Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 27, 2023

Convert -39.825 to a mixed number.

STEP 1

Assumptions1. The number given is -39.825. We need to express this as a mixed number, which is a combination of a whole number and a proper fraction.

STEP 2

First, we need to separate the whole number part from the decimal part. $Whole\, number\, part = -39$ $Decimal\, part = -0.825$

STEP 3

Next, we need to express the decimal part as a fraction. The decimal part is three places to the right of the decimal point, so we can write it over1000.
$Decimal\, part\, as\, fraction = -0.825 = -\frac{825}{1000}$

STEP 4

implify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it.
$GCD\, of\,825\, and\,1000 =25$ $implified\, fraction = -\frac{825}{25} / \frac{1000}{25} = -\frac{33}{40}$

STEP 5

Now, we can write the original number as a mixed number by combining the whole number part and the fraction part.
$Mixed\, number = Whole\, number\, part + Fraction\, part$

STEP 6

Plug in the values for the whole number part and the fraction part to write the mixed number.
$Mixed\, number = -39 - \frac{33}{40}$ The mixed number representation of -39.825 is -39 and33/40.

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