Find the value of 𝑥 plus 𝑧 given 𝑥 equals two-thirds and 𝑧 equals one-half.
We want to add 𝑥 and 𝑧 together. 𝑥 equals two-thirds and 𝑧 equals one-half.
If we want to add fractions together, the first step is finding a common denominator. We need a number that’s divisible by both three and two. Six is divisible by both three and two. Three times two equals six and two times three equals six.
And we remember that if we multiply the denominator by something, we have to multiply the numerator by the same amount to keep our fractions equivalent. So we multiply the numerator two times two which equals four. And for the fraction one-half, we need to multiply one times three which equals three. We now have two equivalent fractions with common denominators.
Our next step is to add the numerators together. Four plus three equals seven. And the denominator doesn’t change. It stays six. Four-sixths plus three-sixths equals seven-sixths. And that means two-thirds plus one-half equals seven-sixths.
𝑥 plus 𝑧 equals seven-sixths.