Operations - ISEE Lower Level Quantitative Reasoning

In order to find the fraction of students who wanted supreme pizza in the two classes combined, we must add the fractions. To add fractions, however, we must first find a common denominator. Since and share the least common multiple , each fraction can be written with a denominator of .

In order to convert into a fraction with a denominator of , we multply the top and bottom by .

In order to convert into a fraction with a denominator of 24, we multiply the top and bottom by .

Now we add the two fractions, but when we add fractions with the same denominator, we only add the numerators. The denominator will remain the same.

Next we simplify by dividing both the numerator and denominator by .

When adding fractions, you must first make sure that the denominators are equal. If they are not equal, then you must make them equal by finding the LCD (lowest common denominator). In this case the LCD is 28. Now set up the new equation:

Then add the numerators to get:

Since the factors cannot be reduced any further, the correct answer is .

If two negative numbers are multiplied, the answer is always positive (greater than ).

The best way to solve this is to turn both mixed numbers into improper fractions. For , multiply the denominator of the fraction by the whole number, and then add the numerator to the answer. is , and . This gives us our new numerator, , which we put over the old denominator, :

.

Using the same process with , we get , or , as our new numerator:

.

To add , the denominators need to match. Find a common multiple of and . works! In order to get to equal , multiply both the numerator, , and denominator, , by :

For the second fraction, multiply both the numerator, , and denominator, , by :

Now we can add the two fractions together:

We need to convert this improper fraction back into a mixed number. To do this, divide by to get with a remainder of . The remainder becomes the numerator of the fraction. remains the denominator. Therefore the answer is .

This problem is asking you to determine the relationship between the two fractions. Think of the fractions as pieces of a pizza. Which fraction has more pieces? does, so that is your answer. Then, you have to pick the correct inequality sign. Since is greater, the point of the inequality sign must be pointing to the lower fraction. Therefore, is the correct sign.

This problem requires adding up all of the different clothing items . The answer is 19.

Elaine is nine years old now, so in five years, she will be years old. Allen will be twice this, or , so now, he is years old.

First, add feet and inches separately.

Since 12 inches make one foot,we divide 23 by 12:

23 inches is equal to 1 foot 11 inches. Therefore,

, and:

+

The sum of two or more numbers in modulo 12 arithmetic is the remainder of the sum when it is divided by 12. Since

and

,

then

The correct response is 9.

Suzie has 110 marbles; she had marbles before being given the bag of 60. Sandy had half this, or marbles; after being given her bag of 60, she now has marbles.

First, add pounds and ounces separately.

Since 16 ounces make one pound, we divide 28 by 16:

28 ounces is equal to 1 pound 12 ounces, so

You can add two hours and thirty minutes to 8:45 AM as follows:

Since one hour is equal to 60 minutes, divide 75 minutes by 60; this is 1 hour 15 minutes, so

making the time 11:15 AM.

The sum of two or more numbers in modulo 9 arithmetic is the remainder of the sum when it is divided by 9. Since

and

,

then

The correct response is 9.

Write the two numbers vertically with decimal points aligned, adding two zeroes to the 0.4 and one to the 0.44. Then add vertically:

Twenty thousand is equal to .

Four hundred is equal to .

Forty-six is equal to .

It follows that twenty thousand, four hundred and forty-six is equal to .

Three times J is equal to 3J. Therefore, three times J plus four is equal to 3J + 4.

Thus, the correct answer is: .