Question

Fill in the missing fractions to create a true equation.(1 point)
 ?/5 − 1/2 =  3/?

1 answer

To solve for the missing fractions, we can use algebraic manipulation.

Let's solve for the missing fraction on the left side of the equation first:

Let the missing fraction on the left side be a/b.

a/b - 1/2 = 3/?

To find a common denominator, we multiply the denominators 5 and 2 together, giving us 10:

2a/10 - 5/10 = 3/?

Combining like terms, we get:

(2a - 5)/10 = 3/?

To isolate the missing fraction, we can cross-multiply:

3 * 10 = 2a - 5

30 = 2a - 5

Adding 5 to both sides:

35 = 2a

Dividing by 2:

a = 35/2 = 17.5

So, the missing fraction on the left side is 17.5/10.

Now, let's solve for the missing fraction on the right side of the equation:

17.5/10 - 1/2 = 3/?

To find a common denominator, we multiply the denominators 10 and 2 together, giving us 20:

(17.5)/20 - 10/20 = 3/?

Combining like terms, we get:

(17.5 - 10)/20 = 3/?

Simplifying the numerator:

7.5/20 = 3/?

Now, let's cross-multiply to isolate the missing fraction:

3 * 20 = 7.5

60 = 7.5

Dividing both sides by 7.5:

60/7.5 = 1

So, the missing fraction on the right side is 1/1, which can also be written as 1.

Therefore, the missing fractions to create a true equation are 17.5/10 - 1/2 = 3/1.