U2 Full Chapter Chapter 5 Ratio Math Skills for Business- Full
5.1 Definition of 45
Ratio is a quantitative comparison of the relative size of two or more
quantities with the same units of measurement. Businesses use
ratios in a variety of situations and it is a powerful tool for making
financial decisions. It is particularly important for analyzing business
profitability and its ability to meet debt payment. As well, knowledge
of ratio helps us make all kinds of comparisons in business. A
common ratio in business is to compare the value of current assets
to that of current liabilities. Another common ratio is to compare
earnings after taxes to equity. Sometimes businesses compare the
cost of raw materials to cost of labour. As well, in the manufacturing
of confectionary products such as bread, candies and muffins, there
are standard proportion of ingredients that each product should ratio can
contain. For a ratio in standard form, all the terms are integers and there
is no common divisor for all the terms. For a ratio with more than two
terms, it is possible for two or more of the terms to have a common
divisor but not for all of the terms. A ratio can always be expressed in
standard form by multiplying and/or dividing each of the terms by the
same number. Multiplying or dividing each of the term of a ratio by the
same number except zero, do not change terms of a ratio, because they
are relative comparison of their sizes. Notation Ratio of quantity A to
quantity B is written in mathematics as follows, A is to B, Bor A to B. A
the first term and B the second term of the ratio. Therefore, A: B is
called a two-term ratio. A: B: C is called a three-term ratio. Terms of
a ratio can be reduced to lowest term just as we reduce fractions
into lowest term. Example 1 : The daily sale at Bagra Enterprises is $1 500 and at Akua
Enterprises $2 000. The ratio of daily sales at Bagra to daily sales at
Akua Enterprises is written as; Daily Sales at Bagra Enterprises :
Daily Sales at Akua Enterprises = $1 500 : $2 000. Each term can be divided by $500 (or by 100 and then by 5) to
reduce them to lowest term: Daily Sales at Bagra Enterprises : Daily
Sales at Akua Enterprises = (1500 ÷ 500) : (2000 ÷ 500) = 3:4.
(What does this mean?) Interpretation: 1. For every 3 dollars in
daily sale at Bagra, there is $4 in sale at Akua. 2. If the total daily
sales for Bagra and Akua are divided into 7 (which is 3 + 4) equal
parts, 3 of the parts are Bagra’s sales and 4 parts are Akua’s sales.
5.3 Finding Ratios of
Quantities Example 2
The hourly wage of a sales associate is $9.50 at Balmort; $10.50 at
Scheers; and $12 at Makola. Find the ratio of the hourly wage of sale
associates at Balmot to that of Scheers and to Makola.
Balmot : Scheers : Makola = $9.50 : $10.50 : $12 then (Multiply each
term by 100 and divide by $) = 950 : 1050 : 120 (Divide each term
by 50, which the common factor) Balmot: Scheers : Makola = 19 :
21 : 24
e 3 dimensions of a rectangular box are length 1m 35cm, width 1m
80cm, and depth 90cm. Find the ratio of the length to the width to
the depth of the box.
Length:Width : Depth = 1m 35cm : 1m 80cm : 90cm then (Change
units to cm = 135cm: 180cm: 90cm then (Divide each term by
45cm)= 3 : 4 : 2 Exampl
e 4 The ratio of 4:2 is not in standard form but 3: 4: 2 is in standard
form. The ratio 4 : 2 is expressed in standard form by dividing both
terms by the common divisor 2; Thus,
ratio; A : B : k any number except zero. = m any number
except zero. A change in the order of a ratio changes the ratio. The
ratio of quantity A to quantityB is not the same as the ratio of
quantity B to quantity A.
e 5s example shows that we can use our understanding of ratio to
calculate unknownquantity. This idea is very important to
understanding proportion. It should be stated that proportion is an
extension of ratio.
Joe’s two-week wages is $800 for 80 hours of work. a) Given this
ratio, how many hours does he have to work in order to
earn$1600?b) If he works 245 hours how much will he earn?
a) Given the ratio, 80 = 10:1 (After diving each term
1600 : h
Since for every $10, he has to work an hour, there are 160 tens in
$1600. So, Joe has to work 160 hours in order to make $1600. Note
that the ratio of wages to hours does not change, except when one of
the terms of the original ratio changes.
b) Again, he has to work 240 hour of an
This example seems very simple athat ishould provide you an insight
into the nature of ratios in mathematics. However, other examples
may not be so simple and they may require a more sophisticated
procedure. Math Skills for Business- Full Chapters
RAn important idea in mathematics is how to compare ratios. It gives
us an idea about the multiplicative relationship between quantities.
