Fractions - ISEE Lower Level (grades 5-6) Mathematics Achievement

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Question

In the number 1,063.8042, what place value is the 2 in?

Answer

From left to right, let's begin with the numbers coming after (or to the right of) the decimal point.

.8042

8 is in the tenths place

0 is in the hundredths place

4 is in the thousandths place

2 is in the ten thousandths place

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Question

What is 75% written as a fraction?

Answer

Let's rewrite 75% as a fraction.

All percents are written out of 100.

So 75% is

75/100.

This fraction can be simplified.

If we divide both the numerator and denominator by 25,

75 ÷ 25 = 3

100 ÷ 25 = 4

Our simplified fraction will be written as

$\dpi{100} \small \frac{3}{4}$

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Question

Write $\frac{3}{4}$ as a decimal.

Answer

$\dpi{100} \frac{3}{4}$ multiply the top and bottom by to get $\dpi{100} \frac{75}{100}$ which equals

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Question

Show $\small 0.5$ as a fraction.

Answer

First we rewrite $\small 0.5$ as a fraction. Since $\small 5$ is in the tenths place, we can write it over $\small 10.$

$\small \frac{5}{10}$

This can be simplified by dividing the top and bottom number by $\small 5$ .

$\small \frac{\left ( 5\div 5 \right )}{\left ( 10\div 5 \right )}$ $\small = \frac{1}{2}$

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Question

Convert the fraction into a percent, rounded to the nearest whole number.

$\frac{5}{8}$

Answer

Divide $\frac{5}{8}=0.625$

Move the decimal two places to the right, 62.5%, then round up to the nearest whole number 63%.

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Question

Janie has a bag full of red, blue, orange, white, and green marbles. There are 5 of each color marble in the bag.

Janie removes all 5 green marbles and all 5 red marbles, then adds 2 blue, 2 orange and 9 white marbles. What percentage of blue marbles are there now?

Answer

The adding and taking away leaves Janie with 7 blue marbles, 7 orange marbles and 14 white, and now 28 total marbles.

$\frac{7}{28}=\frac{1}{4}$ or 25%.

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Question

Which number is largest?

Answer

Thinking about these numbers as fractions, we have

$\frac{9}{10}$ , $\frac{8}{10}$ , $\frac{1}{100}$ , $\frac{1}{10,000}$ , and $\frac{9}{1000}$ .

The larger the number in the denominator is, the smaller the value of the total fraction. However, between $\frac{8}{10}$ and $\frac{9}{10}$ , the larger numerator is the bigger number. Therefore, the correct answer is .9.

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Question

In the number, 24,977.68001, what place is the 8 in?

Answer

As you move away from the decimal point, the places grow from tenths on. Since the 8 is 2 places away from the decimal point, it is the hundredths.

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Question

Find the decimal equivalent to the fraction. Round to the nearest hundredths place, if necessary.

$2\frac{2}{9}$

Answer

When converting a mixed fraction to a decimal, start with the fraction and divide the numerator by the denominator.

$2\frac{2}{9}$

Divide 2 by 9. The quotient is 0.22222…. Round to the nearest hundredth: 0.22.

Then, add in the whole number (2).

The decimal equivalent to $2\frac{2}{9}$ is 2.22.

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Question

At Creek High School 95% of the students buy their lunch from the snack bar, 4% of the students bring their own lunch and 1% of the students do not eat lunch at school. What is the percent of students who bring their lunch written as a decimal?

Answer

Every percent is a ratio of a number to 100 and this ratio can be written in fraction form.

In this case, 4% would be the same as

$\small \fn_cm \frac{4}{100}$ (The percent sign is a hidden denominator of 100)

Using place-value knowledge, the reading of the fraction gives the decimal number format.

$\small \fn_cm \frac{4}{100}$ is read as "four hundredths" which gives the place for the 4 in the decimal number (namely the hundredths place).

