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Algebra I – Signed Numbers Fractions and Percents

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    Study Guide Algebra I – Signed Numbers Frac Ɵ ons and Percents 1. Signed Numbers (Posi Ɵ ve Numbers and Nega Ɵ ve Numbers) What Are Signed Numbers? Signed numbers are numbers that have either a positive (+) sign or a negative ( − ) sign. • A positive number is greater than zero. • A negative number is less than zero. If a number does not show a sign , it is automatically considered positive . Example +5 → positive number − 3 → negative number 7 → positive (because no sign is written) Understanding Number Lines A number line helps us see how numbers are ordered. • Numbers to the right of 0 are positive . • Numbers to the left of 0 are negative . This makes it easy to compare numbers. Figure 1. A number line using integers.

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    Study Guide Important Idea On a number line: • The number farther to the right is always larger . • The number farther to the left is smaller . Example • +2 is greater than +1 • − 1 is greater than − 3 (because − 1 is to the right of − 3) Fractions on a Number Line Fractions can also be placed on a number line. For example: These fractions appear between whole numbers depending on their values. Figure 2. A number line using fractions. Addition of Signed Numbers Now let's learn how to add positive and negative numbers .

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    Study Guide There are two situations to remember. 1. Adding Numbers with the Same Sign If both numbers have the same sign (both positive or both negative): Step 1 Add their absolute values . The absolute value means the number without its sign . Step 2 Keep the same sign . Example 1 +5 + (+7) Step 1: Add the absolute values 5 + 7 = 12 Step 2: Keep the positive sign Answer: +12 Example 2 − 8 + ( − 3)

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    Study Guide Step 1: Add the absolute values 8 + 3 = 11 Step 2: Keep the negative sign Answer: − 11 2. Adding Numbers with Different Signs If one number is positive and the other is negative : Step 1 Subtract the smaller absolute value from the larger absolute value . Step 2 Keep the sign of the number with the larger absolute value . Example +7 + ( − 4) Step 1: Subtract absolute values 7 − 4 = 3 Step 2: The larger absolute value is 7 (positive) Answer: +3 How Addition Problems Can Be Written Addition of signed numbers can appear in two forms: Vertical Form Numbers are written one under the other . Example:

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    Study Guide Horizontal Form Numbers are written side by side . Example: +5 + (+7) = +12 Both forms give the same answer . Example 2 Add the following numbers. We are adding a positive number and a negative number . When the signs are different, follow these steps. Step 1: Compare the absolute values Absolute value means the number without its sign .

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    Study Guide 5 and 7 Step 2: Subtract the smaller value from the larger value 7 − 5 = 2 Step 3: Keep the sign of the number with the larger absolute value Since 7 is larger and it is negative ( − 7) , the answer will be negative. Final Answer +5 + ( − 7) = − 2 Another Example − 59 + (+72) Step 1: Compare the absolute values 59 and 72 Step 2: Subtract the smaller value from the larger value 72 − 59 = 13 Step 3: Keep the sign of the number with the larger absolute value 72 is positive, so the result is positive. Final Answer − 59 + (+72) = +13 Example 3 Add the following numbers.

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    Study Guide Solve each problem using the rules for adding signed numbers. 1. +9 + (+6) 2. Both numbers are positive. 3. Add the values. 9 + 6 = 15 2. − 12 + 9 3. The signs are different. 4. Subtract the absolute values. 12 − 9 = 3 The larger absolute value is 12 , which is negative. Answer: − 3 3. − ( − 5) 4. A double negative becomes positive. Answer: +5

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    Study Guide 4. 23 + ( − 18) 5. Different signs. 23 − 18 = 5 The larger absolute value is 23 , which is positive. Answer: +5 5. 15 Answer: 15 6. 3 Answer: 3 7. 3 Answer: 3 8. 5 Answer: 5 Subtraction of Signed Numbers Subtracting signed numbers is actually very simple. Key Rule To subtract a number, change its sign and then add .

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    Study Guide This means subtraction can be turned into an addition problem . Example 7 − ( − 3) Step 1: Change the sign of − 3 to +3 7 + 3 Step 2: Add the numbers 7 + 3 = 10 Another Example 8 − (+5) Step 1: Change the sign of +5 to − 5 8 + ( − 5) Step 2: Add the numbers 8 − 5 = 3 Subtracting and Working with Signed Numbers When you subtract numbers that have positive (+) or negative ( − ) signs, it helps to remember one important rule: Subtracting a number is the same as adding its opposite. So: This simple idea makes signed number problems much easier.

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    Study Guide Example 4: Subtract the Following Problem Step 1: Change subtraction to addition Subtracting (+4) is the same as adding ( − 4) . Step 2: Add the numbers So, Another Example Start with: Change subtraction to addition: Now add:

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