Insert three rational numbers between 19 and 29.
Step 1: The first step is to write the numbers a and b in the p/q form.
Say: Since 1/9 and 2/9 are already in the p/q form, we need not perform any conversion. We can just take it as it is.
a = 1/9, b = 2/9 >
Step 2: Now, the next step is to make the denominators equal by taking their LCM. But since our denominators are already equal, we can skip that part.
Step 3: We need to multiply the numerator and denominator of both numbers by (n+1), where n is the number of rationals we need to find. Since we need to find 3 rational numbers, n + 1 = 4. Hence we need to multiply both numbers by 4. On multiplying both numbers by 4, we get
1/9 = 4/(4
9) = 4/36,
2/9 = (24)/(49) = 8/36 >
Now the final step is to simply insert the required rational numbers by looking at the numerators. Here, we need to insert 3 rational numbers between 4/36 and 8/36. Here, the numerators are 4 and 8. So, the required numbers would be,
5/36, 6/36 and 7/36
Step 1: The first step is to write the numbers a and b in the p/q form.
Say: Since 1/9 and 2/9 are already in the p/q form, we need not perform any conversion. We can just take it as it is.
a = 1/9, b = 2/9 >
Step 2: Now, the next step is to make the denominators equal by taking their LCM. But since our denominators are already equal, we can skip that part.
Step 3: We need to multiply the numerator and denominator of both numbers by (n+1), where n is the number of rationals we need to find. Since we need to find 3 rational numbers, n + 1 = 4. Hence we need to multiply both numbers by 4. On multiplying both numbers by 4, we get
1/9 = 4/(4
9) = 4/36,
2/9 = (24)/(49) = 8/36 >
Now the final step is to simply insert the required rational numbers by looking at the numerators. Here, we need to insert 3 rational numbers between 4/36 and 8/36. Here, the numerators are 4 and 8. So, the required numbers would be,
5/36, 6/36 and 7/36
