Rename a decimal a mixed number

So in this problem, we need to rename 3.5 which is a decimal as a mixed number. So to rename 3.5 as a mix number, we know that 3.5 is equal to 3 which will be your whole number plus .5 which is your decimal. So to rename a decimal as a mixed number let’s use our following steps.

First step is rename the decimal part as a fraction, so we need to turn our decimal into a fraction, we need to rename it. So to do so, we take our decimal which is .5 and we write it as a fraction which will be the right most digit five, we need to look at what place value it is and 5 is in the tenths place value, so it would be 5/10, so when you take the decimal and you move it to a fraction you need look at the right most digit which is five and look to see what place value that is and it’s in the tenths, so the fraction will be 5/10.

Now we’re going to divide 5/10 by the greatest common factor which is five, and so then we get ½. Now, let’s add the whole number, so that’s our second step, we add our whole number. So we know mixed number is the sum of the whole number in the fraction, so we know that 3.5 is equal to 3 + the fraction, the ½. Therefore 3.5 is equal to 3 ½.

Let’s take a look at the second part of this problem. Here its asking us, is the pair of the numbers equivalent. So we have 3 ¼ and 3.5. So to compare the numbers we need to convert the decimal 3.5 into a mix number. So to rename a decimal as a mix number we need to use the following steps. So our step is to rename the decimal part a fraction in simplest form. So now we’re going to take our decimal and rename it into a fraction, and remember we put it in simplest form.

So here we have the decimal which will be .5 so that’s the decimal part of this 3.5 is .5 and rename it, so we look at the right most digit which is five and we have to look at what place value it is and the five is in the tenth place value. So it becomes 5/10, then we divide 5 and 10 by the greatest common factor which is five, and so we get ½. So now we just renamed our decimal into a fraction, .5 equal ½.

Our second step is you add the whole number. So we know a mix number is the sum of the whole number in the fraction. So 3.5 will equal 3 + the fraction which is the ½, so therefore 3.5 is equal to 3 ½.

So now if we compare, 3 ¼ and 3 1/2 , the whole numbers are the same, so we need to compare the fractions. So now we look at ¼ and the 1/2, when the numerators of two or more fractions are the same, the fraction with the smaller numerator is larger. So ¼ is less than ½. So we know that ¼ is less than ½ therefore we know that 3 ¼ is less than 3 ½, therefore to get back to our question, is the pair of numbers equivalent, the pair of numbers are not equivalent because 3 ¼ is less than 3 ½.

Things to keep in mind, to rename a decimal as a mix number remember we first renamed the decimal part as a fraction in simplest form. For example, we’re going to take 2.5, two is the whole number and .5 is the decimal, so then .5 would equal 5/10 which will be ½ in simplest form. Then we add our whole number to the fraction. So after we change our decimal into a fraction we add our whole number, so for this one, we changed .5 into the simplest form ½, so then we add our fraction, so 2.5 would equal 2 plus that ½ which will be 2 ½.