Answer:
To find the least common denominator (LCD) of
1
5
5
1
and
4
15
15
4
, we can use the following steps:
Step 1: Find the prime factorization of each denominator.
5
=
5
15
=
3
⋅
5
5=5
15=3⋅5
Step 2: Identify the common and uncommon prime factors.
The common prime factor is 5, and the uncommon prime factor is 3.
Step 3: Multiply the common and uncommon prime factors to get the LCD.
�
�
�
=
3
⋅
5
=
15
LCD=3⋅5=15
Therefore, the LCD of
1
5
5
1
and
4
15
15
4
is 151.
To convert
1
5
5
1
and
4
15
15
4
to fractions with a common denominator of 15, we need to multiply the numerator and denominator of
1
5
5
1
by 3, and the numerator and denominator of
4
15
15
4
by 1:
1
5
⋅
3
3
=
3
15
4
15
⋅
1
1
=
4
15
5
1
⋅
3
3
=
15
3
15
4
⋅
1
1
=
15
4
Now that both fractions have the same denominator, we can add them:
3
15
+
4
15
=
7
15
15
3
+
15
4
=
15
7
Therefore, the sum of
1
5
5
1
and
4
15
15
4
with a common denominator of 15 is
7
15
15
7
2.