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ACT Math : Fractions

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Example Questions

Example Question #1557 : Act Math

Simplify the expression:

$\frac{1}{2}-\frac{2}{9}+\frac{5}{6}$

Possible Answers:

$\frac{3}{2}$

$\frac{1}{18}$

$\frac{10}{9}$

$\frac{14}{9}$

$\frac{2}{3}$

Correct answer:

$\frac{10}{9}$

Explanation:

First you want to find the least common denominator (in this case it's 18):

$\frac{9*1}{9*2}-\frac{2*2}{2*9}+\frac{1*15}{1*18}$

$\frac{9}{18}-\frac{4}{18}+\frac{15}{18}$

$\frac{9-4+15}{18}$

$\frac{20}{18}=\frac{10}{9}$

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Example Question #1 : How To Add Fractions

What is the result of adding $20\%$ of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{23}{11}$

$\frac{3}{28}$

$\frac{47}{140}$

$\frac{43}{140}$

$\frac{3}{39}$

Correct answer:

$\frac{43}{140}$

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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Example Question #12 : Operations And Fractions

Which of the following is equal to $\frac{1}{y(y+1)}$ ?

Possible Answers:

$\frac{y}{y-1}$

$\frac{1}{y}-\frac{1}{y+1}$

$\frac{1}{y+1}-\frac{1}{y}$

$\frac{1}{y}+\frac{1}{y+1}$

$\frac{y}{y+1}$

Correct answer:

$\frac{1}{y}-\frac{1}{y+1}$

Explanation:

We have two options here. We can manipulate the answers to work backwards and find a common denominator. This involves simply subtracting or adding two fractions. We can also try to rewrite the numerator by adding and subtracting the value . This serves the purpose of creating a sum in the numerator than can be split into y+1 and . This gives us one of the factors in the denominator in each numerator. When we separate or decompose the fraction, we can divide out by the common factor to re-express this as the difference of two rational expressions.

$\frac{1}{y(y+1)}=\frac{1+y-y}{y(y+1)}=\frac{y+1}{y(y+1)}-\frac{y}{y(y+1)}=\frac{1}{y}-\frac{1}{y+1}$

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of the fraction 3/727?

Possible Answers:

3/727

–727/3

727/3

–3/727

242

Correct answer:

727/3

Explanation:

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.

3/727

Reciprocal 727/3

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the opposite reciprocal of 25/127?

Possible Answers:

–5

25/127

127/25

–127/25

–25/127

Correct answer:

–127/25

Explanation:

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The opposite reciprocal takes the negative of that number.

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Example Question #2 : How To Find The Reciprocal Of A Fraction

Find the negative reciprocal of the following:

$\frac{5}{132}$

Possible Answers:

$-\frac{132}{5}$

$\frac{1}{2}$

$\frac{5}{132}$

$\frac{132}{5}$

$-\frac{5}{132}$

Correct answer:

$-\frac{132}{5}$

Explanation:

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.

$\frac{5}{132}$

Reciprocal $\frac{132}{5}$

Negative Reciprocal $-\frac{132}{5}$

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the slope of any line perpendicular to 4y = 2x + 7 ?

Possible Answers:

$\frac{1}{2}$

$\frac{7}{4}$

$\frac{5}{2}$

Correct answer:

Explanation:

First, we must solve the equation for y to determine the slope: y = (2/4)x + 7/4

By looking at the coefficient in front of x, we know that the slope of this line has a value of 1/2. To find the slope of any line perpendicular to this one, we take the negative reciprocal of it:

slope = m , perpendicular slope = –1/m

slope = 1/2 , perpendicular slope = –2

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Example Question #1 : How To Find The Reciprocal Of A Fraction

Find the reciprocal of the following fraction

$\frac{2}{5}$

Possible Answers:

$\frac{2}{5}$

$\frac{5}{2}$

$-\frac{2}{5}$

$-\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

The reciprocal is defined such that a faction times its recprocal is 1. For you this just means turn the fraction upside down, ie the numerator is the denominator and vice versa.

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of $\frac{2}{17}$ ?

Possible Answers:

$\frac{17}{2}$

$\frac{17}{17}$

This fraction doesn't have a reciprocal.

$-\frac{17}{2}$

$\frac{2}{2}$

Correct answer:

$\frac{17}{2}$

Explanation:

The reciprocal of a fraction is simply exchanging the denominator and numerator of a fraction.

$\frac{n}{d}=\frac{2}{17}\rightarrow \frac{d}{n}=\frac{17}{2}$

You can double check that it works by making sure the product of a fraction and its reciprocal is 1.

$\frac{2}{17}\cdot \frac{17}{2}=1$

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Example Question #1 : How To Find The Lowest / Least Common Denominator

What is the difference between the LCM and GCF for the following set of numbers: 3, 12, and 30?

Possible Answers:

None of the answers are correct

Correct answer:

Explanation:

LCM = least common multiple = 2 x 2 x 3 x 5 = 60

GCF = greatest common factor = 3

Prime factor each number

3 = 3 x 1

12 = 3 x 4 = 3 x 2 x 2

30 = 5 x 6 = 5 x 2 x 3

LCM – GCF = 60 – 3 = 57

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ACT Math : Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1557 : Act Math

Example Question #1 : How To Add Fractions

Example Question #12 : Operations And Fractions

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #2 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Lowest / Least Common Denominator

All ACT Math Resources

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