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0-3: Operations with Integers

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Page 1: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-3: Operations with Integers

Page 2: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-3: Operations with Integers

You can use a number line to add integers Example 1: Use a number line to find -3 + (-4)

Start at 0 Negative numbers move left Positive numbers move right

Resulting position

0 1 2 3 4 5 6 7 8 9 100–1–2–3–4–5–6–7–8–9–10

-3-4

Page 3: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-3: Operations with Integers

When the signs of two integers are the same Add the two integers together, and keep their sign

3 + 5 = 8 -3 + (-5) = -8

When the signs of two integers are different Subtract the smaller integer from the larger, and keep

the sign of the larger 3 + (-5) = -2 -3 + 5 = 2

Page 4: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-3: Operations with Integers

Integers can also be multiplied and dividedWhen the signs of two integers are the same

The product/quotient is positive 3(5) = 15 -3(-5) = 15

When the signs of two integers are different The product/quotient is negative

3(-5) = -15 -3(5) = -15

Page 5: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

Page 6: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

You can use different methods to compare rational numbers. One way is to compare two fractions with common denominators. A second is to compare as decimals

Example 1: Replace ? with <, >, or = to make 2/3 ? 5/6 a true sentence

Common denominator The common denominator of 3 & 6 is 6 2/3 = 4/6

5/6 = 5/6

Since 4 < 5, 2/3 < 5/6

Page 7: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

Example 1: Replace ? with <, >, or = to make 2/3 ? 5/6 a true sentence

Write as decimals 2/3 = 0.666666666667

5/6 = 0.833333333333

Since 0.6 < 0.8, 2/3 < 5/6

Page 8: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

When fractions have the same denominator, simply add or subtract the numerator.

Remember to simplify, if possible Find each sum or difference

3/5 + 1/5

4/5

7/16 – 1/16

6/16 = 3/8

4/9 – 7/9

-3/9 = -1/3

Page 9: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

When fractions have unlike denominators, find the least common denominator.

Convert each fraction using the least common denominator, then add or subtract

Simplify, if possible. Find each sum or difference

1/2 + 2/3

3/6 + 4/6 = 7/6

3/8 – 1/3

9/24 – 8/24 = 1/24

2/5 – 3/4

8/20 – 15/20 = -7/20

Page 10: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

To subtract a negative number, change it to adding its inverse (opposite)

When dealing with decimals, use the rules about adding/subtracting integers from earlier. (Repeated here as a reminder)

When the signs of two decimals are the same Add the two decimals together, and keep their sign

When the signs of two decimals are different Subtract the smaller from the larger, and keep the sign

of the larger

Page 11: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

Find each sum or difference -13.12 + (-8.6)

-21.72 -32.25 – (-42.5)

-32.25 + 42.5 10.25

Page 12: 0-3: Operations with Integers. You can use a number line to add integers Example 1: Use a number line to find -3 + (-4) Start at 0 Negative numbers

0-4: Adding and Subtracting Rational Numbers

Assignment Page P16

1 – 39 (odds)


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