For the given expression, this means evaluating the quotient before finally adding.
- 0.42Ă· 0.8+0.2Let's divide!
- 0.42Ă· 0.8
The calculations are easier if we multiply the divisor and the dividend by the same power of 10 so that the divisor is a whole number. In this case, we will multiply by 10.
- 0.42* 10 &= - 4.2
0.8* 10 &= 8
This means that - 0.42Ă· 0.8 is the same as - 4.2Ă· 8. Next, recall that when dividing real numbers, the quotient will be positive if the signs are the same and it will be negative if the signs are different.
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Same Sign & Different Signs
(+)Ă· (+)=(+) & (+)Ă· (-)=(-)
(-)Ă· (-)=(+) & (-)Ă· (+)=(-)
In our case one number is positive and one number is negative, so the quotient will be negative.
- 4.2Ă· 8=- (4.2Ă· 8)
Let's find the quotient! We will divide, multiply, subtract, and compare as many times as we need.
Since 4.2Ă· 8=0.525, we know that 0.42Ă· 0.8=0.525. This means that - (0.42Ă· 0.8)=- 0.525. With this in mind, we can continue with our addition!
- 0.42Ă· 0.8+0.2 = - 0.525+0.2
Now, we can find the sum of two numbers with different signs. We can do so by subtracting the lesser absolute value from the greater absolute value. Then, we will use the sign of the number with the greater absolute value. First, we can calculate the absolute value of the numbers.
| - 0.525|=0.525and| 0.2|=0.2
Notice that | - 0.525| is greater than | 0.2|. This means that we should subtract | 0.2| from | - 0.525|. Let's do it!
