Ex 3.4, 6

Transcript

Ex 3.4, 6 Can you think of other way(s) to find a rational number between any two rational numbers? We found rational numbers beween any two numbers by Common denominator & Scaling method Let’s look at 3 other methods Method 1: The Averaging Method The Concept If you want to find the exact middle point between two numbers, you add them together and divide by 2 . Step 1 (Add) 1/3+1/2 First, find a common denominator (which is 6 ). 2/6+3/6=5/6 Step 2 (Divide by 2) 5/6÷2 Remember, dividing by 2 is the same as multiplying by 1/2. 5/6×1/2=5/12 The Result 5/12 is exactly halfway between 1/3 and 1/2. Similarly, we can further divide if we want to find more rational numbers Method 2: The Decimal Method The Concept Fractions and decimals are just two different languages for the same number. Sometimes it is easier to "see" the gap in decimal form. Step 1 (Convert to Decimals): 1/3 is approximately 0.33 1/2 is exactly 0.50 Step 2 (Pick a number in between): * We need a decimal between 0.33 and 0.50 . Let's pick an easy one, like 0.40 (or 0.4 ). Step 3 (Convert back to a Fraction): 0.4 read out loud is "four-tenths", which is written as 4/10. Simplify the fraction by dividing the top and bottom by 2 to get 2/5. The Result: 2/5 is safely wedged between 1/3 and 1/2. Method 3: The Mediant Method The Concept: This is a fantastic math trick. For any two positive fractions 𝑎/𝑏 and 𝑐/𝑑, you can find a number strictly between them by simply adding the numerators together and adding the denominators together. The Calculation: * Our fractions are 1/3 and 1/2. Add the top numbers: 1+1=2 Add the bottom numbers: 3+2=5 The Result: 2/5 is between 1/3 and 1/2.