DeSean has 36 rocks
Further explanation
Fraction numbers are known as numerator and denominator
On a number line, fractions are expressed in points that lie between two integers
The general form of fractions is
[tex]\large{\boxed{\bold{\frac{a}{b}} }[/tex]
a = numerator
b = denominator
Mixed fractions consist of whole number and ordinary fractions
There are a number of steps in adding fraction operations
- 1. the denominators must be the same, if not then
a. Multiply top and bottom of each fraction by the denominator of the other. or
b. we can use Least Common Denominator is
the smallest of all the common denominators.
- 2: Add the numerators and put over the denominator
DeSean is Sorting his rock collection [tex]\frac{2}{3}[/tex] are metamorphic, [tex]\frac{3}{4}[/tex] of the remainder are igneous rock and 3 rocks left over are sedimentary
Let x = total rock
- [tex]\frac{2}{3}[/tex] are metamorphic
we translate this sentence into equation
[tex]\displaystyle metamorphic=\frac{2}{3}x[/tex],
- [tex]\frac{3}{4}[/tex] of the remainder are igneous rock
we translate this sentence into equation
[tex]\displaystyle igneous rock=\frac{3}{4}\times\frac{1}{3}x[/tex],
so total of Dean's rock:
[tex]\displaystyle x=\frac{2}{3}x+\frac{3}{4}\times\frac{1}{3}x +3[/tex]
Because the denominator is not the same, so we can use both multiplying or least common denominator.
let we use least common denominator:
List multiples of 3: 3, 6, 9, 12, 15, 18, 21...
List multiples of 12: 12,24,36 ...
the smallest number that is the same: = 12
then addition operation becomes :
[tex]\displaystyle x=\frac{8}{12}x+\frac{3}{12}x +3[/tex]
[tex]\displaystyle x=\frac{11}{12}x+3[/tex]
[tex]\displaystyle \frac{1}{12}x=3[/tex]
[tex]\displaystyle \large{\boxed{\bold{x=36}}}[/tex]
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Keywords : rock collection, fractions addition,metamorphic,igneous rocks
