Question Video: Simplifying an Expression by Combining Like Terms | Nagwa Question Video: Simplifying an Expression by Combining Like Terms | Nagwa

# Question Video: Simplifying an Expression by Combining Like Terms Mathematics • First Year of Preparatory School

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In the diagram, 𝑏 is the quantity of water in a full bottle and 𝑔 is that in a full glass. The total quantity of water in the diagram can be expressed as 𝑏 + 𝑔 + 𝑔 + (1/2 𝑏) + (3/4 𝑏). Simplify this expression.

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### Video Transcript

In the following diagram, 𝑏 is the quantity of water in a full bottle and 𝑔 is that in a full glass. The total quantity of water in the diagram can be expressed as 𝑏 plus 𝑔 plus 𝑔 plus one-half 𝑏 plus three-fourths 𝑏. Simplify this expression.

In this question, we have been given an expression for the quantity of water, and we need to simplify it.

We notice in this expression that there are some like terms, that is, that there are terms with the same variable raised to the same power. We have 𝑏, one-half 𝑏, and three-fourths 𝑏, which are all like terms, and the two terms of 𝑔, which are also like terms. We can rewrite our expression to move the like terms next to one another and also emphasize that 𝑏 is equal to one times 𝑏 and 𝑔 is equal to one times 𝑔.

Next, we add together the coefficients of the like terms. We have one plus one-half plus three-fourths 𝑏 plus one plus one 𝑔. We must be careful, since we have a whole number, a half, and fourths in the coefficient of 𝑏. We can convert all of these values to fourths to make the calculation easier. In terms of fourths, the coefficient of 𝑏 is four-fourths plus two-fourths plus three-fourths. Simplifying these coefficients, we have that the expression is equal to nine-fourths 𝑏 plus two 𝑔.

By writing the coefficient of 𝑏 as a mixed number, we reach our solution, which is that the simplified expression for the total quantity of water is two and a fourth 𝑏 plus two 𝑔.

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