You already know how to work with positive decimals using various combinations of operations. Now we will use and extend this knowledge by looking at questions that involve negative decimals.
Last year you learned the rules for adding, subtracting, multiplying, and dividing decimals. Review those rules here:
Next, remember the rules for when you add, subtract, multiply or divide with integers:
Now we will put all of these rules together to complete operations on positive and negative decimals.
Evaluate $3.4+\left(5.2\right)$3.4+(−5.2)
Think: To evaluate a decimal sum, line up the decimals and perform the operation. Adding a negative number moves left on the number line, so can be rewritten as subtraction. $3.4+\left(5.2\right)=3.45.2$3.4+(−5.2)=3.4−5.2. More importantly, we should notice that the answer must be negative as we are subtracting a larger number from a smaller one.
We will actually find $\left(5.23.4\right)$−(5.2−3.4).
Do:
$5$5  .  $2$2 


$$−  $3$3  .  $4$4 
(Rewrite in vertical form with the decimal points lined up) 
$1$1  .  $8$8 
(Perform the subtraction) 
So this means that $3.4+\left(5.2\right)=1.8$3.4+(−5.2)=−1.8
Reflect: Round these decimals to the nearest whole number and estimate the solution. How does your estimate compare with the actual solution?
Evaluate: $5.4\times\left(3.6\right)$−5.4×(−3.6)
Think: There are two numbers after the decimals in this problem, so our product will have two values to the right of its decimal point. The product of two negative numbers will be positive.
Do: $5.4\times\left(3.6\right)=19.44$−5.4×(−3.6)=19.44
Reflect: Suppose the second number were $3.60$−3.60. Would this change your final answer?
Evaluate: $\left(6.3\right)\div0.15$(−6.3)÷0.15
Think: The quotient of a negative number and a positive number will be negative. We will need to multiply by ten times ten, moving the decimal point twice, because there are two values after the decimal in our divisor.
Do:
$\left(6.3\right)\div0.15$(−6.3)÷0.15 


$=6.3\div0.15$=−6.3÷0.15  $\left[\times10\text{ }\times10\right]$[×10 ×10] 
(Multiply the divisor by two powers of ten) 
$=630\div15$=−630÷15 
(Do to the dividend exactly what we did to the divisor) 

$=42$=−42 
(Perform the division) 
Reflect: Is this answer the same as the solution to $\left(63\right)\div1.5$(−63)÷1.5?
Evaluate $8.5+\left(4.1\right)$8.5+(−4.1).
Evaluate $7.4\times\left(4.1\right)$7.4×(−4.1).
Evaluate $9.3\left(2.2\right)$−9.3−(−2.2)
Jenny takes out a loan of $\$2200$$2200. She pays back $\$42.60$$42.60 each month and doesn't have to pay interest.
If she has made $5$5 repayments so far, how much does Jenny still owe?
Apply and extend previous understandings of operations with fractions to operations with rational numbers.
Apply properties of operations to add and subtract rational numbers, including realworld contexts.
Represent addition and subtraction on a horizontal or vertical number line.
Apply properties of operations to multiply and divide rational numbers, including realworld contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.