find the fractions with common denominators for each pair 3 5and 1 4
3/5 = 6/10 = 9/15 = 12/20 = 15/25
1/4 = 2/8 = 3/12 = 4/16 = 5/20 = 6/24
To find the fractions with a common denominator for each pair, you need to find the least common denominator (LCD) of the two denominators. The LCD is the smallest number that each denominator can evenly divide into.
In this case, the pairs are (3, 5) and (1, 4).
For the first pair, the denominators are 3 and 5. Since these are prime numbers and do not share any common factors, the LCD would be their product: 3 × 5 = 15. So, to convert both fractions to have a denominator of 15, you would multiply the numerator and denominator of each fraction by the appropriate factor:
3/5 = (3 × 3)/(5 × 3) = 9/15
1/4 = (1 × 15)/(4 × 15) = 15/60
Therefore, the fractions with common denominators for the pair (3, 5) are 9/15 and 15/60.
For the second pair, the denominators are 1 and 4. Since 1 is a factor of every number, the LCD would be 4. So, to convert both fractions to have a denominator of 4, you would multiply the numerator and denominator of each fraction by the appropriate factor:
3/5 = (3 × 4)/(5 × 4) = 12/20
1/4 = (1 × 1)/(4 × 1) = 1/4
Therefore, the fractions with common denominators for the pair (1, 4) are 12/20 and 1/4.