How to find a ratio - ISEE Middle Level Math

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Question

What is the least common multiple of 5, 12, and 15?

Answer

You can write out the multiples of each number, and find the first number that is common to all of them.

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

12: 12, 24, 36, 48, 60

15: 15, 30, 45, 60

The correct answer is 60.

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Question

What is the greatest common factor of 12, 24 and 96?

Answer

To find the greatest common factor of three numbers, first factor each number as a product of prime numbers:

$\dpi{100} 96: 2\times 2\times 2\times 2\times 2\times 3$

$\dpi{100} 24: 2\times 2\times 2\times 3$

$\dpi{100} 12: 2\times 2\times 3$

Now take all of the factors that are in common between 12, 24 and 96. In this case, that is 2, 2 and 3.

$\dpi{100} 2\times 2\times 3=12$

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Question

Logan needs to answer 60 questions to finish his test. If he has answered 25% of the questions in 20 minutes, how long will it take him to complete the entire test?

Answer

To solve:

First, find the number of answers completed by calculating:

$\small 60\cdot 0.25=15$

Then, find how long it would take him to complete the 60 question test if for every 20 minutes he answer 15 questions:

$\small 60 \div 15=4$ (sets of 15 questions)

$\small \small \small 4\cdot 20 =80$ minutes altogether to finish the test.

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Question

A car travels miles in hours. At what rate does the car travel?

Answer

Divide the number of miles by the number of hours to get the number of miles per hour.

$\textup {rate}=\frac{\textup {distance}}{\textup {time}}=\frac{\textup {miles}}{\textup {hours}}$

$\frac{684\textup { miles}}{12\textup { hours}} = 57\textup { miles per hour}$

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Question

I have 5 white chocolates, 3 milk chocolates, and 9 dark chocolates. What is the ratio of white chocolates to the other types of chocolates?

Answer

There are 5 white chocolates. There are a total of 12 milk and dark chocolates. The ratio of white to other chocolates is 5:12.

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Question

Which ratio is equivalent to $13 \frac{1}{2} : 1 \frac{1}{2}$ ?

Answer

A ratio can be rewritten as a quotient; do this, and simplify it.

$13 \frac{1}{2} : 1 \frac{1}{2}$

Rewrite as

$13 \frac{1}{2} \div 1 \frac{1}{2} = \frac{27}{2} \div \frac{3}{2} = \frac{27}{2} \cdot \frac{2}{3} = \frac{9}{1} \cdot \frac{1}{1} = \frac{9}{1}$

or

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Question

In February, there were 12 rainy days, 6 cloudy days and 10 sunny days. What was the ratio of sunny days in February?

Answer

Identify the number of sunny days in February :

Then, creating a ratio, show the number of sunny days compared to the total number of days in the month of February (28):

Answer:

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Question

Express the following ratio in simplest form:

Answer

Rewrite this in fraction form for the sake of simplicity, and divide both numbers by :

$\frac{140}{60}=\frac{140\div 20}{60\div 20} = \frac{7}{3}$

The ratio, simplified, is .

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Question

Express this ratio in simplest form: $3 \frac{4}{7} : \frac{5}{7}$

Answer

A ratio of fractions can best be solved by dividing the first number by the second. Rewrite the mixed fraction as an improper fraction, rewrite the problem as a multiplication by taking the reciprocal of the second fraction, and cross-cancel:

$3 \frac{4}{7} \div \frac{5}{7} = \frac{25}{7} \div \frac{5}{7} = \frac{25}{7} \div \frac{7}{5} = \frac{5}{1} \div \frac{1}{1}=\frac{5}{1}$

The ratio, simplified, is .

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Question

Express this ratio in simplest form:

Answer

A ratio involving decimals can be simplified as follows:

First, move the decimal point over a common number of places in each number so that both numbers become whole. In this case, it would be two places:

$2.4 : 0.75 \Rightarrow 240 : 75$ (note the addition of a zero at the end of the first number)

Now, rewrite as a fraction and divide both numbers by :

$\frac{240}{75} = \frac{240 \div 15}{75 \div 15} = \frac{16}{5}$

The ratio, simplified, is

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Question

Write as a unit rate: 450 words typed in 25 minutes.

