Add and subtract rational numbers

Learning Objectives Identify rational numbers expressed as terminating or repeating decimals. Add positive and negative decimals using appropriate rules for signs. Subtract positive and negative decimals by converting subtraction to addition of the opposite. Accurately align decimal points when performing addition and subtraction. Solve real-world problems involving the addition and subtraction of rational numbers in decimal form. Estimate sums and differences of decimals to check for reasonableness. Ever wondered how stores calculate your change or how meteorologists track temperature changes? 🌡️ It all involves adding and subtracting numbers, including those with decimals! In this lesson, you'll learn how to confidently add and subtract rational numbers when they are...

TermDefinitionExample Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. Decimals that terminate or repeat are rational numbers.$0.5$ (which is $\frac{1}{2}$), $-3.25$ (which is $-\frac{13}{4}$), $0.333...$ (which is $\frac{1}{3}$) DecimalA number that uses a decimal point to represent parts of a whole, based on powers of ten.$7.25$, $-0.8$, $123.456$ Terminating DecimalA decimal that has a finite number of digits after the decimal point.$0.75$, $-2.5$, $14.001$ Repeating DecimalA decimal that has a digit or a block of digits that repeats infinitely after the decimal point.$0.333...$ (written as $0.\overline{3}$), $1.272727...$ (written as $1.\overline{27}$) Absolute ValueThe distance of a number from zero on the number...

Adding Decimals with the Same Sign If $a$ and $b$ have the same sign, then $a + b = \pm(|a| + |b|)$ Add their absolute values. The sum will have the same sign as the original decimals. Remember to align decimal points. Adding Decimals with Different Signs If $a$ and $b$ have different signs, then $a + b = \text{sign of larger absolute value } (||a| - |b||)$ Subtract the smaller absolute value from the larger absolute value. The sum will have the sign of the decimal with the larger absolute value. Align decimal points. Subtracting Decimals $a - b = a + (-b)$ To subtract a decimal, add its additive inverse (its opposite). Then follow the rules for adding decimals. Decimal Point Alignment Rule When adding or subtracting decimals, always align the decimal points ve...