What dose lowest terms mean

Mathematics

2 answers:

Phoenix [80]3 years ago

7 0

That's the description of a fraction when the numerator and denominator
don't have any common factor except '1' .

Reil [10]3 years ago

7 0

Lowest terms basically means that the fraction/ mixed number is in simplest form. Which means it can't be divided by anything to get a lower number for both the numerator and denominator because they don't have anymore factors that they share. For example, if I wanted to simplify the fraction, 4/8. I would divide by 4 on both the top and bottom since that is their greatest common factor.
4 ➗ 4=1
8 ➗4=2
1/2 would be the "lowest terms" of 4/8 since 1 and 2 don't have any common factors except 1.

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$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

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Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$