REVIEW: FRACTIONS (CHAPTER 4)

A ___________ describes the number of equal parts of a whole.fraction

In a fraction, the number above the ________ ______ is called the ___________, and the number below is called the _______________.

fraction barnumerator

denominator

If the numerator of a fraction is less than its denominator, the fraction is called a _________ __________. If the numerator of a fraction is greater than or equal to its denominator, the fraction is called an __________ __________.

proper fraction

improper fraction

Each of these fractions is a ______ ____ _____: form of 1

Two fractions are __________ if they represent the same number. ____________ ___________ represent the same portion of a whole.

equivalentEquivalent fractions

To ________ ___ __________, we multiply it by a factor equal to 1 in the form of and so on.

build a fraction

A fraction is in _________ _______ , or _______ _____ , when the numerator and denominator have no common factors other than 1.

simplest form lowest terms

_________ fractions are simplified and built up just like numerical fractions.

Algebraic

To __________________ , multiply the numerators and multiply the denominators. Simplify the result, if possible.

multiply two fractions

When a ______________________________, it indicates that we are to find a part of some quantity using multiplication.

fraction is followed by the word of

The formula for the _______ of a triangle is .area

One number is the ___________ of another if their product is 1. reciprocal

To find the ___________ of a fraction, _______ the numerator and denominator.

reciprocal invert

REVIEW: 4.1-4.2

• Simplify each fraction, if possible.

1545

20 𝑥3

48 𝑥2

66108

117𝑎2𝑏6

208𝑎5𝑏

REVIEW: 4.1-4.2

• Multiply and Simplify.

−34∙227

REVIEW: 4.1-4.2

• Exponential Expressions

( 23 )3

−( 35 )2

4.3 DIVISION WITH FRACTIONS

4.8 SOLVING EQUATIONS

𝑥+15=−

1115

34𝑥=

58𝑥+12

3 𝑦−8=0

1101100

11,000

110,000

1100,000

11,000,000

1101001 ,00010,000100,0001 ,000,000 .

To _______________ to a certain decimal place value, locate the rounding digit in that place.

round a decimal

Look at the ________ directly to the right of the rounding digit.test digit

If the test digit is __________ , round up. If it is 4 or less, round down by keeping the rounding digit and dropping all the digits to its right.

5 or greater

SECTION 5.1- ROUNDING TO A CERTAIN PLACE VALUE.

Round 3,706.0815 to the nearest thousandth.

Round -0.0614 to the nearest tenth.

Round 11.314964 to the nearest ten-thousandth.

SECTION 5.2- ADDING AND SUBTRACTING DECIMALS.

Add: 15.82 + 19 + 32.995.

Write the problem in vertical form and add, column by column, working right to left.

Subtract: 8.4 – 3.029.

SECTION 5.2- ADDING AND SUBTRACTING SIGNED DECIMALS.

Use the same rules that are used for adding and subtracting integers.

Add: -21.35 + (-64.52).

Subtract: -8.62 - (-1.4).

SECTION 5.3- MULTIPLYING DECIMAL NUMBERS

Line up the numbers and multiply like whole numbers.

Move the decimal point in the product the number of decimal places in both factors.

2.76 ∙ 4.3

SECTION 5.3- MULTIPLYING SIGNED DECIMAL NUMBERS

Line up the numbers and multiply like whole numbers and follow the rules for multiplying signed integers.

(−0.03)(−4.1)

Move the decimal point in the product the number of decimal places in both factors.

SECTION 5.3- EXPONENTIAL EXPRESSIONS

The base of an exponential expression can be a positive or negative decimal.

¿

¿

SECTION 5.4- DIVIDING DECIMALS

To divide with a decimal divisor:1. Write the problem in long

division form.2. Move the decimal point of

the divisor so that it becomes a whole number.

3. Move the decimal point of the dividend the same number of places to the right.

4. Write a decimal point in the quotient directly above the decimal point in the dividend.

𝐷𝑖𝑣𝑖𝑑𝑒 :1.4623.4

SECTION 5.4- DIVIDING SIGNED DECIMALS

Use the rules for dividing integers. 𝐷𝑖𝑣𝑖𝑑𝑒 :−1.530.3

SECTION 5.4- EVALUATING EXPRESSIONS AND FORMULAS

Use the rules for ________________ to evaluate expressions and formulas.

37.8−(1.2)2

0.1+0.3

order of operations

SECTION 5.5- FRACTIONS AND DECIMALS

To write a fraction as a decimal, _______ the numerator of the fraction by its denominator.

1325

316

divide

SECTION 5.5- REPEATING DECIMALS

If the division process never gives a remainder of zero (____________), we call the resulting decimal a _________ or non-terminating___ decimal.

56

1112

terminatingrepeating

227

SECTION 5.5- MIXED NUMBERS IN DECIMAL FORM

To write a mixed number in decimal form, we need only find the decimal equivalent for the fractional part of the mixed number.

478

¿ 4 .875

1347

SECTION 5.5- COMPARING THE SIZE OF A FRACTION AND DECIMAL

Write the fraction in its equivalent decimal form.

Compare and 0.07.

350

<0.07

SECTION 5.5- EVALUATING EXPRESSIONS THAT CONTAIN BOTH FRACTIONS AND DECIMALS

To evaluate expressions that can contain both fractions and decimals, we can work in terms of decimals or in terms of fractions.

𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 :16+0.31 ≈0.17+0 .31

≈0 .48

SECTION 5.5- HOMEWORK PROBLEMS

Page 510#1, 3, 4, 8, 113, 114, 115, 116

Page 546# 75-94 (all)

1. equivalent 3. terminating 4. repeating 8. terminating 113-116. Discuss as a class

75. 0.875 76. -0.4 77. 0.5625 78. 0.06 79. 0.54 80. -1.3 81. 3.056 82. 0.57 83. 0.5884. 1.03 85. > 86. = 87. 0.3,, 0.3 88. on board 89. 90. 91. 93 92. 7.305 93. 34.88 94. $22.25