For example, what is the relationship between 1/2 and 2/4? Do you
think that 1/2 and 2/4 equivalent fractions or ratios? With a little
drawing and intuition, it becomes clear that 1/2 and 2/4 are
equivalent fractions or ratios. And that 1/5 and 20/100 are also
equivalent. Ratios are equivalent or equal if their cross-products are
the same, or if they can be written as equal fractions. To compare
ratios do the following: a) Write the ratios as fractions b) Calculate
their cross-products c) Then compare them. If the products are the
same, the ratios are equal or equivalent.
Are the ratios 3 to 4 and 6/8 equal? The ratios . Their cross-
of 3 × 8= 6 × 4 are obviously equal. Since both products are equal,
the ratios are equal.
Are the ratios 1:5 and 4/20 equivalent? Yes, they are equivalent. The
fraction 4/20 canbe reduced to the lowest by dividing the numerator
by 4 (4÷ 4 = 1) and the denominator by 4 (20 ÷ 4 = 5). This gives us
1/5, which is equal to 1/5. Their cross-products give, 1 × 20 = 5 × 4.
Compare 13:17 and 5/7. Are they equal or equivalent ratios? No, they
are not equivalent because their cross-products are not equal: 13 × 7
≠ 17 × 5.
This is the division of a quantity in a given ratio. That is, the given
quantity is divided into piles such that the ratio of quantities in the
piles is equal to the given ratio.
eMaya and Nina’s uncle gave them an amount of $150,000 in his will.
The money is to be divided between them in the ratio of 3 to 2. How
much does each receive? Math Skills for Business- Full Chapters
Since when the $150,000 is divided between them it should
correspond to the given ratio, we can try a few pairs of numbers.
Maya’s share : Nina’s share $100,000 : 50,000
2 :1 After dividing each term by 50,000, you
2: 1 does nocan see that to 3:2. So, we
try another pair: 90,000: 60,000
= 3: 2 After dividing each term by 30,000 Thus, Maya’s share is
$90,000 and Nina’s share is $60,000. This is correct because the
divided quantity corresponds to the given ratio.
Mohammed , Ben , and Rachel earned some money by selling toys
and lemonade at a festival stand. They agreed to share any profit in
the ratio of their ages. Mohammed is 9 years old, Rachel is 10 years
old, and Ben is 7 years old. Ben’s share came to $28. Find the share
of Mohammed and that of Rachel.
The solution to this problem is not so easy, as example one. This is
because the amount of profit they made is not given. First, let us
find the profit they made. Let p stand for the profit they made. The
total ratio is 26 (9 + 10 + 7).
This is how Ben’s share was
= x p =
= 26 = 28 x
We multiply each side by 26 in order to clear the fractions.
We now have 7p = 728 The 728 was obtained after
multiplying 28 by 26. P = 104 After
dividing each side of the equation by 7. Mohammed ’ s share = Rachel’s share = x 104 =
$40 104 =
The ratio is 36: $36
40: 28 = 9: 10: 7 after dividing each
term by 4.
5.5 Review, Exercises and
1. Give two examples of situations in which a business owner may
use ratio for the purpose of comparison.
2. Reduce to the lowest terms a) 12to24 b) 84to56 c) 15to24to39 d)
32: 100 e) 30: 240 f) 50: 49 g)
3. Set up a ratio for each of the following and reduce
to lowest terms.5 quarters b) 6 minutes for 50 metres c) $45 per
day for 12 employees for 20 day d) $2000 sales for 5 days
4. The cost of a unit of a product consists of $4.25 direct materials
cost, $2.75 direct labour cost, and $3.25 overhead cost. What is the
ratio existing between these three elements of cost?
5. Mariam applied for residential mortgage from Seaway Financial
Services. Toligibility for the mortgage, the financial officer used
the following ratio: Personal debts: personal annual income.
a) Mariam’s personal debts were $40,000 and personal annual
income was $50,500. What is her ratio of personal debt to personal
annual income? the financial officer, would you approve the mortgage
for Mariam? Why?
6. a) The gross sales to the number of sales persons ratio for a retail
company is $20,000:5 for the first quarter. What does this mean
to the retailer? What advice would you give to the retailer, if
the total wage bill for the quarter is $15,000?r a grocery store is
600:1 for the third quarter. Explain what this means for the
retail operations. 7. Mike received $100 a week for distributing flyers to houses. He
spent $40 at the movies and $25 on comic books. After buying
$10 worth of ice cream, he saved the rest. a) What is the ratio
of the amount of money he spent on buying comic books and
movies to the amount he saved? Firm Name 2000 2001