Business Math

Business Math
Business mathematics
are mathematics used by commercial enterprises to record and manage business operations.
Commercial organizations use mathematics in accounting, inventory management, marketing,
sales forecasting, and financial analysis.
Percentage
 a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a
hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the
given quantity.
 Examples: 100 % 75% 24% and etc
Fractions
 Two numbers separated by a horizontal or sloping line.
 A fraction represents a part of a whole or, more generally, any number of equal parts
 Ex. Two seventh = 2/7

where as 2 is the Numerator (N) and & 7 is the Denominator (D)
 Type of Fractions
 Proper Fractions
 Proper fractions refer to those fractions where the numerator is smaller than
the denominator. A proper fraction is a part of a whole
 Example: 1/2, 99/100, 67/ 85 and etc
 Improper fractions
 Improper fractions are those fractions where the numerator is greater than the
denominator. They are greater than a whole.
 Example: 4/3, 105/ 75, 58/40 and etc
 Mixed fractions
 When we combine a whole number and a proper fraction together, we get a

mixed fraction.
 Example 2 1/2, 100 99/100, 24 2/8 and etc

Decimal
 In algebra, a decimal number can be defined as a number whose whole number part
and the fractional part is separated by a decimal point. The dot in a decimal number is
called a decimal point. The digits following the decimal point show a value smaller than
one.
 Ex. .59, .75, .58 and etc
Now let’s discuss the fundamental operations in fractions
Converting of Improper Fraction into Mixed Fraction

 Simply divide the numerator by the denominator. If there is a nonzero remainder, write the
remainder over the denominator.
 Change 20/3 convert into mixed number
 20 divided by 3 is 6(your new whole number) remainder 2(your new numerator) and
just copy your old denominator
 Hence, 6 2/3
Converting of Mixed Fraction into Improper Fraction

 To change a mixed number to an improper fraction, multiply the denominator by the
whole number and add the numerator. Write the sum on the numerator over the
denominator to form the improper fraction.
o 6 2/3 convert into improper fraction
o 6 times 3 is 18 plus 2 and equals to 20(your new denominator) and copy yout
denominator
o hence 20/3
ALWAYS EXPRESS YOUR ANSWER IN LOWEST TERM
 A common fraction can be simplified if the numerator and denominator can be divided by
the same number.
 The number is called the greatest common factor.
 When both the numerator and the denominator cannot be divided by the same number,
the fraction is already in its lowest terms.
 Let’s simplify the 9/18
 Find the greatest common factor for 9 and 18 which is 9
 9(Numerator) divided by 9(GCF) is 1 (Your new Numerator)
 18(Denominator) divided by 9(GCF) is 2 (Your new Denominator)
 Hence 1/2
Mathematical Operations of Fractions
Addition of Fractions
To add fractions with like denominators:
o Add the numerators
o The denominator remains the same
o Convert an improper fraction to a mixed number, if necessary
 ¼ + ¾ + ¼ = 5/4 or 1 ¼
Adding fractions with different denominators

o You must first find the lowest common denominator (LCD).
 Least common denominator (LCD), the simplest expression that is
divisible by all of the denominators in all of the expressions.
 For example, the least common denominator for the fractions
2/9 and 5/12 is 36
 because 36 is the smallest positive number divisible by both 9 and
12.
 36(LCD) divided by 12(Denominator) = 3, 3 times 5(Numerator) =
15, hence 15/36
 36 divided by 9(Denominator) = 4, 4 times 2 = 8(Numerator),
hence 8/36
o After Converting the fractions

o Add the numerator and the denominator will remain
 6/7 + 2/5 =?
 30/35 + 14/35 = 44/35
 44/35 or 1 9/35
Adding fractions with Mixed numbers
 convert them to Improper Fractions

 then add them (using Addition of Fractions)
 then convert back to Mixed Fractions
o 2 3/4 + 3 1/2
o 2 3/4 = 11/4 and 3 1/2 = 7/2
o 11/4 stays as 11/4 and 7/2 becomes 14/4 (LCD: 4)
o 11/4 + 14/4 = 25/4
o 25/4 or 6 1/4
Word Problem:
It took Benok 6 hours on the first duty, 5 hours the second shift, and 3 hours the third shift in
mcdobals, How long did Benok work, as a fraction of a 24-hour day?
- 6/24 + 5/24 + 3/24
- 6 + 5 + 3 / 24 = 14 /24 or 7/12
Subtraction of Fractions
Subtract fractions with like denominators:

 Subtract the smaller numerator from the greater one.
 The denominator remains the same.
o 5/8 – 3/8 = 2/8
o Reduce to lowest terms, if necessary.
o 2/8 = 1/4
Subtract fractions with unlike denominators

 Determine the least common denominator (LCD).
 Change each unlike fraction to an equivalent fraction with the LCD.
 Subtract the resulting fractions.
• 7/12 – 1/4 = ?
• LCD is 12
• 7/12 – 3/12 =
• 4/12 or 1/3
Subtracting Fractions from Whole Numbers