Answer

Divide the number of words by the number of minutes to get words per minute:

$450 \div 25 = 18$ words per minute

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Question

In March, there were 8 rainy days, 13 sunny days and 10 cloudy days. What is the ratio of sunny days to total days in March?

Answer

Identify the number of sunny days in March:

Create a ratio showing sunny days in March to toal days in March (31 day month):

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Question

A 32-ounce bottle of Emerald Cola costs $1.39. What is the cost per ounce, taken to the nearest tenth of a cent?

Answer

To find the cost per ounce, divide the total cost, $1.39, by the number of ounces, 32.

$$1.39 \div 32 = $ 0.0434375$

This rounds to 4.3 cents per ounce.

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Question

A batting average is defined as the ratio of hits to turns at bat. It is expressed as a decimal rounded to the nearest thousand.

In 2013, Carlos Beltran's batting average was 0.296. If he maintains this same batting average over the 2014 baseball season, how many turns at bat should he expect to need to achieve 40 hits? (Nearest whole number)

Answer

Since a batting average is a ratio of hits to turns at bat,

$\textrm{avg} = \frac{\textrm{hits }}{\textrm{at bat}}$

Let be the number of turns at bat Beltran needs to get 40 hits. Then solve for in this equation:

$0.296= \frac{40}{N}$

$\frac{0.296}{1}= \frac{40}{N}$

$0.296 \cdot N= 40$

$N = 40\div 0.296 \approx 135$

Beltran should need 135 turns at bat.

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Question

A class has girls and boys. What is the ratio of girls to boys?

Answer

The question asks to compare the number of girls to the number of boys. The ratio is .

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Question

A furlong is a unit of length used in horse racing. Eight furlongs are equal to one mile. How many feet are equal to twelve furlongs?

Answer

Multiply 12 furlongs by $\small \frac { 1 }{8 }$ miles per furlong, and by 5,280 feet per mile:

$\small 12 \times \frac{1}{8} \times 5,280 = 7,920$ feet.

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Question

A fathom is a unit of underwater depth equal to 6 feet. How many fathoms are equal to two miles?

Answer

Multiply 2 miles by 5,280 feet per mile by $\frac{1}{6}$ fathoms per foot:

$2 \times 5,280 \times \frac{1}{6} = 1,760$ fathoms.

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Question

If the ratio of boys to girl in a class is 2:3 and there are 18 boys in the class, how many girls are there?

Answer

Since you know the ratio and the number of boys, you can set up a proportion from that ratio: $\left(\frac{2}{3}=\frac{18}{x}\right)$ .

Since $2\times 9=18,$ you can multiply the denominator by 9 as well. Therefore, $3\times 9=27$ and there are 27 girls in the class.

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Question

In a pet shop, there are 21 animals. There are 7 hamsters and 2 dogs. There are also equal numbers of cats, rabbits, and guinea pigs. What is the ratio of hamsters to guinea pigs?

Answer

In a pet shop, there are 21 animals. Since there are 7 hamsters and 2 dogs, this leaves 12 animals that are neither a hamster nor a dog.

Given that there are also equal numbers of cats, rabbits, and guinea pigs, this means that the remaining number of animals must be divided by 3 to find the number of each species.

$12\div3=4$

There are 4 cats, 4 rabbits, and 4 guinea pigs.

The ratio of hamsters to guinea pigs is therefore 7:4 because there are 7 hamsters and 4 guinea pigs.

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Question

A boardgame has 22 pieces. Half of the pieces are blue and the other half are red. John has hidden 4 red pieces and 3 blue pieces. Of the remaining pieces, what is the ratio of red pieces to blue pieces?

Answer

If there is a boardgame in which there are 22 pieces, half of which are blue and half of which are red, this means that there are 11 blue pieces and 11 red pieces. If John has hidden 4 red pieces and 3 blue pieces, there are therefore 7 red pieces remaining and 8 blue pieces remaining.

Thus, the ratio of red pieces to blue pieces (of what remains) is .

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