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Zorluk: OrtaFraction 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

Cevap

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}.

Adım Adım Çözüm

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.

Anahtar Kavram

Comparing and Ordering Fractions
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Konular

Fraction Operations

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