Question Video: Evaluating the Difference between Rational Numbers Mathematics • 7th Grade

Video Transcript

Evaluate one twelfth minus negative one-third minus 0.75, giving the answer as a fraction in its simplest form.

In this question, we are asked to evaluate an expression involving the difference of rational numbers. We want to give our answer as a fraction in its simplest form.

To answer this question, we can start by recalling that in order to add and subtract fractions, we want their denominators to be equal. In general, we have 𝑎 over 𝑐 plus 𝑏 over 𝑐 is equal to 𝑎 plus 𝑏 over 𝑐. And 𝑎 over 𝑐 minus 𝑏 over 𝑐 is equal to 𝑎 minus 𝑏 over 𝑐. In other words, we can add or subtract fractions with the same denominator by adding or subtracting their numerators. We can use this to evaluate the expression by rewriting each rational number as a fraction with the same denominator.

Let’s start by rewriting 0.75 as a fraction. We can recall that 0.25 is one-quarter. So we can multiply this by three to see that three-quarters is 0.75. Next, we can simplify the expression we want to evaluate by recalling that subtracting a negative number is the same as adding the positive value. So we obtain one twelfth plus one-third minus three-quarters.

We now want to rewrite all of the fractions so that they have the same denominator. To do this, we need to find the lowest common multiple of the denominators. We can start by noting that the lowest common multiple of 12 and three is 12, since 12 is a multiple of three. Similarly, we can note that 12 is a multiple of four. So the lowest common multiple of the denominators is 12.

Therefore, we want to rewrite each fraction to have a denominator of 12. We note that the first fraction already has this denominator. We can multiply the numerator and denominator of the second fraction by four and the numerator and denominator of the third fraction by three so that they are equivalent fractions with denominators equal to 12.

We can now evaluate each of the products. Remember, we want the denominators to be equal to 12. We get one twelfth plus four twelfths minus nine twelfths.

Now that the denominators are equal, we can add and subtract all of the fractions by adding and subtracting their numerators. We obtain one plus four minus nine all over 12. We can then calculate that one plus four minus nine is negative four. So we get negative four over 12. Remember, we need to give our answer as simplified as possible. We can cancel the shared factor of four in the numerator and denominator to get negative one-third. We cannot simplify this fraction any further. Hence, one twelfth minus negative one-third minus 0.75 is equal to negative one-third.