0 - there are no ones

0.0 - there are no tenths

0.04 - there are 4 hundredths

The correct answer is

(read "four hundredths")

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Question

Write as a decimal:

$\frac{3}{5}$

Answer

$3\div 5= 0.6$ , making this the decimal equivalent.

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Question

Write as a fraction in lowest terms:

Answer

is hundredths, so write it as a fraction: $0.72 = \frac{72}{100}$

, so simplify by dividing nuerator and denominator by .

$0.72 = \frac{72}{100} = \frac{72 \div 4}{100 \div 4} = \frac{18}{25}$

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Question

Place the following expressions in order, from lowest to highest: $2\frac{1}{8}$ , , $\frac{15}{7}$ ,

Answer

You don't have to figure out the exact decimal values of the fractions in order to solve this problem. Written as a mixed number, $\frac{15}{7}=2\frac{1}{7}$ .

You can see that is the lowest number, because is less than $\frac{1}{10}$ , and $\frac{1}{8}$ and $\frac{1}{7}$ are greater than $\frac{1}{10}$ .

Next comes $2\frac{1}{8}$ , because a larger denominator means a smaller number (if, of course, the numerator is the same).

Then comes $\frac{15}{7}$ , and finally , which in decimal form (remember: "percent" = "per hundred") equals , which is clearly greater than $2\frac{1}{5}$ .

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Question

Which fraction is between $\frac{3}{5}$ and $\frac{9}{10}$ ?

Answer

Since 3 is greater than half of 5, we know that $\frac{3}{5}$ is greater than $\frac{1}{2}$ .

That eliminates $\frac{1}{2}$ , $\frac{5}{11}$ , and $\frac{4}{9}$ , which are all less than or equal to $\frac{1}{2}$ .

That leaves $\frac{7}{9}$ , which is between $\frac{3}{5}$ and $\frac{9}{10}$ .

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Question

What is the sum of 4.7 and 2.5?

Answer

4.7 and 2.5 add up to 7.2.

0.2 is equal to $\frac{1}{5}$ , so the correct answer is $7\frac{1}{5}$ .

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Question

Ashley has $13\frac{1}{8}$ feet of garland, and she uses $8\frac{3}{4}$ feet of it to go around the door frame. How many feet of garland does she have left?

Answer

For this problem, you will need to find a common denominator for the fraction part of the mixed numbers:

$13\frac{1}{8}-8\frac{3}{4}= 13\frac{1}{8}- 8\frac{6}{8}$

Next, we want for the fraction in the mixed number we are subtracting from to be larger than the other fraction. We can do this by "taking" (or $\frac{8}{8}$ ) from the and add it to the $\frac{1}{8}$ . This gives us:

$12\frac{9}{8}-8\frac{6}{8}$ .

This should look less threatening now. Simply subtract the whole numbers and the fractions, and you are left with: $4\frac{3}{8}$ .

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Question

Write as a fraction.

Answer

Rewrite as $\frac{2}{10}$ .

Reduce the fraction:

$\frac{1}{5}$

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Question

The triangle below is divided into eight identical smaller triangles.

What fraction of the larger triangle is shaded, if the figure is drawn to scale?

Answer

Remember that fractions are:

$\frac{part}{whole}$

So, the triangle has a total of 8 parts, and 3 are shaded in. Therefore the fraction of the area that is shaded is $\frac{3}{8}$ .

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Question

What fraction is equivalent to ?

Answer

The first place value after the decimal is the tenths place, so is six-tenths, or $\frac{6}{10}$ .

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Question

In a survey, 8 out of the 32 people interviewed stated that they prefered vanilla over chocolate. What percentage of people preferred chocolate over vanilla?

Answer

The question asks for the percentage of people who chose chocolate over vanilla. If 8 people out of 32 preferred vanilla over chocolate, then people preferred chocolate over vanilla.

$\frac{24}{32}=.75*100=75$

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