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- 2. Hello!I am JerryMath I am here because I love to introduce some tips to solve math problems. You can contact me at https://gifted.elearningtrees.com/contact-us
- 3. Compare Positive Integers Q1. Compare 1106526425 and 762376287 Check number of digits The number with more digits wins so 1106526425 (10 digits) > 762376287 (9 digits)
- 4. Compare Positive Integers (continue) Q2. Compare 123768 and 123976 Compare digits from left to right 123768<123976
- 5. Compare Negative/Positive Integers Q3. Compare -745 and 36 Negative number < any positive number and 0 so -745 (negative number) < 36 (positive number)
- 6. Compare Negative/Positive Integers (Continue) Q4. Compare -435768 and -3878 Compare positive parts and revert 435768>3878, ---> -43768<-3878
- 7. Compare Decimals Q5. Compare 32.087 and 15.9 Compare the integer part of the decimal so 32.087 > 15.9
- 8. Compare Decimals (continue) Q6. Compare 245.09 and 245.13 Compare decimal part from left to right 245.09<245.13
- 9. Compare Decimals (continue) Q7. Compare 687.23 and 687.235 Extra decimal digit 687.23<687.235
- 10. Compare Decimals (continue) Q8. Compare -37.1 and -37.15 Negative decimal: compare without sign and revert 37.1<37.15, then -37.1>-37.15
- 11. Compare Fractions Q9. Compare 𝟐 𝟏𝟑 and 𝟐 𝟏𝟕 Same numerator Compare denominator, larger is smaller so 2 13 > 2 17
- 12. Compare Fractions (continue) Q10. Compare 𝟔 𝟏𝟑 and 𝟖 𝟏𝟑 Same denominators Compare numerator, the larger is bigger so 6 13 < 8 13
- 13. Compare Fractions (continue) Q11. Compare 476 𝟔 𝟏𝟗 and 475 𝟖 𝟏𝟗 Compare integer part So 476 6 19 > 475 8 19
- 14. Compare Fractions (continue) Q12. Compare 38 𝟏𝟓 𝟐𝟑 and 38 𝟗 𝟐𝟑 Same integer part Compare fraction part So 38 15 23 > 38 9 23
- 15. Compare Fractions (continue) Q13. Compare -874 𝟐 𝟏𝟑 and - 873 𝟐 𝟏𝟕 Negative fraction: compare without sign and revert so -874 2 13 < - 873 2 17
- 16. Bonus: How to Find Common Denominators Example: 𝟓 𝟔 and 𝟒 𝟏𝟓 1.Find the least common multiple (LCM) of denominators. LCM(6, 15)=30 2.Calculate factor: 30/6=5 and 30/15=2 3.Multiply the factor 𝟓 𝟔 = 𝟓𝑿𝟓 𝟔𝑿𝟓 = 𝟐𝟓 𝟑𝟎 , 𝟒 𝟏𝟓 = 𝟒𝑿𝟐 𝟏𝟓𝑿𝟐 = 𝟖 𝟑𝟎
- 17. Compare Exponents Q14. Compare 𝟐 𝟑𝟎𝟎 and 𝟐 𝟓𝟎𝟎 Same base and base>1 Compare power so 2300 < 2500
- 18. Compare Exponents (continue) Q15. Compare 𝟐 𝟑𝟎𝟎 and 𝟑 𝟑𝟎𝟎 Same power Compare base so 2300 < 3300
- 19. How to make a number larger Add a positive value Minus a negative value Multiply a value which is greater than 1 Divide by a positive value which is smaller than 1 Get the square root of the number if this number is smaller than 1 and it is a positive number.
- 20. Solution to Hard Problem in the Question Set Compare 𝟎. 𝟗 𝟎.𝟗 and 𝟎. 𝟖 𝟎.𝟖 81 > 80 9 × 9 > 10 × 8 9 × 9 × 9 > 10 × 8 × 8 9 × 9 × 97 > 10 × 8 × 87 99 > 10 × 88 𝟗 𝟗 𝟏𝟎 𝟗 > 𝟖 𝟖 𝟏𝟎 𝟖 0.99 > 0.88 0.90.9 > 0.80.8
- 21. Solution to Hard Problem in the Question Set 1 82 + 1 92 + 1 102 +. . + 1 642 < 1 8×8 + 1 8×9 + 1 9×10 +. . + 1 63×64 = 1 64 + ( 1 8 − 1 9 ) + ( 1 9 − 1 10 )+. . +( 1 63 − 1 64 ) = 1 8
- 22. Thanks!
Editor's Notes
- We notice that the first number has 10 digits and the second number has 9 digits. Because both numbers are positive numbers, the number with more digits is bigger. Therefore, 1106526425 is larger than 762376287.
- For positive numbers with the same number of digits, we compare each digit from the left most digit until we find a different value, the bigger value on that digit indicate the number is bigger. Therefore, 123768 is smaller than 123976.
- Negtive number is always less than any positive number and 0.
- When comparing two negative numbers, we compare the numbers without sign first and revert the order. Because 435768 is larger than 3878, we have -43768 smaller than -3878.
- Compare the integer part of the decimal, the bigger value indicate the number is bigger so 32.087 > 15.9
- we found the integer part are the same, then we compare the decimal part one digit by one digit until we find different or no more digits on one number, the number with the larger value is bigger. 245.09<245.13
- When comparing two decimal numbers with same integer part, we compare the decimal part one digit by one digit until we find different or no more digits on one number, the number with the larger value or more digit indicate larger value 687.23<687.235
- When comparing two negative numbers, we compare the numbers without sign first, we found the integer part are the same, then we compare the decimal part one digit by one digit until we find different or no more digits on one number, the number with the larger value or more digit indicate larger value, and finally we need to revert the order. 37.1<37.15, then -37.1>-37.15
- When the numerator are the same, the number with larger denominator is smaller, so 2 13 > 2 17
- When the denominators are the same, the number with larger numerator is bigger, so 6 13 < 8 13
- When comparing mixed fraction, if fraction part is less than 1, the number with larger integer part is bigger, So 476 6 19 > 475 8 19
- When comparing mixed fraction, if integer part are the same, the number with larger fraction part is is bigger So 38 15 23 > 38 9 23
- When we compare negative fraction numbers, we compare the mixed fraction numbers and find the one with larger mixed fraction value, in the final result, the one with larger mixed fraction value is smaller because of the negative sign so -874 2 13 < - 873 2 17
- Bonus: How to Find Common Denominators 1. Find the least common multiple (LCM) of both denominators. For example, find common denominator of 𝟓 𝟔 and 𝟒 𝟏𝟓 ,LCM(6, 15)=30 Multiply the numerator and denominator by the factor (common denominators divided by the denominator). The factor in the example is 30/6=5 and 30/15=2. So 𝟓 𝟔 = 𝟓𝑿𝟓 𝟔𝑿𝟓 = 𝟐𝟓 𝟑𝟎 , 𝟒 𝟏𝟓 = 𝟒𝑿𝟐 𝟏𝟓𝑿𝟐 = 𝟖 𝟑𝟎
- When comparing exponent, if the base is greater than 1, the larger the power is the larger is the exponent, so 2 300 < 2 500
- When comparing exponent, if the power is the same, the larger the base is the larger is the exponent, so 2 300 < 3 300
- When comparing exponent, if the power is the same, the larger the base is the larger is the exponent, so 2 300 < 3 300
- When comparing exponent, if the power is the same, the larger the base is the larger is the exponent, so 2 300 < 3 300