Question Video: Evaluating Numerical Expressions Involving Exponents and Fractions Mathematics • 6th Grade

Given that 𝑥 = 3/4 and 𝑦 =− 2/5, find the value of (𝑥 + 𝑦)².


Video Transcript

Given that 𝑥 is equal to three-quarters and 𝑦 is equal to negative two-fifths, find the value of 𝑥 plus 𝑦 all squared.

In this question, we are given the values of two rational numbers 𝑥 and 𝑦 and asked to use these values to evaluate the expression 𝑥 plus 𝑦 all squared.

To do this, we first need to substitute the given values of 𝑥 and 𝑦 into the expression. This gives us three-quarters plus negative two-fifths all squared.

We can recall the order of operations by using the acronym PEMDAS. The P means that we start with expressions inside the parentheses. And we can see that we have three-quarters plus negative two-fifths inside the parentheses. We can then recall that adding a negative number is the same as subtracting the positive of that number. So we can rewrite the expression as three-quarters minus two-fifths all squared.

We still need to evaluate the operation inside the parentheses. And since this is a subtraction of rational numbers, we need them to have the same denominator. We can note that the lowest common multiple of the denominators is 20. We can rewrite three-quarters as 15 over 20 by multiplying its numerator and denominator by five. And we can rewrite two-fifths as eight over 20 by multiplying its numerator and denominator by four. This gives us 15 over 20 minus eight over 20 all squared.

We can now evaluate the subtraction by recalling that we can subtract fractions with the same denominator by finding the difference in their numerators. In general, we have that 𝑎 over 𝑐 minus 𝑏 over 𝑐 is equal to 𝑎 minus 𝑏 all over 𝑐, provided that 𝑐 is nonzero. Since 15 minus eight is equal to seven, our expression simplifies to be seven over 20 all squared.

We now need to evaluate the square of a rational number. And we can do this by recalling that we can square a rational number by squaring its numerator and denominator separately. In general, we have that 𝑎 over 𝑏 all squared is equal to 𝑎 squared over 𝑏 squared provided that 𝑏 is nonzero. Applying this result with 𝑎 equal to seven and 𝑏 equal to 20 gives us seven squared over 20 squared.

Finally, we can calculate that seven squared is seven times seven, which is equal to 49, and 20 squared is 20 times 20, which is equal to 400, giving us 49 over 400. We cannot simplify this any further. So we have shown that 𝑥 plus 𝑦 all squared will be equal to 49 over 400.

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