ISEE Lower Level Math : Operations

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #13 : How To Subtract

What is the value of the expression below, simplified?

\(\displaystyle 2(-\frac{9}{3}-\frac{6}{2})\)

Possible Answers:

\(\displaystyle 15\)

\(\displaystyle -10\)

\(\displaystyle -15\)

\(\displaystyle -12\)

Correct answer:

\(\displaystyle -12\)

Explanation:

The first step is the reduce the fractions in the expression. 

\(\displaystyle 2(-\frac{9}{3}-\frac{6}{2})\)

Next, we need to convert each of the fractions to a form in which they both have the same denominator. We can do this by cross-multiplying:

\(\displaystyle 2(-\frac{(9\cdot 2)}{(3\cdot 2)}-\frac{(6\cdot 3)}{(2\cdot 3)})\)

\(\displaystyle 2(-\frac{18}{6}-\frac{18}{6})\)

\(\displaystyle 2(-3-3)\)

\(\displaystyle 2\cdot (-6)\)

\(\displaystyle -12\)

Example Question #14 : How To Subtract

If Greg's older brother, Boris, is five years older than Greg but three years younger than their oldest brother, Jerry, how old is Greg if Jerry is eighteen years old?

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 10\)

\(\displaystyle 12\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 10\)

Explanation:

Given that Boris is \(\displaystyle 3\) years younger than Jerry, Boris is \(\displaystyle 15\).

\(\displaystyle 18-3=15\)

Given that Greg is \(\displaystyle 5\) years younger than Boris, Greg will be \(\displaystyle 10\) years old. 

\(\displaystyle 15-5=10\)

Therefore, \(\displaystyle 10\) is the correct answer. 

Example Question #15 : How To Subtract

Lisa is reading a book that is \(\displaystyle 360\) pages long. She has one-sixth of the book to read before she is finished. How many pages has she read so far?

Possible Answers:

\(\displaystyle 260\)

\(\displaystyle 60\)

\(\displaystyle 300\)

\(\displaystyle 180\)

Correct answer:

\(\displaystyle 300\)

Explanation:

One-sixth of \(\displaystyle 360\) is \(\displaystyle 60\). Therefore, if Lisa has \(\displaystyle 60\) more pages to read before she is finished with the book, the number of pages that she has read so far is equal to \(\displaystyle 360-60=300\). Therefore, \(\displaystyle 300\) is the correct answer.

Example Question #16 : How To Subtract

Maria has a playlist of eighteen songs. She deletes half of the songs and then adds three new songs. If she listens to the first \(\displaystyle 25\%\) of the new playlist, how many songs will she have listened to?

Possible Answers:

\(\displaystyle 4.5\)

\(\displaystyle 2\)

\(\displaystyle 4\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 3\)

Explanation:

If Maria has a playlist of \(\displaystyle 18\) songs and deletes half of them, this leaves \(\displaystyle 9\) remaining songs on the playlist. If she then adds \(\displaystyle 3\) new songs, there will be \(\displaystyle 12\) songs on the play list. If she listens to the first \(\displaystyle 25\%\) of the new playlist, she will have listened to \(\displaystyle 3\) songs. This is because \(\displaystyle 25\%\) is equal to \(\displaystyle \frac{1}{4}\) and \(\displaystyle \frac{1}{4}\cdot12=3\).

Example Question #322 : Numbers And Operations

Alex and Andrew are brothers who want to get their mother a present that costs $350. Their father gives them $100 to help them pay for it, and their sister gives them another $100 to help them pay for it. If Alex and Andrew pay for the rest of the present in equal parts, how much money (in dollars) must each one of them pay?

Possible Answers:

\(\displaystyle 50\)

\(\displaystyle 150\)

\(\displaystyle 100\)

\(\displaystyle 75\)

Correct answer:

\(\displaystyle 75\)

Explanation:

If Alex and Andrew want to get their mother a present that costs $350, and their father gives them $100 to help them pay for it, and their sister gives them another $100 to help them pay for it, they will have to pay the remaining $150. If Alex and Andrew pay for the rest of the present, they will each have to pay $75 each, because $150 divided by 2 is $75. 

Example Question #331 : Numbers And Operations

What is the difference between \(\displaystyle 26.32\) and \(\displaystyle 18.78\)?

Possible Answers:

\(\displaystyle 7.42\)

\(\displaystyle 8.42\)

\(\displaystyle 45.1\)

\(\displaystyle 7.54\)

\(\displaystyle 6.58\)

Correct answer:

\(\displaystyle 7.54\)

Explanation:

Finding the difference means subtracting the smaller number from the larger number. First line up the decimal points, then subtract. You'll need to borrow to get the right answer.

Subtract2

Example Question #332 : Numbers And Operations

Evaluate:

\(\displaystyle 17-19+(-4)\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle -2\)

\(\displaystyle -8\)

\(\displaystyle 8\)

\(\displaystyle -6\)

Correct answer:

\(\displaystyle -6\)

Explanation:

The first step to solving this problem is to find the difference between: 

\(\displaystyle 17-19=-2\)

Then find the sum of \(\displaystyle -2+-4\) which equals a total of \(\displaystyle -6.\)

Example Question #333 : Numbers And Operations

Solve:

\(\displaystyle (2-6)+(11\times 3)-4\)

Possible Answers:

\(\displaystyle -24\)

\(\displaystyle 29\)

\(\displaystyle 25\)

\(\displaystyle 38\)

\(\displaystyle -38\)

Correct answer:

\(\displaystyle 25\)

Explanation:

To solve this problem, first evaluate the expression in parentheses:

\(\displaystyle (2-6)+(11\times 3)-4\)

\(\displaystyle -4+33-4\)

Then simplify: 

\(\displaystyle 29-4=25\)

Example Question #334 : Numbers And Operations

Evaluate:

\(\displaystyle 9\times8-(-4\times 8)\)

Possible Answers:

\(\displaystyle -44\)

\(\displaystyle -40\)

\(\displaystyle 40\)

\(\displaystyle -104\)

\(\displaystyle 104\)

Correct answer:

\(\displaystyle 104\)

Explanation:

To evaluate this problem correctly, first find the product of \(\displaystyle 9\times8\) and find the product of \(\displaystyle -4\times8\).

\(\displaystyle 9\times8=72\)

\(\displaystyle -4\times8=-32\)

Then find the difference between \(\displaystyle 72\) and \(\displaystyle -32\):

\(\displaystyle 72- -32= 72+32=104\)

Example Question #335 : Numbers And Operations

Group A has \(\displaystyle \$55.44\). Group B has \(\displaystyle \$23.76\). Group C has \(\displaystyle \$61.80\). What is the difference between the sum of Groups A & B with the amount of money in Group C?

Possible Answers:

\(\displaystyle \$38.04\)

\(\displaystyle \$31.48\)

\(\displaystyle \$17.40\)

\(\displaystyle \$12.40\)

\(\displaystyle \$31.68\)

Correct answer:

\(\displaystyle \$17.40\)

Explanation:

Firstly, find the sum of group A and group B:

\(\displaystyle 55.44+23.76=79.20\)

Then find the difference between this sum and the original amount of money in group C:

\(\displaystyle 79.20-61.80=17.40\)

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