Find the value of 𝑥 plus 𝑦 divided by 𝑧, given 𝑥 is equal to negative seven-quarters, 𝑦 is equal to five-thirds, and 𝑧 is equal to two.
We will begin by adding the fractions 𝑥 and 𝑦, negative seven over four or negative seven-quarters and five over three or five-thirds. Note that we can consider either the new numerator or denominator of the negative fraction to be negative, but not both. When adding or subtracting any two fractions, we firstly need to find a common denominator. In this case, the lowest common multiple of four and three is 12.
We have multiplied the denominator of the first fraction by three. This means we need to do the same to the numerator. Negative seven multiplied by three is negative 21. We have multiplied the denominator of the second fraction by four, as three multiplied by four is equal to 12. Multiplying the numerator by four gives us 20. The calculation negative seven over four plus five over three could be rewritten as negative 21 over 12 plus 20 over 12.
Our final step is to add the numerators. Negative 21 plus 20 equals negative one. The denominator stays the same. So 𝑥 plus 𝑦 is equal to negative one twelfth. The second step of this calculation is to divide by 𝑧. We need to divide negative one twelfth by two. Dividing any number by two is the same as multiplying by one-half.
We need to multiply negative one twelfth by one-half. Recalling that multiplying a negative number by a positive gives us a negative answer, then negative one twelfth multiplied by a half is equal to negative one over 24. The value of 𝑥 plus 𝑦 divided by 𝑧 is negative one over 24 or negative one twenty-fourth.