Topic 1 Review

Topic 1 Review

Vocabulary Review

Use page 6 in your workbook to help you with the following questions.

Multiple Choice

A decimal that ends is a(n) _.

• additive inverse

• complex fraction

• terminating decimal

• repeating decimal

Multiple Choice

Two numbers that have a sum of 0 are _.

• additive inverses

• complex fractions

• terminating decimals

• repeating decimals

Multiple Choice

A _ is a fraction $$\frac{a}{b}$$ where a and/or b are fractions and b is not equal to 0.

• additive inverse

• complex fraction

• terminating decimal

• repeating decimal

Lesson 1-1 Review

Quick Review

Integers are the counting numbers, their opposties, and 0. Opposite integers are the same distance from 0 in opposite directions. Opposite quantities combine to make 0.

The descent of her climb is represented by -3. She has to climb 3 miles to return to her starting point.

A climber descends 3 miles into a canyon. What integer represents the descent of her climb? How far does she have to climb to return to her starting point?

Example

Lesson 1-2 Review

Quick Review

All rational numbers have an equivalent decimal form. The decimal equivalent will be either a terminating decimal or a repeating decimal. A terminating decimal ends in repeating zeros. A repeating decimal has a never-ending pattern of the same digits.

Example

Multiple Select

Which fractions have a decimal equivalent that is a repeating decimal. If possible, select all that apply.

• $$\frac{13}{65}$$

• $$\frac{141}{47}$$

• $$\frac{11}{12}$$

• $$\frac{19}{3}$$

Lesson 1-3

Quick Review

To add integers with the same sign, add the absolute value of each integer. The sign of the sum will be the same as the sign of the addends. To add integers with different signs, find the difference of the absolute value of each integer. The sign of the sum will be the same as the sign of the greater addend.

Example

Multiple Choice

Stella walks down a flight of stairs to the basement. Then she walks back up the stairs and up another flight of stairs to the second floor of her house. Each flight of stairs represents a change of 12 feet in height. How far is Stella above the ground?

• 0 ft

• -12 ft

• 12 ft

• 24 ft

Find the sum for each of the following

Multiple Choice

$$64+\left(-15\right)=$$

• 49

• -49

• 79

• -79

Multiple Choice

$$-121+\left(-34\right)=$$

• 155

• -155

• -87

• 87

Multiple Choice

$$-86+92=$$

• 178

• -178

• -6

• 6

Multiple Choice

$$109+\left(-162\right)=$$

• -271

• 271

• -53

• 53

Lesson 1-4 Review

Quick Review

To subtract integers, use the additive inverse to write an equivalent addition expression. Then follow the rules for addition. When the signs are the same, find the sum of the absolute values. When the signs are different, find the difference. Use the sign of the number with the greater absolute value.

Example

Find the difference for each of the following

Multiple Choice

$$82-\left(-14\right)=$$

• 96

• -96

• 68

• -68

Multiple Choice

$$-18-\left(-55\right)=$$

• -73

• 73

• 37

• -37

Multiple Choice

$$-17-44=$$

• -27

• 27

• -61

• 61

Multiple Choice

$$70-\left(-101\right)=$$

• 171

• -171

• -31

• 31

Lesson 1-5 Review

Quick Review

Positive and negative rational numbers and decimals can be added and subtracted following the same rules as adding and subtracting integers.

Example

Find the sum or difference for each of the following problems.

Lesson 1-6

Quick Review

Multiply integers the same way you multiply whole numbers. If the signs of the factors are the same, the product is positive. If the signs of the factors are different, the product is negative.

Multiply integers the same way you multiply whole numbers. If the signs of the factors are the same, the product is positive. If the sign of the factors are different, the product is negative.

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Lesson 1-6 Review

Multiple Select

Which expressions have a product of -18? If possible, select all that apply

• $$-2\cdot-9$$

• $$-6\cdot3$$

• $$-3\cdot6$$

• $$-9\cdot2$$

The same rules for multiplying integers apply to multiplying rational numbers. If the signs of the factors are the same, the product will be positive. If the signs of the factors are different, the product will be negative.

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Lesson 1-7 Review

Divide integers the same way you divide whole numbers. The quotient is positive if the signs of the dividend and divisor are the same. The quotient is negative if the signs of the dividend and divisor are different.

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Lesson 1-8 Review

Multiple Select

Which expressions have a quotient of -4? If possible, select all that apply.

• $$\frac{-24}{6}$$

• $$-36\div-9$$

• $$-72\div18$$

• $$\frac{84}{-21}$$

The same rules for dividing integers apply to dividing all rational numbers. The quotient is positive when the numbers being divided have the same signs. The quotient is negative when the numbers being divided have different signs. Complex fractions have a fraction in the numerator, the denominator, or both. To divide a fraction, rewrite as multiplication by its multiplicative inverse, or reciprocal.

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Lesson 1-9 Review

Lesson 1-10 Review

Quick Review

You can use rational numbers to solve problems in the same way that you use whole numbers. Be sure to make sense of the problem you are solving to help you choose the correct operations and determine which values will be positive and which will be negative.

Example