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MATH 009 JIM DAWSON

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1.1 WHOLE NUMBERS Memorize the place values from ones(units) through trillions to see the pattern. Write 26,709 in standard form: Twenty-six thousand seven hundred nine

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**Write five thousand forty-four in standard form.**

5,044 Write 200,493 in expanded form. 200,

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**1.4 MULYIPLYING WHOLE NUMBERS**

Memorize the multiplication table up to 12 x 12. Factors- numbers that are multiplied together to equal a PRODUCT( the answer to a multiplication problem).

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**1.5 DIVISION OF WHOLE NUMBERS**

Division is used to separate objects into equal groups. Quotient- the answer to a division problem. Most mistakes in division are made in the subtraction portion.

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1.6 EXPONENTS Base- the number being multiplied. Exponent- the number to the top right of the base telling you how many times the number by itself.

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**ORDER OF OPERATIONS AGREEMENT**

Do all operations inside parentheses( other grouping symbols as well) Solve exponents Multiply and divide as they occur from left to right

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PEMDAS Add and subtract as they occur from left to right 5 x (8-4)-2; 8-4=4 5 x 4 – 2; 5 x 4=20 20-2=18

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1.7 PRIME FACTORING Questions(steps) Is the number prime? Yes- prime No – prime factor the number and move to question #2.

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**#2- is the number an even number? Yes- start with 2**

N0- go to question #3 Add the digits of the number together, if the answer is divisible by 3-Yes- start with 3

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No- go to question #4 Does the number end with a 5? Yes- start with 5 N0- start with 7 and continue until a prime number works ( hit or miss).

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2.1 FINDING THE LCM AND GCF LCM- Least Common Multiple Factor the numbers and place them in a chart. Circle the largest product of each set of numbers( prime numbers).

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LCM AND GCF Multiply the numbers( the answer will be equal to or greater than the largest number given).

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GCF GCF- Greatest Common Factor Factor the numbers and place the answer in a chart Circle the smallest product in each set of numbers that are in common.

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2.2 CONVERTING FRACTIONS Conversion #1- to change an improper fraction to a mixed number or whole number. Numerator divided by the denominator and write the remainder as a fraction.

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CONVERTING FRACTIONS Conversion #2- convert a mixed number or whole number to an improper fraction. Multiply the whole number times the denominator and add the numerator. The denominator stays the same.

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**CONVERTING FRACTIONS Conversion #3- Building equivalent fractions.**

Divide the new denominator by the original denominator and multiply the answer by the original numerator to place the fraction in higher terms.

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CONVERTING FRACTIONS Conversion #4- Simplest form or Reducing fractions. Prime factor the numerator and denominator then cancel the common numbers. Multiply the top and bottom to finish reducing.

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2.4 ADDITION OF FRACTIONS Find the LCM(LCD) of the denominators. Use the LCM process, if needed. Place the fractions in higher terms (conv. # 3).

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ADDITION Add the numerators ONLY. Place the answer in simplest form by using conversions # 1 and/or #4. You may use one , both, or neither. Add the whole numbers.

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**2.5 SUBTRACTION OF FRACTIONS**

Find the LCM(LCD) of the denominators. Use the LCM process, if needed. Place the fractions in higher terms.

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SUBTRACTION Subtract the numerators, borrow if needed. Reduce , if needed. Subtract the whole numbers.

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**2.6 MULTIPLYING FRACTIONS**

Change the mixed nos. or whole nos. to improper fractions. Early reducing ( cross-cancel) Multiply numerators and denominators. Change improper to mixed nos.

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2.7 DIVISION OF FRACTIONS Change mixed nos. or whole nos. to improper fractions. Change division to multiplication and invert the fraction after the divided by symbol.

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DIVISION Early-reducing(cross-cancel) Multiply numerators and denominators Change an improper fraction to a mixed no. and reduce the proper fraction

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**Order, Exponents, Order of Operations**

Order using the inequality symbols Find the common denominators Place the fractions in higher terms.

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Order continued 3. Compare the numerators and place the correct inequality symbol in the answer.

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Fractional Exponents Write the original problem out and use the steps for multiplying fractions. Cross-cancel and multiply the numerators and the denominators.

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Order Relation To compare two fractions with different denominators; find the common denominator, place the fractions in higher terms, then compare the numerators and place the correct inequality symbol between the fractions.

