ASVAB Arithmetic Reasoning Operations on Fractions Practice Test 725008 Results

Your Results Global Average
Questions 5 5
Correct 0 3.38
Score 0% 68%

Review

1

What is \( \frac{4}{6} \) + \( \frac{6}{10} \)?

60% Answer Correctly
\( \frac{3}{10} \)
1 \( \frac{4}{30} \)
1\(\frac{4}{15}\)
1 \( \frac{8}{30} \)

Solution

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 5}{6 x 5} \) + \( \frac{6 x 3}{10 x 3} \)

\( \frac{20}{30} \) + \( \frac{18}{30} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{20 + 18}{30} \) = \( \frac{38}{30} \) = 1\(\frac{4}{15}\)


2

Simplify \( \frac{36}{48} \).

77% Answer Correctly
\( \frac{4}{17} \)
\( \frac{1}{2} \)
\( \frac{3}{4} \)
\( \frac{6}{17} \)

Solution

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{48} \) = \( \frac{\frac{36}{12}}{\frac{48}{12}} \) = \( \frac{3}{4} \)


3

What is \( \frac{7}{4} \) - \( \frac{4}{12} \)?

61% Answer Correctly
\( \frac{9}{16} \)
2 \( \frac{4}{12} \)
1\(\frac{5}{12}\)
2 \( \frac{3}{12} \)

Solution

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 3}{4 x 3} \) - \( \frac{4 x 1}{12 x 1} \)

\( \frac{21}{12} \) - \( \frac{4}{12} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{21 - 4}{12} \) = \( \frac{17}{12} \) = 1\(\frac{5}{12}\)


4

What is \( \frac{2}{8} \) x \( \frac{2}{6} \)?

72% Answer Correctly
\(\frac{1}{72}\)
\(\frac{1}{2}\)
\(\frac{1}{12}\)
\(\frac{2}{3}\)

Solution

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{2}{6} \) = \( \frac{2 x 2}{8 x 6} \) = \( \frac{4}{48} \) = \(\frac{1}{12}\)


5

What is \( \frac{2}{8} \) ÷ \( \frac{4}{7} \)?

68% Answer Correctly
\(\frac{1}{8}\)
1\(\frac{3}{4}\)
\(\frac{7}{16}\)
\(\frac{1}{54}\)

Solution

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{8} \) ÷ \( \frac{4}{7} \) = \( \frac{2}{8} \) x \( \frac{7}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{7}{4} \) = \( \frac{2 x 7}{8 x 4} \) = \( \frac{14}{32} \) = \(\frac{7}{16}\)