Number Foundations

${\displaystyle \frac{3}{4}}\times 100\mathrm{\%}=75\mathrm{\%}$.

$0.2={\displaystyle \frac{2}{10}}={\displaystyle \frac{1}{5}}$.

$0.15\times 80=12$.

${\displaystyle \frac{3}{5}}=0.6$ and $58\mathrm{\%}=0.58$.

Since $0.6>0.58>0.55$, the largest is ${\displaystyle \frac{3}{5}}$.

$24=2^3\cdot 3$ and $36=2^2\cdot 3^2$.

Shared primes at their lowest powers: $2^2$ and $3$.

$\text{HCF}=4\cdot 3=12$.

$6=2\cdot 3$ and $8=2^3$.

Highest powers: $2^3$ and $3$.

$\text{LCM}=8\cdot 3=24$.

$51=3\cdot 17$, $57=3\cdot 19$, $63=7\cdot 9$.

$59$ has no factor up to $\sqrt{59}<8$, so $59$ is prime.

$60=2\cdot 30=2\cdot 2\cdot 15=2^2\cdot 3\cdot 5$.

$3\times 4=12$, then $2+12=14$.

$(5+1{)}^2=6^2=36$, then $36÷4=9$.