Arrange the following fractions and mixed numbers in ascending order (from smallest to lar… — Armed Services Vocational Aptitude Battery (ASVAB)

Arrange the following fractions and mixed numbers in ascending order (from smallest to largest).

The correct ascending order is

\frac{7}{8}

1 \frac{1}{4}

\frac{3}{2}

, and

1 \frac{3}{4}

The proper fraction

\frac{7}{8}

is the only value less than 1, placing it first. Converting

\frac{3}{2}

1 \frac{1}{2}

(or

1.5

) allows easy comparison with

1 \frac{1}{4}

(1.25) and

1 \frac{3}{4}

(1.75), confirming the correct ascending sequence.

Identify values less than 1.

\frac{7}{8}

is the only proper fraction (less than 1), making it the smallest.

Proper fractions are always less than mixed numbers or improper fractions.

Convert the improper fraction to a mixed number to make comparison easier.

\frac{3}{2} = 1 \frac{1}{2}

Matching the format of the other numbers allows for a direct comparison of the fractional parts.

Find a common denominator for the fractional parts of the values greater than 1 (

1 \frac{1}{4}

1 \frac{1}{2}

, and

1 \frac{3}{4}

The common denominator is 4.

1 \frac{1}{2}

becomes

1 \frac{2}{4}

Common denominators allow you to directly compare the numerators.

Order the mixed numbers by their fractional parts.

1 \frac{1}{4}

is smaller than

1 \frac{2}{4}

(which is

\frac{3}{2}

), and

1 \frac{2}{4}

is smaller than

1 \frac{3}{4}

Since the whole numbers are identical, the fractions determine the order.

Ordering mixed numbers and improper fractions

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