You are given three expressions: negative 𝑥 plus 𝑦, 𝑥𝑦, and 𝑥 divided by 𝑦. When 𝑥 equals negative three and 𝑦 equals negative seven, which expression has the largest value? You must show your working.
We’re told that 𝑥 is equal to negative three. And 𝑦 is equal to negative seven. Before starting this question, it is worth remembering that when multiplying or dividing two negative numbers, we get a positive answer. Also when two negative signs are touching or we’re subtracting a negative number, our answer becomes positive. We will now substitute our values of 𝑥 and 𝑦 into the three expressions.
The first expression is negative 𝑥 plus 𝑦. Substituting in our values gives us negative negative three plus negative seven. Adding a negative number is the same as subtracting. So in the bracket, we need to subtract seven from negative three. This is equal to negative 10.
If we consider a number line, subtracting seven from negative three takes us down to negative 10. As mentioned earlier, subtracting a negative number or two negatives touching each other turns into a positive. This means that negative of negative 10 is equal to 10. The first expression, negative 𝑥 plus 𝑦, gives us an answer of 10 when 𝑥 equals negative three and 𝑦 equals negative seven.
The second expression, 𝑥𝑦, means 𝑥 multiplied by 𝑦. In this case, we need to multiply negative three by negative seven. Two negative numbers multiplied together make a positive number. And three multiplied by seven is equal to 21. Therefore, negative three multiplied by negative seven is also equal to 21.
Finally, we have 𝑥 divided by 𝑦. This is equal to negative three divided by negative seven. When dividing two negative numbers, the answer is also positive. This means that negative three divided by negative seven is equal to three-sevenths. We now have three values for our expressions, 10, 21, and three-sevenths. All three are positive. And the largest number is 21. And the smallest number is three-sevenths.
We can therefore conclude that when 𝑥 is equal to negative three and 𝑦 is equal to negative seven, the expression which has the largest value is 𝑥𝑦.