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# Business Mathematics Reviewer - 1st Grading ## Basic Concepts - **Fraction:** Refers to a part of a whole. - **Decimal:** Refers to a special form or system of numbers whose base is in the power of ten. - **Percentage:** Refers to a special form of numbers in each hundred, thus it is a num...

# Business Mathematics Reviewer - 1st Grading ## Basic Concepts - **Fraction:** Refers to a part of a whole. - **Decimal:** Refers to a special form or system of numbers whose base is in the power of ten. - **Percentage:** Refers to a special form of numbers in each hundred, thus it is a number’s ratio to 100. ## Conversion 1. **Expressing fractions to decimal:** - Express the fraction to an equivalent fraction whose denominator is a power of 10. Then, express it to a decimal. - Perform the usual long division wherein the numerator is the dividend and the denominator is the divisor. 2. **Expressing mixed fractions to decimal:** - To express mixed fractions to a decimal, divide the numerator by the denominator. Afterward, rewrite the whole number with the quotient. 3. **Expressing decimal to fractions:** - To express decimal to fractions, apply the concept of place value and reduce the said fraction to the lowest term. 4. **Expressing decimal to percent:** - To express a decimal to a percent, move the decimal point two places to the right and affix the percent sign (%). 5. **Expressing fractions to percent:** - To express fractions to percent, change the fraction into a decimal (by performing division) and move the decimal point two places to the right, then put the percent symbol (%). 6. **Expressing percent to decimal:** - A percent which means "per hundred" is a representation of a fraction whose denominator is 100. Thus, expressing a number in percent is like comparing it with 100. - To express percent to decimal, move the decimal point two places to the left (as in dividing by 100 ) and drop the recent sign (%). This is exactly the opposite of what we did when we converted decimal to percent. 7. **Expressing percent to fraction:** - To express percent to a fraction, first change percent to decimal, then change the decimal to a fraction and reduce to lowest terms. ## Ratios - A ratio is a comparison of two quantities with the same unit. - **Odds Notation:** $ a:b$ where the symbol ":" is read as "is to". - **Fractional Notation:** $ \frac{a}{b}, b≠0$ - **Rate:** A ratio that compares quantities of different units. - **Unit Rate:** A rate that has a denominator of 1, that is, a rate for one unit of a given quantity. ## Proportion - A proportion is the relationship between two quantities. It is an equation showing two ratios that are equal. It is a statement that expresses the same relationship between two quantities. ### Types of Proportions - **Direct Proportion:** Has two values that may vary, but the ratio between them remains the same. In this proportion, as one value decreases, the other value also decreases, and as one increases, the other also increases. For quantities a and b, $\frac{a1}{b1} = \frac{a2}{b2}$ - **Inverse Proportion:** Means that an increase in one quantity results into a decrease in another, or, as one quantity decreases, the other increases. For quantities a and b, $\frac{a1}{a2} = \frac{b2}{b1}$ - **Partitive Proportion:** Is when a whole is partitioned to equal or unequal ratios. For ratio a:b:c, $ax: bx: cx = k$ $ax + bx + cx = k$ - Where, a, b, and c are the variables, x is the unknown unit, and k is the given value to be partitioned. - **Note:** To know the partitioned value of each variable, multiply the value of x to each of them. ## Terms related to Proportion - **Base (B):** Refers to a number of which a certain number of hundredths is taken. - It is the basis of comparison. - It is preceded by the words "of", "as much as," "as large as," "as many as" & "as great as". - **Rate (R):** Refers to the number of hundredths taken. - It is expressed in percent, decimal, or fraction. - **Percentage (P):** - Is the part considered in its quantitative relation to the whole. - It is a part of the whole. - **Formula:** $Percentage = Base \times Rate$ ## Terms related to Prices - **Mark-up:** The amount that the seller charges to a product which is over the cost to obtain profit. - **Mark-on:** The price of a product increase after another increase. - **Markdown:** A reduction in the selling price of a product which occurs in response to a certain market condition. ## Terms related to Business - **Selling Price:** the price which the seller put on a certain product or service. - **Cost:** The price paid to obtain or purchase an item. - **Expenses:** The cost of which a business spent on their operation.