Answer:
The two pieces together make a length of [tex]\frac{20}{24}[/tex] yard are [tex]\frac{3}{6}[/tex] and [tex]\frac{1}{3}[/tex].
Step-by-step explanation:
Given : Mary has three lengths of cable, [tex]\frac{3}{6}[/tex] yard, [tex]\frac{1}{4}[/tex] yard long ,and [tex]\frac{1}{3}[/tex] yard long.
To find : Which two pieces together make a length of [tex]\frac{20}{24}[/tex] yard?
Solution :
First we convert the denominator of cable into 24.
Cable 1 - [tex]\frac{3}{6}[/tex] multiply the numerator and denominator by 4,
[tex]\frac{3}{6}=\frac{3\times 4}{6\times 4}=\frac{12}{24}[/tex]
Cable 2 - [tex]\frac{1}{4}[/tex] multiply the numerator and denominator by 6,
[tex]\frac{1}{4}=\frac{1\times 6}{4\times 6}=\frac{6}{24}[/tex]
Cable 3 - [tex]\frac{1}{3}[/tex] multiply the numerator and denominator by 8,
[tex]\frac{1}{3}=\frac{1\times 8}{3\times 8}=\frac{8}{24}[/tex]
Now, we see that on adding which two numerator we get sum 20.
i.e. 12+8=20
So, we add cable 1 and cable 3
As [tex]\frac{12}{24}+\frac{8}{24}=\frac{12+8}{24}=\frac{20}{24}[/tex]
Therefore, the two pieces together make a length of [tex]\frac{20}{24}[/tex] yard are [tex]\frac{3}{6}[/tex] and [tex]\frac{1}{3}[/tex].
