Ratio and Proportion - ISEE Lower Level Quantitative Reasoning

Add .

Since both of these fractions have the same denominator, we just rewrite 3 on the bottom. When you add fractions, then add straight across the top, .

This gives us .

We can turn this into a mixed number by dividing with a remainder of 1. We place the orginal one as our whole number, and the remainder over the 3 for the fraction, .

As the denominator gets bigger, the fractions gets smaller, so when looking for the largest fraction, we are looking for one with the highest numerator and the lowest denominator. In this case, has the largest numerator and the smallest denominator.

To solve this, I need to set up a proportion, and then solve algebraically.

feet, the height of the tree, is equivalent in our proportion to feet, the building's height.

feet, the tree's shadow, is equivalent in our proportion to , the building's shadow.

Cross-multiply:

Divide each side by :

The first step is to convert the length of the movie from hours to minutes. A movie that is 2 hours and 8 minutes long is 128 minutes long.

128 divided by 16 is 8. Therefore, 8 minutes is of the movie.

If there are 18 tea bags in a box and Beth uses 2 tea bags, Brad uses 1 tea bag, and Joe uses 1 tea bag, then 14 tea bags will remain.

Given that , the correct answer is .

If Katie's computer has 60% of its power left after being on for 2 hours, then that means 40% of the battery was used to power the 2 hours. X represents the total number of hours that the battery can last.

Next, we divide each side of the equation by 40. This results in:

.

Since 60% of 5 is equal to 3, the correct answer is 3.

If Marcus is 9 years old and has been playing soccer for 3 years, he will be 10 years old during his 4th year. He has therefore played soccer for 4 out of 10 years, or

of his life.

Percentages are fractions out of 100, so the way to solve the problem is to have the denominator be 100. In order to do this we must multiply 20 by 5 in order to get 100.

If we multiply the denominator by 5, we must do the same to the numerator.

When we do this, we are left with which is 25%

If Katie's computer has 60% of its power left after being on for 2 hours, then that means 40% of the battery was used to power the 2 hours. X represents the total number of hours that the battery can last.

Next, we divide each side of the equation by 40. This results in:

.

Since 60% of 5 is equal to 3, the correct answer is 3.

Since there are customers who order orange juice, is the first number of our ratio.

The second number of our ratio is , because people order coffee.

Therefore, our ratio is :

We know that Stacy has 1946 dimes.

We also know that she has twice as many wheat pennies, so we must multiply by to find the total number of wheat pennies.

We also know that Stacy has three times as many 1986 quarters, so we multiply by to find the total number of 1986 quarters.

Now our ratio of wheat pennies to 1986 quarters is , but this can be simplified because both numbers are divisible by .

So our ratio becomes

Counting Steve, there are forty attendees so far, fifteen of whom are girls and twenty-five of whom (including Steve) are boys. To obtain a two-to-one girl to boy ratio, he needs to invite a total of fifty girls, so he needs to invite thirty-five more.

Given that there are 3 peanuts for every 1 chocolate chip and 2 raisins, the proportion of raisins can be found by dividing the number of raisins by the sum of all the items in the mix. This results in:

.

Therefore, is the correct answer.

If Scott's mother bakes 12 cookies and he eats half of them, that means he will eat 6 cookies, leaving 6 uneaten cookies.

If Scott's mom then puts red frosting on 4 cookies and blue frosting on the rest of the cookies, 2 cookies will get blue frosting. ().

Therefore, the ratio of cookies with red frosting to cookies with blue frosting is , which is equal to .

The ratio of Jose to Michael's height is .

Thus, if Jose is inches taller than Michael must be times shorter.

We can write this as the expression, .

Also, an equivalent ratio for = .

An equivalent ratio of is .

This is the furthest simplification of the ratio.
The greatest common divisor is needed to simplify the expression.

Both and are divisible by , and .

Thus, the correct answer is .

To solve this problem the relationship between the two numbers in the first ratio needs to be established.

Since, is times larger than , an equivalent ratio must have the same relationship.

Thus, must be times larger than , and

Thus,

First, find the number of boys in the class by subtracting the number of girls in the class from the total number of students.

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is .

We can express that ratio as the following fraction:

First, find the number of girls in the class by subtracting the number of boys in the class from the total number of students.

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is .

We can express that ratio as the following fraction:

The ratio wants us to compare the number of white puppies to the number of black puppies.

We can say the ratio of white puppies to black puppies is . When we write that as a fraction, it becomes , so we can also say that the ratio of white puppies to black puppies is or .