For instance, if we take the fraction 4/8 and multiply both the numerator and denominator by 2, we get (4×2)/(8×2) = 8/16. These two fractions are equivalent. (4×2)/(8×2) is essentially the same as 4/8 × 2/2 Remember that when multiplying two fractions, we multiply across, meaning numerator to numerator and denominator to denominator. Notice that 2/2 equals 1 when you carry out the division. Thus, it’s easy to see why 4/8 and 8/16 are equivalent since multiplying 4/8 × (2/2) = 4/8 still. The same way it’s fair to say that 4/8 = 8/16. Any given fraction has an infinite number of equivalent fractions. You can multiply the numerator and denominator by any whole number, no matter how large or small to obtain an equivalent fraction.
For instance, let’s look at 4/8 again. If, instead of multiplying, we divide both the numerator and denominator by 2, we get (4 ÷ 2)/(8 ÷ 2) = 2/4. 2 and 4 are both whole numbers, so this equivalent fraction is valid.
For example, take the fractions 4/8 and 8/16 again. The smaller denominator is 8, and we would have to multiply that number x2 in order to make the larger denominator, which is 16. Therefore, the number in this case is 2. [4] X Expert Source David JiaAcademic Tutor Expert Interview. 23 February 2021 For more difficult numbers, you can simply divide the larger denominator by the smaller denominator. In this case 16 divided by 8, which still gets us 2. The number may not always be a whole number. For example, if the denominators were 2 and 7, then the number would be 3. 5.
For instance, if we take the fraction 4/8 from step one and multiply both the numerator and denominator by our previously determined number 2, we get (4×2)/(8×2) = 8/16. Thus proving that these two fractions are equivalent.
For instance, if we take the fraction 4/8 from step one and multiply both the numerator and denominator by our previously determined number 2, we get (4×2)/(8×2) = 8/16. Thus proving that these two fractions are equivalent.
For instance, take our previously used 4/8. The fraction 4/8 is equivalent to saying 4 divided by 8, which 4/8 = 0. 5. You can solve for the other example as well, which is 8/16 = 0. 5. Regardless of the terms of a fraction, they are equivalent if the two numbers are exactly the same when expressed as a decimal. Remember that the decimal expression may go several digits before the lack of equivalence becomes apparent. As a basic example, 1/3 = 0. 333 repeating while 3/10 = 0. 3. By using more than one digit, we see that these two fractions are not equivalent.
For instance, let’s look at 4/8 again. If, instead of multiplying, we divide both the numerator and denominator by 2, we get (4 ÷ 2)/(8 ÷ 2) = 2/4. 2 and 4 are both whole numbers, so this equivalent fraction is valid.
When a fraction is in its simplest terms, its numerator and denominator are both as small as they can be. Neither can be divided by the any whole number to obtain anything smaller. To convert a fraction that’s not in simplest terms to an equivalent form that is, we divide the numerator and denominator by their greatest common factor. The greatest common factor (GCF) of the numerator and denominator is the largest number that divides into both to give a whole number result. So, in our 4/8 example, since 4 is the largest number that divides evenly into both 4 and 8, we would divide the numerator and denominator of our fraction by 4 to get it in simplest terms. (4 ÷ 4)/(8 ÷ 4) = 1/2. For our other example of 8/16, the GCF is 8, which also results in 1/2 as the simplest expression of the fraction.
Take our two examples of 4/8 and 8/16. These two don’t contain a variable, but we can prove the concept since we already know they’re equivalent. By cross multiplying, we get 4 x 16 = 8 x 8, or 64 = 64, which is obviously true. If the two numbers are not the same, then the fractions are not equivalent.
For example, let’s consider the equation 2/x = 10/13. To cross multiply, we multiply 2 by 13 and 10 by x, then set our answers equal to each other: 2 × 13 = 26 10 × x = 10x 10x = 26. From here, getting an answer for our variable is a matter of simple algebra. x = 26/10 = 2. 6, making the initial equivalent fractions 2/2. 6 = 10/13.
For instance, let’s consider the equation ((x + 3)/2) = ((x + 1)/4). In this case, as above, we’ll solve by cross multiplying: (x + 3) × 4 = 4x + 12 (x + 1) × 2 = 2x + 2 2x + 2 = 4x + 12, then we can simplify the equation by subtracting 2x from both sides 2 = 2x + 12, then we should isolate the variable by subtracting 12 from both sides -10 = 2x, and divide by 2 to solve for x -5 = x
For example, let’s look at the equation ((x +1)/3) = (4/(2x - 2)). First, let’s cross multiply: (x + 1) × (2x - 2) = 2x2 + 2x -2x - 2 = 2x2 - 2 4 × 3 = 12 2x2 - 2 = 12.
Some values may equal 0. Though 2x2 - 14 = 0 is the simplest form of our equation, the true quadratic equation is 2x2 + 0x + (-14) = 0. It will probably help early on to mirror the form of the quadratic equation even when some values are 0.
x = (-b +/- √(b2 - 4ac))/2a. In our equation, 2x2 - 14 = 0, a = 2, b = 0, and c = -14. x = (-0 +/- √(02 - 4(2)(-14)))/2(2) x = (+/- √( 0 - -112))/2(2) x = (+/- √(112))/2(2) x = (+/- 10. 58/4) x = +/- 2. 64
To convert to an improper fraction, multiply the whole number component of the mixed number by the denominator of the fractional component and then add it to the numerator. For example, 1 2/3 = ((1 × 3) + 2)/3 = 5/3. Then, if desired, you can convert as needed. For instance, 5/3 × 2/2 = 10/6, which is still equivalent to 1 2/3. However, we don’t have to convert to an improper fraction as above. If we don’t, we ignore the whole number component, convert the fractional component alone, then add the whole number component back in unchanged. For instance, for 3 4/16, we’ll just look at 4/16. 4/16 ÷ 4/4 = 1/4. So, adding our whole number component back in, we get a new mixed number, 3 1/4.
