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REAL NUMBERS

REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the

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Page 1: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the

REAL NUMBERS

Page 2: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 3: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 4: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 5: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the

2|512 2|256 2|128 2| 64 2| 32 2| 16 2| 8 2| 4 2| 2 1

512 = 29 2|280 2|140 2| 70 5| 35 7| 7 1

280 = 23𝑥 5 𝑥 7

HCF (512, 280) = 23 = 8 LCM (512, 280) = 29 𝑥 5 𝑥 7 = 17920

Page 6: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 7: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 8: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 9: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 10: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the
Page 11: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the

(i) (−2)2+ (−1)2+ (0)2+ (1)2= 4 + 1 + 0 + 1 = 6

(ii) 4 consecutive numbers are; n, n+1, n+2 and n+3. (𝑛)2+(𝑛 + 1)2+(𝑛 + 2)2+(𝑛 + 3)2= 𝑛2 + 𝑛2 + 2𝑛 + 1 + 𝑛2 + 4𝑛 + 4 + 𝑛2 + 6𝑛 + 9 = 4𝑛2 + 12𝑛 + 14 = 2(2𝑛2 + 6𝑛 + 7) an even number as 2 is a factor.

Page 12: REAL NUMBERS · Rational Numbers Q = {Any number that can be written in the form where a. b e Z. b O} Rational numbers are also called fractions. All integers can be written in the