 Subtract 1 from the whole number.
 Write 1 as a fraction with the same denominator as the fraction to be subtracted.
 Since these are like fractions, perform subtraction as usual.
o 4 – 6/7 =?
o 3 7/7 – 6/7 =?
o 3 7/7 – 6/7 = 3 1/7
Subtracting Mixed Numbers
 Bring the fractions to improper fractions.
 Proceed to subtraction if the fractions are like.
 Find the LCD if fractions are unlike.
• 5 7/9 – 3 1/3 = ?
• LCD is 9
• 5 7/9 – 3 1/3
• 5 7/9 – 3 3/9 = 2 4/9
• 2 4/9
Word Problem:
 You have 11/12 meter of fabric. You need 5/6 meter for place mat. Will you have enough
left for table napkins that will use 3/4 meter?
 Subtract 5/6 from 11/12
 11/12 – 10/12 = 1/12 meter
 Compare 1/12 and 3/4
 1/12 (Remaining fabric) < 9/12 (Fabric needed for table napkins)
 Since 1/12 < 9/12 there will not be enough material for table napkins.
Multiplication of Fractions
 In multiplying fractions, multiply the numerators to find the numerator of the product.
Multiply the denominators, too, to find the denominator of the product. Then simplify the
product if necessary.
 Example
=3x5
10 6
= 3x5
10x6
= 15
60
=15/15 = 1
60/15 = 4 (Simplify)
Division of Fractions
 In dividing fractions, get the reciprocal (flip the fraction) of the fraction after the division
sign.
 Then, get the product of the first and the reciprocal of the second fraction.
 9÷3½
 9 ÷ 7
1 2
 9x2
1x7
 18
7
 2 4/7
 Word Problem:
Warehouse has 1 Ton of grains for the 8 cities. One of the city received 2/5 of it and the
remaining part will be equally distributed.
How many tons will be distributed to the 5 remaining cities?
 8/8 – 3/8 = 5/8
 5/8 ÷ 7
 5 x 1 = 5 Tons of grains
8 x 7 56
Conversion of FRACTIONS, DECIMALS AND PERCENTAGES
From Percent to Decimal

 To convert from percent to decimal divide by 100 and remove the % sign.
 An easy way to divide by 100 is to move the decimal point 2 places to the left:
From Decimal to Percent

 To convert from decimal to percent multiply by 100%
 An easy way to multiply by 100 is to move the decimal point 2 places to the right:
From Fraction to Decimal
 To convert a fraction to a decimal divide the top number by the bottom number:
 2/5 convert into decimals
From Decimal to Fraction

 First, write down the decimal "over" the number 1: .75/01
 Multiply top and bottom by 10 for every number after the decimal point (10 for 1
number,100 for 2 numbers, etc):
.75 x 100
1 x 100
 This makes a correctly formed fraction: 75/100
 Then Simplify the fraction: 3/4
From Percentage to Fraction

• Remove The Percentage sign and put 100 as the denominator
Example: 125% 125/100
• Simplify the fraction
125/100 divide N and D by GCF (25)
= 5/4 or 1 1/4
C. Activity:
Solve the following problems.
1. Aling Purita bought 3/4 kilo of kasim, 1 1/2 kilos of chicken, and 12/8 kilo of chicken liver

for her adobo. How many kilograms of meat does her adobo have?
2. Chocolate crinkles calls for 2 3/4 cups of confectioner sugar for a serving. How many cups of
sugar is needed for eight servings?
3. Cynthia practices playing the violin 2 1/5 hours each week. How many weeks will it take for
her to cover 35 hours of practice?
4. A Batangueño who is studying in Manila budgets his weekly allowance. He spends 2/5 of his
allowance on food,7/10 on school supplies, 1/10 on transportation, then he saves the rest. If
his allowance is ₱2,500, how much does he spend on each? How much does he save?
5. A potter needs 3 1/6 pounds of clay for a vase. How many vases can be made from 28 pounds
of clay?
FRACTION DECIMAL PERCENT

85/2
650%
1.6
200%
47/5

Business Math

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Business Math

 Examples: 100 % 75% 24% and etc

 Ex. Two seventh = 2/7

 Example: 1/2, 99/100, 67/ 85 and etc

 Example: 4/3, 105/ 75, 58/40 and etc

 When we combine a whole number and a proper fraction together, we get a

 Example 2 1/2, 100 99/100, 24 2/8 and etc

Now let’s discuss the fundamental operations in fractions

Converting of Improper Fraction into Mixed Fraction

 Change 20/3 convert into mixed number

Converting of Mixed Fraction into Improper Fraction

ALWAYS EXPRESS YOUR ANSWER IN LOWEST TERM

Mathematical Operations of Fractions

Adding fractions with different denominators

o After Converting the fractions

 convert them to Improper Fractions

- 6/24 + 5/24 + 3/24

Subtract fractions with like denominators:

Subtract fractions with unlike denominators

Subtracting Fractions from Whole Numbers

 8/8 – 3/8 = 5/8

Conversion of FRACTIONS, DECIMALS AND PERCENTAGES

From Percent to Decimal

From Decimal to Percent

From Decimal to Fraction

From Percentage to Fraction

1. Aling Purita bought 3/4 kilo of kasim, 1 1/2 kilos of chicken, and 12/8 kilo of chicken liver

FRACTION DECIMAL PERCENT

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