Unit 1: Fractions and Decimals. ACTIVITIES 1 - SOLUTIONS Mathematics - 3º ESO

SOLUTIONS

Exercise 1

a) +133.45+45.55+63.99−17.50−220=£ 5.49b) −459.77+6.50−17.85=−£ 471.12

Exercise 2

a) 55+32−100=−13 ° Cb) −15−28+75−17=+15 ° Cc) −22−12−2+53=+17 ° C

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Unit 1: Fractions and Decimals. ACTIVITIES 1 - SOLUTIONS Mathematics - 3º ESO

Exercise 3

Compute

a)

−5+4 ∙ (−2+1 )3— (9+6 )2=−5+4 ∙ (−1 )3−(−3 )2=−5+4 ∙ (−1 )−9=¿−5−4−9=−18

b) −6−2 ∙ [−4+5 : (−1 ) ]=−6−2 ∙ [−4−5 ]=−6−2 ∙ (−9 )=−6+18=12

c) 12−2 ∙ [25: (−4−1 )+(−2 )— (−6−10 ) ]=12−2 ∙ [25 : (−5 )−2− (−16 ) ]=¿¿12−2 ∙ [−5−2+16 ]=12−2 ∙ (+9 )=12−18=−6

d) −7−(−3 )+(−8 ) ∙ (−1 )−(−12 ) : (−4 )=−7+3+(+8 )−(+3 )=¿¿−7+3+8−3=+1

e) (−1 )4−(−2 )3+18 : (−9 )−(−4+2 )=1−(−8 )−2−(−2 )=¿¿1+8−2+2=9

f) (−5−4 ) ∙ (−2 )+28 : (−7 )+ (−2 )3=(−9 ) ∙ (−2 )−4+(−8 )=18−4−8=6

g) −5−4 ∙ [−8 :2−2 ∙ (−3 ) ]=−5−4 ∙ [−4+6 ]=−5−4 ∙ (+2 )=−5−8=−13

h) 6−5 ∙ [−4−1+(−2 )2−32 ]=6−5 ∙ [−4−1+4−9 ]=¿¿6−5 ∙ (−10 )=6+50=56

i) 12−8∙ [−2+4 : (−1 )−(−3+2 )4 ]=12−8 ∙ [−2−4− (−1 )4 ]=¿¿12−8 ∙ [−2−4−(+1 ) ]=12−8∙ (−7 )=12+56=68

j) (−2 )5 : (3+1 )2+2∙ (−5−4+3 )=−32 : (4 )2+2 ∙ (−6 )=¿¿−32:16−12=−2−12=−14

k) 10−10∙ [−6+5 ∙ (−4+7−3 ) ]=10−10 ∙ [−6+5 ∙0 ]=10−10 ∙ (−6 )=¿¿10+60=70

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Unit 1: Fractions and Decimals. ACTIVITIES 1 - SOLUTIONS Mathematics - 3º ESO

Exercise 4Each one of the following operations has one mistake. Highlight/circle and describe the mistake in words.

a) 100−25÷5=75÷5=15

The mistake is related to the order of operations (BEDMAS).The last thing you do is the addition and subtraction.The right solution would be:

100−25÷5=100−5=95

b) 4+(7−1 )2=4+62=4+12=16

62≠12

c) −32+8÷ (−2 )=9+8÷ (−2 )=9+ (−4 )=5

The base is 3 and the minus sing is not affected by the exponent 2.

d) (5 ∙4 ) ∙3=(4 ∙5)∙3Because there are parentheses, this represents the associative property.

This expression represents the conmutative property of multiplication: we can change the order of multiplication of natural numbers without changing the result.

5 ∙4=4 ∙5

The associative property of multiplication states that we can change the grouping of multiplication without changing the result.

(5 ∙4 ) ∙3=4 ∙ (5 ∙3 )

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