Video: Subtraction of Rational Numbers into Simplest Form

Evaluate (7/4) − (−1/2), giving the answer in its simplest form.

04:56

Video Transcript

Evaluate seven-fourths minus negative one-half, giving the answer in its simplest form.

We have the expression seven over four minus negative one over two. We recognize that both of these values are fractions. However, they do not have the same denominator. And we know in order to add or subtract fractions, we need to first find a common denominator. We’re looking for the least common multiple between two and four, sometimes called the LCM. If we think about multiples of two, we have two, four, and six. But four is already a multiple of two. And that means the least common multiple of two and four will be four.

We won’t make any changes to seven-fourths, but we’ll rewrite negative one-half as a fraction with the denominator of four. Two times two is four. And negative one times two is negative two. This means our new expression will be seven-fourths minus negative two-fourths. We also remember that when we’re subtracting a negative value, we can rewrite that as addition. So, seven-fourths minus negative two-fourths is equal to seven-fourths plus two-fourths.

Once we have fractions with a common denominator, we add them together by adding their numerators. Seven plus two is nine. And the denominator doesn’t change. Seven- fourths plus two-fourths is equal to nine-fourths. We wanna give this answer in simplest form. And that means we want to check and see if there are any common factors in the numerator and the denominator. Nine and four don’t share any common factors apart from one. And that makes the fraction nine-fourths in its simplest form.

In our final question, we’ll put all these skills together as we subtract values in three different formats.

Evaluate five twelfths minus negative one-third minus 0.75.

In this expression, we have fractions with uncommon denominators and we have a decimal value. In order to do this subtraction, we’ll need all three of these values in the same format. And that means we’ll need to rewrite each of these values as fractions with common denominators. Before we deal with common denominators, let’s start with our decimal value and write it as a fraction.

0.75 has a five in the hundredths place, which means, as a fraction, 0.75 can be written as 75 over 100. But both 75 and 100 are divisible by 25. 75 divided by 25 equals three, and 100 divided by 25 equals four. Seventy-five hundredths equals three-fourths. It’s also possible that this is a value you already know. It’s a common decimal and a common fraction. Seventy-five hundredths equals three-fourths.

Our new expression is then five-twelfths minus negative one-third minus three-fourths. And we need a common denominator from 12, three, and four. To find this common denominator, we want the least common multiple. If we list the multiples of three, we have three, six, nine, 12, 15. We do the same thing for four, where we have four, eight, 12, and 16. At this point, we recognize that 12 is a multiple of both three and four. And that means 12 will be the least common multiple between these three values.

We then want to rewrite all of these fractions with the denominator of 12. Five twelfths remains the same. At this point, we can also say that subtracting negative one-third is the same thing as adding. If we want to write one-third as a fraction with the denominator of 12, we need to multiply it by four over four. And then, to rewrite the fraction three-fourths with the denominator of 12, we multiply the numerator and the denominator by three, which means our new expression will be five twelfths plus four twelfths minus nine twelfths.

Once we have common denominators, we can add and subtract by just adding and subtracting the numerators. And the denominator wouldn’t change. So, we have five plus four minus nine over 12. Five plus four is nine, and nine minus nine is zero. Zero twelfths equals zero. And that means five twelfths minus negative one-third minus 0.75 equals zero.

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