Løsning del 1 utrinn Vår 15 eksempeloppgave

Oppgave 1

a) $987+589=1576$

b) $8643-4789=3854$

c) $345\cdot 678=233910$

d) $32:0.64=50$

Oppgave 2

a) $205\text{min}=3\text{h}25\text{min}$

b) $8000\text{mg}=0.008\text{kg}$

c) $750\text{mL}=0.75\text{L}$

d) $1\text{daa (dekar)}=1000m^2$

$11500m^2=11.5\cdot 1000m^2=11.5\text{daa (dekar)}$

Oppgave 3

a) $\frac{3}{10}\cdot 15=\frac{3\cdot 15}{10}=\frac{45}{10}=\frac{9}{2}=4\frac{1}{2}$

b) $6:\frac{3}{4}=6\cdot \frac{4}{3}=\frac{6\cdot 4}{3}=\frac{24}{3}=8$

Oppgave 4

a) $1+2\cdot (3-4{)}^2=3$

b) $-5\cdot (-2+4{)}^2-\frac{2^3}{4}=-22$

Oppgave 5

a) $x+3=-3x+7$

$x+3x+3=7$

$x+3x=7-3$

$4x=4$

$x=1$

b) $\frac{x}{6}-\frac{2-x}{4}=\frac{x}{3}+1$

$\frac{x}{6}-(\frac{2}{4}+\frac{-x}{4})=\frac{x}{3}+1$

$\frac{x}{6}-(\frac{2}{4}-\frac{x}{4})=\frac{x}{3}+1$

$\frac{x}{6}-\frac{2}{4}+\frac{x}{4}=\frac{x}{3}+1$

$\frac{x}{6}+\frac{x}{4}=\frac{x}{3}+1+\frac{2}{4}$

$\frac{x}{6}+\frac{x}{4}-\frac{x}{3}=1+\frac{2}{4}$

$\frac{x}{6}\cdot 12+\frac{x}{4}\cdot 12-\frac{x}{3}\cdot 12=1\cdot 12+\frac{2}{4}\cdot 12$

$x\cdot 2+x\cdot 3-x\cdot 4=12+2\cdot 3$

$x=18$