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Order of Operations Use PEMDAS the same way as Chapter 1.

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Combining Like Terms Combine the terms that have the same variable part using the steps for addition and subtraction of fractions.

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**Solving for the Unknown**

If the variable and fraction are connected by addition use subtraction in both sides of the equation to solve the unknown. If they are connected by subtraction use addition on both sides to solve. If the variable and unknown are connected by multiplication use division on both sides.

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Decimal Notation Standard Form: To write a decimal as a number( the place values tenths through hundred-billionths MUST be memorized). Standard Form to Words: To write a decimal from a number to words. Rounding: Find the place value being rounded and look ONE place to the right and use the same rules for rounding whole numbers.

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**Addition and Subtraction of Decimals**

Add and subtract decimals just the same as whole numbers and place the decimal point in the answer.

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Multiplying Decimals Count the total number of place values in all of the numbers. Set the problem up like whole numbers and multiply. Move the decimal point from right to left in the answer.

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Division of Decimals Make the divisor a whole number by moving the decimal point. Move the decimal point the same number of places on the dividend. Divide the same as whole numbers.

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**Converting a Fraction to a Decimal**

To change a fraction to a decimal: NUMERATOR divided by the DENOMINATOR. Round if asked to in the directions or the answer will terminate.

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**Change a Decimal to a Fraction**

Write the decimal as a fraction by using a multiple of 10 in the denominator and the number part in the numerator. Reduce the answer if possible.

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**Change a Decimal with a Fraction to a Fraction**

Drop the decimal point and multiply the mixed number times 1 over 100.

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Ratios and Rates Ratio- A comparison of two quantities with the same units( apples to apples…etc.) Write the ratio as a fraction in simplest form(reduce) then with a colon (: ) and the word ( to ). Rate- A comparison of two quantities that different units( apples to oranges…etc.) Write as a fraction and reduce then STOP!

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Unit Rates Unit Rate- A comparison of two quantities that have different units per 1. Write the unit rate as a rate(fraction) then divide: NUMERATOR divided by the DENOMINATOR. This will make the answer per 1. Label the answer.

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**Proportions Proving the proportion True or Not True.**

Cross-multiply: If the answers are the same it is a True (T) proportion. If the answers are not the same it is a Not True (NT) proportion. Solve for n: Cross-multiply the common numbers and divide the number across from n.

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More Proportions Word problems: Write the two rates with like units in both numerators and like units in both denominators. Cross-multiply and divide the number across from n.

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**Converting Between Fractions, Decimals, and Percents**

Change a percent to a decimal (then to a fraction). Move the decimal point TWO places from left to right and drop the percent symbol. Multiply by 0.01. Change the decimal to a fraction and reduce if needed.

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**Change a Decimal to a Percent**

To change a decimal: Move the decimal point TWO places from left to right or multiply by 100%. If the decimal has a fraction move the decimal point TWO places from left to right and drop the decimal point.

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**Change a Fraction to a Percent**

Change the fraction to a decimal ( numerator divided by denominator) first. Move the decimal point TWO places from left to right. In the division, if the answer does not terminate by hundredths, write the remainder as a fraction in simplest form.

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**Round to the nearest tenth ( of a percent ).**

Change the fraction to a decimal to the ten-thousandths place value. Move the decimal point TWO places from left to right and round the percent to the nearest tenth of a percent.

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**Change a Percent with a Fraction to a Fraction**

If the percent has a fraction in it: Drop the % symbol and multiply by 1 OVER 100 to convert to a fraction.

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**The Basic Percent Equation**

The basic percent equation is used to solve problems when one of the quantities is missing. Percent x Base = Amount is the basic percent equation. Read the problem and label the equation with P x B = A.

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Solving for the Amount If the Amount is missing: Change the percent to a decimal or a fraction by using the correct conversion process. Multiply the converted percent by the Base and the answer is the Amount.

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**Solving for the Percent**

Read and label the equation. If the Percent is missing: Divide the Base into the Amount and change the answer to a Percent using the proper conversion process. The answer could be written using a fraction after the division process is completed.

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**Solving for the Base Read and label the problem.**

If the Base is missing: Change the percent to a decimal or fraction. Divide the converted Percent into the Amount; the answer will be the Base.

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