Question Video: Evaluating an Algebraic Expression Involving Rational Numbers | Nagwa Question Video: Evaluating an Algebraic Expression Involving Rational Numbers | Nagwa

# Question Video: Evaluating an Algebraic Expression Involving Rational Numbers Mathematics • First Year of Preparatory School

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If 𝑥 = 2 1/3, 𝑦 = 3/4, and 𝑧 = 0.7, evaluate 𝑥𝑧 − 𝑦.

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### Video Transcript

If 𝑥 is equal to two and one-third, 𝑦 is equal to three-quarters, and 𝑧 is equal to 0.7, evaluate 𝑥 times 𝑧 minus 𝑦.

In this question, we are asked to evaluate an expression involving the product and difference of rational numbers. We could do this by using a calculator. However, it is useful to be able to solve these problems without a calculator.

When applying operations to rational numbers, it is a good idea to have the numbers in the same form, since this is the easiest way to combine them. In general, it is easiest to multiply rational numbers written as fractions. So we can rewrite 𝑥 and 𝑧 as fractions. We have that 𝑥 is equal to seven-thirds and 𝑧 is equal to seven-tenths.

We can now substitute our values for 𝑥, 𝑦, and 𝑧 into the expression to obtain seven-thirds times seven-tenths minus three-quarters. This is the expression that we need to evaluate. We can evaluate this expression by first recalling that we evaluate the product before the subtraction and that we can multiply two fractions by multiplying their numerators and denominators separately. In general, we have that 𝑎 over 𝑏 times 𝑐 over 𝑑 is equal to 𝑎𝑐 over 𝑏𝑑.

Therefore, we can rewrite our expression as seven times seven over three times 10 minus three-quarters. We can then evaluate the products in the numerator and denominator to obtain 49 over 30 minus three-quarters.

To subtract two fractions, we need their denominators to be equal. We can note that the lowest common multiple of 30 and four is 60. We can rewrite both fractions to have a denominator of 60. We multiply the numerator and denominator of the first fraction by two and the numerator and denominator of the second fraction by 15. Therefore, we have 98 over 60 minus 45 over 60.

Since the denominators of the two fractions are now the same, we can subtract the numerators to get 53 over 60. We cannot simplify this fraction since the greatest common factor of the numerator and denominator is one. So we leave our answer as 53 over 60.

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