Video: Using the Order of Operations to Evaluate an Expression Including Decimals

Calculate ((3.4 + 9.2)/(4.2)) − 0.3 × 2.

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Video Transcript

Calculate 3.4 plus 9.2 divided by 4.2 minus 0.3 multiplied by two.

In order to answer this question, we need to recall our order of operations, often referred to by the acronym PEMDAS. The letters refer to parentheses, exponents, multiplication, division, addition, and subtraction. The pairs of multiplication and division, along with addition and subtraction, have equal priority. This means that if we have two or more of either of these, we work from left to right. In some locations, instead of PEMDAS, we use BIDMAS, where B stands for brackets, I for indices, and the division and multiplication are reversed.

The first fractional part of our calculation is referred to as a grouping. We simplify this at the same time as any parentheses. In a fractional grouping, we evaluate all of the numerator and all of the denominator before performing the division. We begin by simplifying the numerator, 3.4 plus 9.2, which is equal to 12.6. We could work this out using column addition if required. The calculation simplifies to 12.6 divided by 4.2 minus 0.3 multiplied by two. We now have a multiplication and division calculation. We need to divide 12.6 by 4.2 and multiply 0.3 by two.

At this point, we would usually work from left to right. However, in this case, we can work out both calculations at the same time. We might notice that 12.6 is three times as big as 4.2. So 12.6 divided by 4.2 is three. An alternative method would be to multiply the numerator and denominator of the fraction by 10. This would give us an equivalent fraction of 126 over 42. We could simplify this by dividing the numerator and denominator by two. This gives us 63 over 21.

We could continue to simplify this fraction or just divide 63 by 21, giving us an answer of three. 0.3 multiplied by two is equal to 0.6, as three multiplied by two is six. We have one digit after the decimal point in the question. So there must be one digit after the decimal point in the answer. Our calculation simplifies to three minus 0.6. Our final step is to work out this calculation, which gives us an answer of 2.4. 3.4 plus 9.2 divided by 4.2 minus 0.3 multiplied by two is equal to 2.4.

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