To find the Least Common Denominator (LCD) for two fractions, we need to find the smallest number that both denominators (the bottom numbers) can divide into evenly.
Here is the step-by-step solution for each pair:
a) $\frac{1}{6}$ and $\frac{2}{3}$
* Denominators are 6 and 3.
* Multiples of 6: 6, 12...
* Multiples of 3: 3,
6, 9...
* The smallest common number is 6.
*
LCD = 6
b) $\frac{1}{4}$ and $\frac{5}{6}$
* Denominators are 4 and 6.
* Multiples of 4: 4, 8,
12, 16...
* Multiples of 6: 6,
12, 18...
* The smallest common number is 12.
*
LCD = 12
c) $\frac{5}{8}$ and $\frac{4}{9}$
* Denominators are 8 and 9.
* Since 8 and 9 share no common factors other than 1, we multiply them: $8 \times 9 = 72$.
*
LCD = 72
d) $\frac{1}{6}$ and $\frac{2}{9}$
* Denominators are 6 and 9.
* Multiples of 6: 6, 12,
18, 24...
* Multiples of 9: 9,
18, 27...
* The smallest common number is 18.
*
LCD = 18
e) $\frac{2}{3}$ and $\frac{1}{8}$
* Denominators are 3 and 8.
* They share no common factors, so we multiply them: $3 \times 8 = 24$.
*
LCD = 24
f) $\frac{5}{6}$ and $\frac{2}{3}$
* Denominators are 6 and 3.
* Since 6 is a multiple of 3 ($3 \times 2 = 6$), the larger number is the LCD.
*
LCD = 6
g) $\frac{1}{5}$ and $\frac{2}{3}$
* Denominators are 5 and 3.
* Multiply them: $5 \times 3 = 15$.
*
LCD = 15
h) $\frac{1}{2}$ and $\frac{1}{4}$
* Denominators are 2 and 4.
* Since 4 is a multiple of 2 ($2 \times 2 = 4$), the larger number is the LCD.
*
LCD = 4
i) $\frac{3}{10}$ and $\frac{1}{5}$
* Denominators are 10 and 5.
* Since 10 is a multiple of 5 ($5 \times 2 = 10$), the larger number is the LCD.
*
LCD = 10
j) $\frac{7}{8}$ and $\frac{4}{10}$
* Denominators are 8 and 10.
* Multiples of 8: 8, 16, 24, 32,
40...
* Multiples of 10: 10, 20, 30,
40...
* The smallest common number is 40.
*
LCD = 40
k) $\frac{1}{6}$ and $\frac{2}{4}$
* Denominators are 6 and 4.
* Multiples of 6: 6,
12, 18...
* Multiples of 4: 4, 8,
12, 16...
* The smallest common number is 12.
*
LCD = 12
l) $\frac{8}{9}$ and $\frac{2}{3}$
* Denominators are 9 and 3.
* Since 9 is a multiple of 3 ($3 \times 3 = 9$), the larger number is the LCD.
*
LCD = 9
Final Answer:
a) 6
b) 12
c) 72
d) 18
e) 24
f) 6
g) 15
h) 4
i) 10
j) 40
k) 12
l) 9
Parent Tip: Review the logic above to help your child master the concept of common denominator worksheet 4th grade.
