Summary
Highlights
Rational numbers are all numbers that can be written as a fraction where the numerator and denominator are integers. Natural and whole numbers are subsets of rational numbers. Fractions can result in integers, finite decimals, or infinite periodic decimals.
To convert a fraction to a decimal or integer, perform the division. Examples include -48/12 simplifying to -4 and 27/4 converting to 6.75. Activity 1 covers converting 100/33 to 3.03 (periodic) and 250/32 to 7.8125 (finite decimal).
To convert a finite decimal to a fraction, multiply the numerator and denominator by a power of 10 corresponding to the number of decimal places. For example, 2.15 becomes 215/100, which simplifies to 43/20.
For decimals with a period immediately after the decimal point, subtract the non-periodic part from the whole number (without decimal) to form the numerator. The denominator consists of nines, with the count matching the number of digits in the period. Example: 7.34 periodic becomes (734-7)/99 결과를 727/99.
For decimals with a non-periodic part between the decimal point and the periodic part, the numerator is the whole number (without decimal) minus the non-periodic part. The denominator is formed by nines (for the periodic part) followed by zeros (for the non-periodic part between the decimal and period). Example: 3.5264 periodic becomes (35264-3526)/9000, simplifying to 15869/4500.
A birthday gift of 20,000 pesos. 3/4 is saved (15,000 pesos) and a pair of socks costs 4,000 pesos. The remaining money is calculated: 20000 - 15000 = 5000, then 5000 - 4000 = 1000 pesos left.
To locate a fraction, divide the unit into sections based on the denominator and count the parts indicated by the numerator. For decimals, approximate their position, especially for infinite periodic decimals. Examples include -7/2 and 1.23 periodic.
Convert 5.02 periodic to 452/9 and 2.046 periodic to 1013/495, applying the rules for converting periodic decimals to fractions.
Locate 3/5 on the number line (between 0 and 1) and -0.25 (between 0 and -0.5), demonstrating how to plot both fractions and finite decimals.
Out of 50 guests, 7/10 are from the same city. So, 35 guests are local, meaning 15 guests (50 - 35) are from other cities.
Recap of rational numbers, their definition, and subsets. Summary of converting fractions to decimals and decimals to fractions (finite and different types of periodic) and how to locate both on a number line, emphasizing approximation for periodic decimals.