Double sentence
The two-clause is a term from mathematics didactics . It provides a calculation method for proportional value pairs based on the proportionality factor (basic value). The term comes from the fact that this proportionality problem is typically formulated and solved in two sentences.
- I. The given basic ratio (corresponding value for the base unit).
- II. The corresponding value for a multiplicity of the basic set.
Before applying the double sentence, it must always be checked whether the prerequisite for a proportional allocation (in example 1: no progressive price discounts, in example 2: constant speed) is met.
For the calculation, the basic value is multiplied by the multiple.
Examples
example 1
One kg of apples costs 2 euros. How much does 3 kg cost?
Invoice:
Apples in kg | Price in € | Calculate: | |
1. | 1 | 2 | · 3 |
2. | 3 | 6th |
Solution: 3 kg of apples cost 6 euros.
Example 2
I drive at 80 km / h. How far can I get in 3 hours?
Invoice:
Time in hours | Distance in km | Calculate: | |
1. | 1 | 80 | · 3 |
2. | 3 | 240 |
Solution: I can travel 240 km.
Example 3
Ohm's law : an ohmic resistance is 25 V / A. What voltage does the resistor drop when a current of 3 A flows through it?
Invoice:
Current in amps | Voltage in volts | Calculate: | |
1. | 1 | 25th | · 3 |
2. | 3 | 75 |
Solution: A voltage of 75 V drops.
Note: The Ohm's Law in the Description chapter contains a reminder for this example.
variants
version 1
Sometimes several sizes can be varied.
- Example: Each chicken lays one egg per day. How many eggs do 10 chickens lay in a week?
Variant 2
The opposite direction (calculation of the average) also often plays a role if the value is given for a larger amount.
- Example: My 20 employees earn 200,000 euros a month. How much does each employee earn on average per month (per day)?
These average values are required if you want to deduce from one ratio to another (see rule of three ).
Web links
literature
- Otto Schulz, FL Striez, HW Ule (Hrsg.): Schulblatt für die Provinz Brandenburg . First issue. L. Oehmigke, Berlin 1839, p. 270 f . ( limited preview in Google Book search).