Examkin

Question

Difficulty: MediumFraction Operations

A quality control inspector is verifying the thickness of four different steel plates. Arrange the following plate thicknesses in order from thinnest to thickest.

  1. 115161\frac{5}{16} inches
  2. 2111321\frac{11}{32} inches
  3. 31381\frac{3}{8} inches
  4. 42316\frac{23}{16} inches

Answer

The correct order from thinnest to thickest is 15161\frac{5}{16} inches, 111321\frac{11}{32} inches, 1381\frac{3}{8} inches, and 2316\frac{23}{16} inches.
To accurately compare these lengths, they must all be expressed with a common denominator. The lowest common denominator for 8, 16, and 32 is 32. Converting the values yields 1516=42321\frac{5}{16} = \frac{42}{32}, 11132=43321\frac{11}{32} = \frac{43}{32}, 138=44321\frac{3}{8} = \frac{44}{32}, and 2316=4632\frac{23}{16} = \frac{46}{32}. Ordering by the numerators from lowest to highest gives the sequence 15161\frac{5}{16}, 111321\frac{11}{32}, 1381\frac{3}{8}, and 2316\frac{23}{16}.

Step-by-Step Solution

1
Convert all mixed numbers to improper fractions.
138=1181\frac{3}{8} = \frac{11}{8}; 1516=21161\frac{5}{16} = \frac{21}{16}; 11132=43321\frac{11}{32} = \frac{43}{32}. The fraction 2316\frac{23}{16} is already in improper form.
Working with improper fractions simplifies the process of finding a common denominator.
2
Determine the lowest common denominator (LCD) for the fractions 118\frac{11}{8}, 2316\frac{23}{16}, 2116\frac{21}{16}, and 4332\frac{43}{32}.
The LCD for 8, 16, and 32 is 32.
A common denominator is required to accurately compare the absolute sizes of the fractions.
3
Convert each fraction into an equivalent fraction with a denominator of 32.
118=4432\frac{11}{8} = \frac{44}{32}; 2316=4632\frac{23}{16} = \frac{46}{32}; 2116=4232\frac{21}{16} = \frac{42}{32}; 4332\frac{43}{32} remains 4332\frac{43}{32}.
This normalization allows for direct comparison of the numerators to determine size.
4
Order the numerators from smallest to largest and map them back to their original forms.
The numerators in order are 42<43<44<4642 < 43 < 44 < 46. This corresponds to 4232\frac{42}{32} (15161\frac{5}{16}), 4332\frac{43}{32} (111321\frac{11}{32}), 4432\frac{44}{32} (1381\frac{3}{8}), and 4632\frac{46}{32} (2316\frac{23}{16}).
When the denominators are identical, the magnitude of the fraction is directly proportional to its numerator.

Key Concept

Comparing and Ordering Fractions
Rate this question

Topics

Fraction Operations

More questions from this topic