Question Video: Subtraction of Rational Numbers into Simplest Form Mathematics • 7th Grade

Calculate (7 1/4) − (4 5/8). Give your answer as a mixed number.


Video Transcript

Calculate seven and one-fourth minus four and five-eighths. Give your answer as a mixed number.

When we look at the expression seven and one-fourth minus four and five-eighths, they’re both mixed numbers. However, the fraction portion of the mixed numbers do not have a common denominator. And we know in order to work with these values, we need them to be in the same format. Since we’re dealing with denominators four and eight and we know that four is a factor of eight, four times two equals eight, which means we could rewrite one-fourth as two-eighths. Once we do that, we have seven and two-eighths minus four and five-eighths.

However, we’re still not quite ready to subtract because we’re trying to take five-eighths from two-eighths. And that means that for our first mixed number seven and two-eighths, we need to borrow from the whole number portion. If we take one whole away from seven, we leave six. And that whole value that we took away is equal to the fraction eight-eighths. If we add two-eighths plus eight-eighths, we get ten-eighths. The mixed number six and ten-eighths is the same value as seven and one-fourth written in a different format.

Now, we’re ready to subtract, six and ten-eighths minus four and five-eighths. To subtract the fraction portion, since we have common denominators, we’ll say 10 minus five. That is, we’re subtracting the values of the numerator. And the denominator isn’t changing. Ten-eighths minus five-eighths equals five-eighths. And then, we subtract the whole number portions. Six minus four equals two, giving us the result of two and five-eighths. Five-eighths can’t be simplified any further. Two and five-eighths is a mixed number and is our final answer.

So far, we’ve only been calculating values that are already given in the same format. In our next example, we’ll have to find the difference between a decimal and a fraction.

Find the difference between negative 0.85 and two-fifths giving your answer as a fraction in its simplest form.

The difference between negative 0.85 and two-fifths can be written as negative 0.85 minus two-fifths. But once we get to this point, we have a problem. And that is that our two values are given in different formats, which means we have a choice to make. We can convert two-fifths to a decimal so that we’re subtracting a decimal from a decimal. Or we can convert negative 0.85 into a fraction so that we’re subtracting a fraction from a fraction. Both methods will work, but we’ve been told to give the answer as a fraction in its simplest form. And that means it’s probably worth it to subtract a fraction from a fraction.

And that means we need to think about how we would write negative 0.85 as a fraction. Since the five in negative 0.85 is in the hundredths place, we say that this is negative eighty-five hundredths. And as a fraction that is negative 85 over 100. But before we move on, we might want to see if we can simplify eighty-five hundredths. Both 85 and 100 are divisible by five. Negative 85 divided by five equals negative 17, and 100 divided by five equals 20, which means we’re trying to say negative 17 over 20 minus two-fifths.

However, we now see that we don’t have common denominators in our two fractions. But we know that five times four equals 20. And that means we can multiply two-fifths by four over four. Two times four is eight, and five times four is 20. We now have negative seventeen twentieths minus eight twentieths. Since we have common denominators, we can do subtraction by subtracting the numerators, which will be negative 17 minus eight. The denominator doesn’t change. That remains 20. Negative 17 minus eight will be equal to the negative value of 17 plus eight. That’s negative 25.

So, we have negative 25 over 20. Both of these values are divisible by five. Negative 25 divided by five equals negative five. 20 divided by five equals four. And this means negative 0.85 minus two-fifths is equal to negative five-fourths.

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