3Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

INTEGERNUMBERS

- Key -

4 Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

1.

2.

4 + 5 = 9 four plus five equals nine.3 – 6 = three minus six equals negative three8 + (-8) = eight plus negative eight2 · (-4) = two times negative four3 · 6 – 4 = three times six minus four-8 / 2 = negative eight divided by two12 /(-3) = twelve divided by negative three5 + 4 – 6 = five plus four minus six2 · (-8) + 5 = two times negative eight plus five62 = six squared33 – 9 = three cubed minus nine(-3)2 + 32 = negative three, square plus three square

a) 2 (–7 – 4)b) (-12) • 3c) (-20) + 16d) 33/(-11)e) 2 (90+(-22))f) 3 ((-16)/8)g) 7 • 19 -8h) 52

i) 35

j) √93

5Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

3.

4. 5.

6.

Order statement containing numbers and operations

The number of times the base occurs as a factor. +, -, x, :

Expression some form of arrangement

Repeated factor in a power [ ], ( )

Another name for exponent exponent

The numbers or expressions multiplied to form a product. base

Grouping symbols a shorter process

Evaluate power

Operation factors

Simplify find the answer to

negative integersoppositesintegerspositive integersabsolute valuesigned numbers

• above / above• below / below• right / left of zero• opposite• zero• - 4 / >• 1 / <

(xm) x (xn) = x(m + n) power of a product

(xm) / (xn) = x(m - n) negative exponent

(xm)n = x(m x n) quotient law

(xy)m = xm x ym power of a power

(x/y)m =xm / xm product law

x(-m) = 1 / xm power of a quotient

6 Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

8.

9.

number line.positivenegativeinfinitypositive signnegative signoriginoppositesabsolute valuezero

a) 300m below sea level. -300b) Your brother made $55 babysitting last week. +55c) You owe your Dad $20. -20

a) -5 < 1 b) 6 > -1c) -8 < -2 d) - 3 > -5e) -3 < 0 f) -1 < 9

a) -4 < 5 and -4 > -6 becomes -6 < -4 < 5b) 1 < 6and -3 < 1 becomes -3 < 1 < 6c) 0 < 2 and 0 > -4 becomes -4 < 0 < 2

a) Find 5 less than 1 : -4 c) Find 4 less than 2: -2b) Find 2 less than -5: -7 d) Find 3 less than -2: -5

a) A loss of $31,310 on an investment. - 31,310b) 20 units to the left of -14 on a number line. - 34c) Deposit $88 into a bank account. +88d) One hundred fifty-one feet below sea level. -151e) 10 below zero. -10

f) The opposite of -147. 147g) A pay cut of $2,000. -2000h) A gain of ten pounds. +10i) A loss of seventeen pounds. -17j) The stock market went up 225 points today. +225

-40º, -12º, -3º, 0º, 5º, 10º, 40

-1 positive negative negative one

5 positive negative positive five

10 positive negative positive five

-6 positive negative negative six

 

7Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

-17, 34, 8, -31, 2, 5, -15, -9, 27, -11-31, -17, -15, -11, -9, 2, 5, 8, 27, 348, -2, 2, 12, -14, 9, 4-14, -2, 2, 4, 8, 9, 1210, -14, -26, 4, -8, 22-26, -14, -8, 4, 10, 228, -12, -16, 7, 18, 6, -6, 16, -8, -10, 5, -17, 4, 3, 15-17, -16, -12, -10, -8, -6, 3, 4, 5, 6, 7, 8, 15, 16, 18

a) 4 × 6 × (0 + 1) × 6 = 144b) 7 × 6 - (3 - 7) - 6 = 28c) 4 × 6 × 7 + (0 - 4) - 3 = 161d) 2 - 7 × (4 + 5) = -61e) (0 × 6) + 7 × 3 = 21f) 2 + (1 + 7) = 10g) 7 × 5 × (7 + 5) + 2 – 1 = 421h) 3 + (5 - 7) × 6 = -9i) 1 × (7 × 5) + 1 × 0 = 35j) 4 × 1 + (0 + 5) = 9

9 + (-28) = -19-36 + 85 = 49-45 = (-13) – 32(-17) - (-94) = 7724 + (-5) = 1948 = (-35) - (-83)(-89) - 70 = -159-90 + (-66) = -15640 - (-72) = 112

10. 11.

a) |-5 |> 8 falseb) |-3| = -3 falsec) 0 > |-6| falsed) |-5| = 5 true

a) | 2 – 5 |= 3b) | 0(–4) |= 0c) | 2 + 3(–4) |= 10d) –| –4 |= -4e) –| (–2)2 |= -4f) –| –2 |2 = -4g) (–| –2 |)2 = 4

8 Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

12.

Square roots: the inverse relationship between the square root and the square power.Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself.

square of n = n2

square of 5 = 5 x 5 = 52 = 25

The square root of a number, n, written below is the number that gives n when multiplied by itself.

nThe perfect squares are the squares of the whole numbers.

perfect squares:1, 4, 9, 16, 25, 36, 49, 64, 81, 100

ExamplesHere are the square roots of all the perfect squares from 1 to 100.

TO TEACH ON THE BOARD IN ORDER TO HAVE STUDENTS TAKING NOTES

1 = 1 since 12 = 1

4 = 2 since 22 = 4

9 = 3 since 32 = 9

16 = 4 since 42 = 16

25 = 5 since 52 = 25

36 = 6 since 62 = 36

49 = 7 since 72 = 49

64 = 8 since 82 = 64

81 = 9 since 92 = 81

100 = 10 since 102 = 100

9Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

13.

14.

a) 10 x 10 x 10 x 10 x 10 x 10 = 106

b) 11 x 11 x 11 = 113

c) 8 x 8 x 8 = 83

a) 25 = 32b) 33 x 102 = 2700c) 23 x 53 = 1000

a) (52 )3 = 56

b) (43 )2 = 46

a) 6b) 9c) 7d) 5

a) 113 = 1331b) 43 x 102 = 6400c) 54 x 24 = 10000

a) 113 = 1331b) 43 x 102 = 6400c) 54 x 24 = 10000

numerical valueorder of operationsparenthesesbracketsmultiplications and divisionsadditions and subtractions

a) a2

b) 57

c) a2

d) 20

a) (10 x 5)4 = 6250000

b) = 27125

a) = m2

b) 34 x 33 = 37

a)

b)

a2

10 Material AICLE. 1º de ESO: Integer Numbers (Solucionario)

15.

16.

9 − 7 + 5 + 2 − 6 + 8 − 4 = 73 • 2 − 5 + 4 • 3 − 8 + 5 • 2 = 1510 : 2 + 5 • 3 + 4 − 5 • 2 − 8 + 4 • 2 − 16 : 4 = 1023 + 10 : 2 + 5 • 3 + 4 − 5 • 2 − 8 + 4 • 22 − 16 : 4 = 26(15 − 4) + 3 − (12 − 5 • 2) + (5 + 16 : 4) −5 + (10 − 23)= 18[15 − (23 − 10 : 2 )] • [5 + (3 •2 − 4 )] − 3 + (8 − 2 • 3 ) = 8314 − {7 + 4 • 3 - [(-2)2 • 2 - 6)]}+ (22 + 6 - 5 • 3) + 3 - (5 - 23 : 2) = -6

A. 57 yardsB. (-63)(-126)C. +3D. 235 piecesE. 7 lawns moreF. -98 and -104G. 340 Super ChompersH. 27 membersI. 8 membersJ. 27 friends