Choose the steps that you could use to subtract a negative fraction from a positive decimal? Select all that apply.
A. Subtract the absolute value of the decimal.
B. Convert both numbers into fraction form.
C. Convert both numbers into decimal form.
D. Add the negative number to the positive number.
E. Add the opposite of the negative number to the positive number.
The Correct Answer and Explanation is:
The correct steps to subtract a negative fraction from a positive decimal are:
B. Convert both numbers into fraction form.
E. Add the opposite of the negative number to the positive number.
Explanation:
When you’re tasked with subtracting a negative fraction from a positive decimal, the goal is to perform the operation in a way that simplifies the process. Let’s break down the options:
- A. Subtract the absolute value of the decimal – This option is incorrect because the absolute value of the decimal represents its positive magnitude. Subtracting the absolute value would not give the correct result when dealing with a negative fraction. The correct approach involves working directly with both numbers’ signs.
- B. Convert both numbers into fraction form – This option is correct. Converting both the positive decimal and the negative fraction into fractions is a valid approach. To subtract fractions, they need to have a common denominator. So, converting a decimal to a fraction (such as turning 0.5 into 1/2) allows you to align both numbers in the same form and carry out the subtraction. This approach is useful for maintaining accuracy and ensuring correct results.
- C. Convert both numbers into decimal form – This option is not ideal in this context. While decimals can be directly added or subtracted, working with fractions often provides clearer steps when one of the numbers is already in fractional form. Additionally, when subtracting a negative fraction, dealing with the numbers as fractions makes it easier to handle the negative sign.
- D. Add the negative number to the positive number – This option is incorrect. Subtracting a negative number is equivalent to adding its positive counterpart. However, in this context, you’re not just adding the negative fraction directly; you need to account for the fact that subtracting a negative fraction changes the operation to addition.
- E. Add the opposite of the negative number to the positive number – This option is correct. Subtracting a negative number is mathematically equivalent to adding the positive of that number (its opposite). This makes the operation simpler. For example, subtracting -1/2 from 0.75 is the same as adding 1/2 to 0.75.
In conclusion, the best approach is to convert both numbers into fractions and then add the opposite of the negative fraction to the positive number, which makes the operation easier to manage and ensures the result is accurate.