × quantity = total price; Speed × time = distance, etc. When solving problems, we can find equivalence relations according to these quantitative relations.
For example, the retail price of a certain clothing is 50 yuan 1 set, and now it is in 250 yuan. How many sets of clothes can I buy?
According to the quantitative relationship of "unit price × quantity = total price", the equation 50x=250 can be listed.
According to the commonly used calculation formula, find out the equivalence relation.
When solving some application problems of geometric shapes, the related formulas can be regarded as equivalent relations.
For example, the area of a trapezoid is 30 square decimeters, its upper bottom is 4 decimeters and its lower bottom is 8 decimeters. Find the height of the trapezoid.
Let's take the trapezoid area formula as the equivalent relationship, that is, "(upper bottom+lower bottom) × height ÷2= trapezoid area" to list the equation. Let: the height of the trapezoid is x decimeter, (4+8)×X÷2=30.