Answer: 1
Step-by-step explanation: 1 Find the Least Common Denominator (LCD) of \frac{1}{4}, \frac{1}{3}, \frac{1}{6}, \frac{1}{8}, \frac{1}{8}
4
1
,
3
1
,
6
1
,
8
1
,
8
1
.
Method 1: By Listing Multiples
List out all multiples of each denominator, and find the first common one.
Multiples of 4 : 4, 8, 12, 16, 20, 24, ...
Multiples of 3 : 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 6 : 6, 12, 18, 24, ...
Multiples of 8 : 8, 16, 24, ...
Multiples of 8 : 8, 16, 24, ...
Therefore, the LCD is 2424.
Method 2: By Prime Factors
List all prime factors of each denominator, and find the union of these primes.
Prime Factors of 4 : 2, 2
Prime Factors of 3 : 3
Prime Factors of 6 : 2, 3
Prime Factors of 8 : 2, 2, 2
Prime Factors of 8 : 2, 2, 2
Therefore, the LCD is 2\times 2\times 2\times 3=242×2×2×3=24.
LCD = 2424
2 Make the denominators the same as the LCD.
\frac{1\times 6}{4\times 6}+\frac{1\times 8}{3\times 8}+\frac{1\times 4}{6\times 4}+\frac{1\times 3}{8\times 3}+\frac{1\times 3}{8\times 3}
4×6
1×6
+
3×8
1×8
+
6×4
1×4
+
8×3
1×3
+
8×3
1×3
3 Simplify. Denominators are now the same.
\frac{6}{24}+\frac{8}{24}+\frac{4}{24}+\frac{3}{24}+\frac{3}{24}
24
6
+
24
8
+
24
4
+
24
3
+
24
3
4 Join the denominators.
\frac{6+8+4+3+3}{24}
24
6+8+4+3+3
5 Simplify.
\frac{24}{24}
24
24
6. Cancel 2/4 2/4.=
1
