To solve this equation, we need to fill in the blanks with the appropriate mathematical sign (either +, -, x, or ÷) to make the equation true.

The equation consists of three fractions: 7/4, 19/7, and 17/14, and the answer we are trying to reach is 1/4.



To solve this equation, we need to follow the order of operations, which is typically remembered using the acronym PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

In this equation, there are no parentheses or exponents, so we will move straight to multiplication and division.



We need to determine whether we should multiply or divide the fractions. To do this, we need to compare the numerators and denominators of each fraction.

Comparing the first two fractions, 7/4 and 19/7, we can see that the numerator of the first fraction (7) is smaller than the numerator of the second fraction (19), while the denominator of the first fraction (4) is larger than the denominator of the second fraction (7).

This means that we need to multiply these two fractions to make them equal, which gives us:

7/4 x 19/7 = 133/28

Comparing the third fraction, 17/14, with the result of the first multiplication, 133/28, we can see that the numerator of the second fraction (133) is larger than the numerator of the third fraction (17), while the denominator of the second fraction (28) is larger than the denominator of the third fraction (14).

This means that we need to multiply the second fraction (133/28) by the third fraction (17/14), which gives us:

133/28 x 17/14 = 491/98

After this multiplication, we are left with the equation:

7/4 __ 19/7 __ 491/98 = 1/4

Now, we need to determine whether we should add or subtract the fractions to reach the answer.



To determine whether we should add or subtract the fractions, we can simplify them so that they have a common denominator.

Looking at the fractions in the equation, we can see that the denominators are all multiples of 4. Therefore, we can convert each fraction to have a denominator of 4 by multiplying the numerator and denominator by the appropriate factor.

7/4 can stay the same since its denominator is already 4. Multiplying 19/7 by 4/4 gives us 76/28, and multiplying 491/98 by 2/2 gives us 491/196.

Our equation now looks like this:

7/4 __ 76/28 __ 491/196 = 1/4

To add or subtract fractions

+ , - , × , ÷