Final answer:
To arrange the fractions 3/4, 1/8, 9/16, 1 1/4, and 3/8 from smallest to largest, convert them to decimals which are 0.75, 0.125, 0.5625, 1.25, and 0.375 respectively. The ordered sequence from smallest to largest is 1/8, 3/8, 9/16, 3/4, and 1 1/4.
Step-by-step explanation:
To arrange the fractions 3/4, 1/8, 9/16, 1 1/4, and 3/8 from smallest to largest, we need to understand their size relative to each other. A helpful approach is to convert all the numbers to have a common denominator or to convert them to decimals. In this instance, since we have a mixed number (1 1/4), it might be easiest to convert everything to decimals for comparison.
- 1/8 converts to 0.125
- 3/8 converts to 0.375
- 3/4 converts to 0.75
- 9/16 converts to 0.5625
- 1 1/4 converts to 1.25 (since 1 + 1/4 is equivalent to 1 + 0.25)
Now, we can easily compare the decimals to see which is smallest and which is largest:
- 1/8 (0.125)
- 3/8 (0.375)
- 9/16 (0.5625)
- 3/4 (0.75)
- 1 1/4 (1.25)
This gives the fractions in order from smallest to largest: 1/8, 3/8, 9/16, 3/4, and 1 1/4.