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. This is also called the Least Common Multiple (LCM).
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 3: 3,
6, 9...
* Multiples of 6:
6, 12...
* The smallest number they share 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 number they share is 12.
*
LCD = 12
c) $\frac{5}{8}$ and $\frac{4}{9}$
* Denominators are 8 and 9.
* Since 8 and 9 have 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 number they share is 18.
*
LCD = 18
e) $\frac{2}{3}$ and $\frac{1}{8}$
* Denominators are 3 and 8.
* They have 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 3 goes into 6 evenly ($3 \times 2 = 6$), 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 2 goes into 4 evenly ($2 \times 2 = 4$), the larger number is the LCD.
*
LCD = 4
i) $\frac{3}{10}$ and $\frac{1}{5}$
* Denominators are 10 and 5.
* Since 5 goes into 10 evenly ($5 \times 2 = 10$), 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 number they share is 40.
*
LCD = 40
k) $\frac{1}{6}$ and $\frac{2}{4}$
* Denominators are 6 and 4.
* Multiples of 4: 4, 8,
12...
* Multiples of 6: 6,
12...
* The smallest number they share is 12.
*
LCD = 12
l) $\frac{8}{9}$ and $\frac{2}{3}$
* Denominators are 9 and 3.
* Since 3 goes into 9 evenly ($3 \times 3 = 9$), 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 finding the least common denominator fractions worksheet.
