Decimals with Fractions - ACT Math

Card 0 of 20

Question

Simplify:

$0.35+\frac{0.75}{0.2}-0.4*\frac{0.5}{0.1}$

Answer

Begin by multiplying all of your decimal fractions by $\frac{100}{100}$ :

$0.35+\frac{0.75}{0.2}\frac{100}{100}-0.4\frac{0.5}{0.1}\frac{100}{100}$

Simplify:

$0.35+\frac{75}{20}-0.4\frac{50}{10}=0.35+\frac{15}{4}-0.45$

Now perform the multiplication:

$0.35+\frac{15}{4}-2$

The easiest thing to do next is to subtract from :

$0.35+\frac{15}{4}-2=\frac{15}{4}-1.65$

Next, convert into the fraction $\frac{165}{100}$ :

$\frac{15}{4}-\frac{165}{100}$

Now, the common denominator can be :

$\frac{15}{4}\frac{25}{25}-\frac{165}{100}=\frac{375}{100}-\frac{165}{100}$

Simplify:

$\frac{375}{100}-\frac{165}{100}=\frac{210}{100}=\frac{21}{10}$

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Question

Convert 0.825 into a fraction.

Answer

0.825 in fraction form is $\frac{825}{1000}$ . Simplifying the fraction equals $\frac{33}{40}$ .

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Question

Simplify:

$\frac{0.9}{0.7}+\frac{1}{10}+\frac{0.2}{0.9}+2$

Answer

1. Convert all of your decimal fractions to normal fractions by multiplying each by $\frac{100}{100}$ :

$\frac{0.9}{0.7}\times \frac{100}{100}=\frac{90}{70}$

$\frac{0.2}{0.9}\times \frac{100}{100}=\frac{20}{90}$

2. Find the least common denominator for all of the fractions and use that denominator:

In this case it's 7 x 9 x 10 = 630

$\frac{90}{70}\times \frac{9}{9}=\frac{810}{630}$

$\frac{20}{90}\times \frac{7}{7}=\frac{140}{630}$

$\frac{2}{1}\times \frac{630}{630}=\frac{1260}{630}$

$\frac{1}{10}\times \frac{63}{63}=\frac{63}{630}$

3. Add together all of the fractions you now have:

$\frac{810}{630}+\frac{140}{630}+\frac{1260}{630}+\frac{63}{630}=\frac{2273}{630}$

4. Simplify this fraction into a mixed number:

$\frac{2273}{630}=3\frac{383}{630}$

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Question

Simplify:

$\frac{0.21}{0.75}\times \frac{0.1}{0.45}$

Answer

1. Multiply the two fractions together in decimal form:

$\frac{0.21}{0.75}\times \frac{0.1}{0.45}= \frac{0.021}{0.3375}$

2. Multiply the new fraction by 10,000/10,000:

$\frac{0.021}{0.3375}\times \frac{10,000}{10,000}=\frac{210}{3375}$

3. Simplify this fraction using the greatest common factor:

In this case the GCF is 15:

$\frac{210}{3375}=\frac{14\times 15}{225\times 15}=\frac{14}{225}$

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Question

What is the decimal value for $\frac{6}{20}$ ?

Answer

$\frac{6}{20}=\frac{6\cdot 5}{20\cdot 5}=\frac{30}{100}$

$30\div100=0.3$

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Question

What is the fraction value of 0.833?

Answer

$5\div6 = 0.833$

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Question

A '95 Chevy Silverado acheives maximum fuel efficiency on a level highway and ideal road conditions at 25 mpg. Driving in the city, the fuel efficiency decreases to about 15 mpg. What is the percent fuel efficiency the truck has in city driving conditions?

Answer

Finding the % fuel efficiency for city driving starts with setting up a fraction with the maximum niles per gallon as your denominator and your actual mpg as your numerator:

$\frac{15mpg}{25mpg}$

This fraction can be simplified into a decimal:

$\frac{15mpg}{25mpg}=0.6$

Which, when multiplied by 100% will give you your % fuel efficiency:

0.6 x 100% = 60%

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Question

Wind energy is big business in countries like the Netherlands. If a wind turbine is designed to spin at a maximum rate of 250 rotations per minute (RPM) but due to large trees and other obstructions, the mill only spins at 185 RPM, what is the percent efficiency?

Answer

$\frac{185}{250}=0.74$

0.74 x 100% = 74% Efficiency

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Question

What is the fraction value of the decimal 0.11?

Answer

If we were to divide 1 by the decimal value we get:

$\frac{1}{0.11}\approx9$

From this we can determine that 1 is our numerator and 9 is our denominator, giving us:

$\frac{1}{9}$

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Question

There is a high proportion of people who work in investment banking who are also involved with fraud. Industry specialists place the figure at a decimal value of 0.05. If a firm hires 200 stock brokers, how many of them are likely involved with fraudulent schemes?

Answer

The decimal value 0.05 can be put into fraction form as such:

$\frac{1}{0.05}=20$

$0.05 = \frac{1}{20}$

Now that we know the fraction proportion of fraudulent investors, we can determine how many of the 200 employed may be guilty of fraud:

$\frac{1}{20}\cdot200=\frac{200}{20}=10$

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Question

What is the decimal value of $\frac{42}{87}$ ?

Answer

$42\div87=0.48$

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Question

There are 12 slices in a large pizza. If a decimal value of 0.583 of the pizza has been eaten, how many slices remain?

Answer

We can determine how many slices of pizza have been eaten by multiplying tyhe decimal value by the total number of slices:

$0.583\cdot12=7$

7 slices have been eaten, leaving us with 5 remaining 12 slices.

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Question

There are 200 parking spaces at the local shopping mall and a decimal value of 0.85 (1.0 being 100% of spaces) of the spaces are occupied by parked cars. What is the simplified fraction value of the proportion of spaces that area still available?

Answer

Since 0.85 (85%) of the spaces are occupied, we can conclude that 0.15 (15%) are vacant. We can calculate the number of available spaces by multipling the decimal by the total number of spaces:

$0.15\cdot200=30$

To get a fraction value, we put the number of vacant spaces as the numerator and the total number of spaces as the denominator and begin to simplify:

$\frac{30}{200}=\frac{3}{20}$

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Question

0.3 < 1/3

4 > √17

1/2 < 1/8

–|–6| = 6

Which of the above statements is true?

Answer

The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.

1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.

√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.

Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.

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Question

Which of the following numbers is between 1/5 and 1/6?

Answer

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

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Question

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

Answer

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

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Question

An acid-water solution is made in which 65% of the solution is water by volume. How many liters of acid are there in 50 liters of the solution?

Answer

35% of the solution is acid, therefore 0.35 * 50 = 17.5.

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Question

If $\frac{1}{3} < x < 0.76$ , can equal which of the following?

Answer

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.

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Question

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Answer

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

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Question

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

Answer

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

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