Video: Finding an Unknown in a Given Equation Using the Commutative Property

Find the missing term in the equation ( −1/3) × (2/9) = _ × (−1/3).

02:05

Video Transcript

Find the missing term in the equation negative one-third multiplied by two-ninths is equal to something multiplied by negative one-third.

In order to answer this question, we need to remember the commutative property of multiplication. This states that 𝑎 multiplied by 𝑏 is equal to 𝑏 multiplied by 𝑎. For example, five multiplied by seven is equal to 35. And, seven multiplied by five is also equal to 35. It doesn’t matter which order we multiply two terms. The answer will still be the same.

In this particular question, we have negative one-third on both sides of the equation. Multiplying negative one-third by two-ninths must give us the same answer as multiplying two-ninths by negative one-third. We can therefore conclude that the missing term in the equation is two-ninths.

We could check this by firstly multiplying the two fractions on the left-hand side and then the two fractions on the right-hand side. In order to multiply two fractions, we multiply the two numerators, and then separately, the two denominators. Negative one multiplied by two is equal to negative two. And, three multiplied by nine is equal to 27. This means that negative one-third multiplied by two-ninths is equal to negative two over 27. Multiplying the two fractions, two-ninths and negative one-third, in the opposite order also gives us an answer of negative two over 27. This proves that we did have the correct missing term of two-ninths.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.