Numbers and Operations - ISEE Lower Level Quantitative Reasoning

Card 0 of 6100

Question

Add:

$\frac{3}{5}+ \frac{3}{10} = ?$

Answer

$\frac{3}{5}+ \frac{3}{10} =$

In order to add fractions, each fraction must have the same denominator. We must convert the fraction $\frac{3}{5}$ into a fraction that has a denominator of 10.

We multiply the numerator and denominator by 2.

$\frac{3}{5}\frac{2}{2}=\frac{32}{5*2}=\frac{6}{10}$

So, now we have $\frac{6}{10} + \frac{3}{10}$

Then we add the numerators together: .

We keep the same denominator (10), and the answer is $\frac{9}{10}$ .

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Question

Ms. Thompson and Mr. Bloomberg decided to throw a pizza party for their class. While taking orders, they found that $\small \frac{1}{4}$ of the students in Ms. Thompson's class, and $\small \frac{1}{6}$ of the students in Mr. Bloomberg's class wanted supreme pizza. What fraction of the two classes combined wanted supreme pizza?

Answer

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 $\small 4$ and $\small 6$ share the least common multiple $\small 24$ , each fraction can be written with a denominator of $\small 24$ .

In order to convert $\small \frac{1}{4}$ into a fraction with a denominator of $\small 24$ , we multply the top and bottom by $\small 6$ .

$\small \frac{(1\cdot 6)}{(4\cdot 6)}=\frac{6}{24}$

In order to convert $\small \frac{1}{6}$ into a fraction with a denominator of 24, we multiply the top and bottom by $\small 4$ .

$\small \frac{(1\cdot 4)}{(6\cdot 4)}=\frac{4}{24}$

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.

$\small \frac{6}{24}+\frac{4}{24}=\frac{10}{24}$

Next we simplify $\small \frac{10}{24}$ by dividing both the numerator and denominator by $\small 2$ .

$\small \frac{(10/2)}{(24/2)}=\frac{5}{12}$

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Question

Add. Reduce to the lowest terms, if necessary.

$\frac{1}{4}+\frac{2}{7}=$

Answer

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:

$\frac{7}{28}+\frac{8}{28}=$

Then add the numerators to get:

$\frac{15}{28}$

Since the factors cannot be reduced any further, the correct answer is $\frac{15}{28}$ .

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Question

If and are negative numbers, which of the following statements is true?

Answer

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

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Question

Add $2\frac{1}{4}$ to $5\frac{2}{3}$ .

Answer

The best way to solve this is to turn both mixed numbers into improper fractions. For $2\frac{1}{4}$ , multiply the denominator of the fraction by the whole number, and then add the numerator to the answer. $4\times2$ is , and . This gives us our new numerator, , which we put over the old denominator, :

$2\frac{1}{4}=\frac{9}{4}$ .

Using the same process with $5\frac{2}{3}$ , we get $3\times5+2$ , or , as our new numerator:

$5\frac{2}{3}=\frac{17}{3}$ .

To add $\frac{9}{4}+\frac{17}{3}$ , 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 :

$\frac{9}{4}\times\frac{3}{3}=\frac{27}{12}$

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

$\frac{17}{3}\times\frac{4}{4}=\frac{68}{12}$

Now we can add the two fractions together:

$\frac{27}{12}+\frac{68}{12}=\frac{95}{12}$

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 $7\frac{11}{12}$ .

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Question

$\frac{1}{9} \square \frac{5}{12}$

Compare the fractions and fill in the box with the appropriate sign.

Answer

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? $\frac{5}{12}$ does, so that is your answer. Then, you have to pick the correct inequality sign. Since $\frac{5}{12}$ is greater, the point of the inequality sign must be pointing to the lower fraction. Therefore, is the correct sign.

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Question

Felicity has 4 jackets, 5 sweaters, and 10 t-shirts. How many pieces of clothing does she own?

Answer

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

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Question

In five years, Allen will be twice as old as his sister Elaine, who is nine years old now. How old is Allen now?

Answer

Elaine is nine years old now, so in five years, she will be years old. Allen will be twice this, or $2 \times 14 = 28$ , so now, he is years old.

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Question

Which of the following is the sum of eight-ninths and one-third?

