Løsning del 1 utrinn Vår 14

Oppgave 1

a) <math>831+1196=2027</math>

b) <math>987-789=198</math>

c) <math>14,2 \cdot 3,1 = 44,02</math>

d) <math>1620:120= \frac{1620}{120} = \frac{162}{12} = 13,5</math>

Oppgave 2

a) <math>3,25 \mathrm{h}=3 \cdot 60 \mathrm{min} + 25 \mathrm{min} =205 \mathrm{min} </math>

b) <math>9,3 \mathrm{t} =9,3 \cdot 1000 \mathrm{kg}=9300 \mathrm{kg}</math>

c) <math> 2400 \mathrm{ cm^3 } = 2400 \mathrm{mL} = 2,4 \mathrm{L}</math>

d) <math> 36 \mathrm{km/h}= \frac{36}{3,6} \mathrm{m/s}=10 \mathrm{m/s}</math>

Oppgave 3

a) <math> 62000=6,2 \cdot 10^4 </math>

b) <math> ((-3)^2)^2-3^0=9^2-1=81-1=80</math>

Oppgave 4

a) <math> \frac{1}{5} + \frac{2}{5}= \frac{1+2}{5} = \frac{3}{5}</math>

b) <math> \frac{5}{2}- \frac{2}{3}= \frac{5 \cdot 3}{2 \cdot 3}- \frac{2 \cdot 2}{3 \cdot 2}= \frac{15}{6}- \frac{4}{6}= \frac{15-4}{6}= \frac{11}{6}</math>

c) <math> \frac{1}{4} \cdot \frac{2}{4}= \frac{1 \cdot 2}{4 \cdot 4}= \frac{2}{16} = \frac{1}{8}</math>

d) <math> 4: \frac{2}{3}= 4 \cdot \frac{3}{2}= \frac{12}{2}=6 </math>

Oppgave 5

a)

<math>3x=x+8</math>

<math>3x-x=x+8-x</math>

<math>2x=8</math>

<math>x= \frac{8}{2}=4 </math>

b)

<math>(x+2)^2=x^2+6</math>

<math>x^2+4x+4=x^2+6</math>

<math>4x+4=6</math>

<math>4x=6-4</math

<math>x= \frac{2}{4} = \frac{1}{2} </math>

Oppgave 6

Lønn for 1 times arbeid på kvelden: <math> 130 \mathrm{Kr} \cdot 1,25 = 162,50 \mathrm{Kr}</math>. Fire timers arbeid blir <math> 4 \cdot 162,5 \mathrm{Kr} = 650 \mathrm{Kr}</math>.

Oppgave 7

a) <math> \frac{6a^3}{2a^2}= \frac{2 \cdot 3 \cdot a \cdot a \cdot a}{2 \cdot a \cdot a}=3a</math>

b) <math> \frac{6a-6}{12b^2}: \frac{a-1}{4b^3}= \frac{6(a-1)}{12b^2} \cdot \frac{4b^3}{a-1}= \frac{24 \cdot b \cdot b \cdot b}{12 \cdot b \cdot b} =2b</math>