Answer

$\frac{8}{9} + \frac{1}{3} = \frac{8}{9} + \frac{1 \times 3 }{3 \times 3 } = \frac{8}{9} + \frac{ 3 }{9 } = \frac{8+3}{9} = \frac{11}{9}$

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Question

Add:

$4 \textrm{ ft }7\textrm{ in }$

$6 \textrm{ ft }11\textrm{ in }$

$+ ; \underline{3 \textrm{ ft }5\textrm{ in}}$

Answer

First, add feet and inches separately.

$4 \textrm{ ft }7\textrm{ in }$

$6 \textrm{ ft }11\textrm{ in }$

$+ ; \underline{3 \textrm{ ft }5\textrm{ in}}$

$13 \textrm{ ft }23\textrm{ in }$

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

$23 \div 12 = 1 \textrm{ R }11$

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

$13 \textrm{ ft }23\textrm{ in } = 13 \textrm{ ft } + 1 \textrm{ ft } 11\textrm{ in }$ , and:

$13 \textrm{ ft }$

+ $\underline{1 \textrm{ ft }11\textrm{ in }}$

$14 \textrm{ ft }11\textrm{ in }$

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Question

Add in modulo 12:

Answer

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

$33 \div 12 = 2 \textrm{ R } 9$ ,

then

$5 + 5 + 11 + 4 + 8 \equiv 9 \mod 12$

The correct response is 9.

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Question

Suzie had twice as many marbles as Sandy. Each child was given a bag of 60 marbles, and now Suzie has 110 marbles. How many marbles does Sandy have now?

Answer

Suzie has 110 marbles; she had marbles before being given the bag of 60. Sandy had half this, or $50 \div 2 = 25$ marbles; after being given her bag of 60, she now has marbles.

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Question

Which of the following is the sum of two-thirds and five-sixths?

Answer

$\frac{2}{3} + \frac{5}{6} = \frac{2 \times 2 }{3 \times 2} + \frac{5}{6} = \frac{4 }{6} + \frac{5}{6}= \frac{4 + 5 }{6} = \frac{9 }{6} = \frac{9 \div 3 }{6 \div 3} = \frac{3}{2}$

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Question

Which of the following is the sum of one-tenth and one-sixth?

Answer

$\frac{1}{10} + \frac{1}{6} = \frac{1 \times 3}{10 \times 3} + \frac{1 \times 5}{6 \times 5} = \frac{ 3}{30} + \frac{ 5}{30} = \frac{ 3+5}{30} =\frac{ 8}{30} =\frac{ 8 \div 2}{30 \div 2} = \frac{4}{15}$

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Question

Add:

$4 \textrm{ lbs } 13 \textrm{ oz }$

$3 \textrm{ lbs } 6 \textrm{ oz }$

$+\underline{5\textrm{ lbs } 9 \textrm{ oz }}$

Answer

First, add pounds and ounces separately.

$4 \textrm{ lbs } 13 \textrm{ oz }$

$3 \textrm{ lbs } 6 \textrm{ oz }$

$+\underline{5\textrm{ lbs } 9 \textrm{ oz }}$

$12 \textrm{ lbs } 28 \textrm{ oz }$

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

$28 \div 16 = 1 \textrm{ R } 12$

28 ounces is equal to 1 pound 12 ounces, so

$12 \textrm{ lbs } 28 \textrm{ oz } = 12 \textrm{ lbs } + 1 \textrm{ lb } +12 \textrm{ oz } =1 3\textrm{ lb }12 \textrm{ oz }$

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Question

The time is 8:45 AM. What time will it be in two hours and thirty minutes?

Answer

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

$8 \textrm{ hrs }45 \textrm{ min }$

$+ \underline{2 \textrm{ hrs }30 \textrm{ min }}$

$10 \textrm{ hrs }75 \textrm{ min }$

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

$10 \textrm{ hrs }75 \textrm{ min } = 10 \textrm{ hrs }+ 1\textrm{ hr }+15 \textrm{ min } =1 1\textrm{ hr } 15 \textrm{ min }$

making the time 11:15 AM.

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Question

Add in modulo 9:

Answer

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

$31 \div 9 = 3 \textrm{ R }4$ ,

then

$7 + 5 + 8 + 4 + 7 \equiv 4 \mod 9$

The correct response is 9.

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Question

Give the sum of 0.4, 0.44, and 0.444.

Answer

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:

$+ \underline{0.444}$

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Question

Which of the following is a numerical expression of twenty thousand, four hundred and forty-six?

Answer

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 .

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Question

Which expression is equal to three times J plus four?

Answer

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

Thus, the correct answer is: .

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