Estimate the value of each expression. Put them in order from least to greatest. 13.5 ÷ 2/5 −26/3 + 16 1/4 34 × 5/3

Let’s calculate each expression step-by-step and then put them in order from least to greatest.

1. For ( 13.5 div frac{2}{5} ):

– Dividing by a fraction is the same as multiplying by its reciprocal:

[

13.5 div frac{2}{5} = 13.5 times frac{5}{2} = frac{13.5 times 5}{2} = frac{67.5}{2} = 33.75

]

2. For ( -frac{26}{3} + 16 frac{1}{4} ):

– First, convert ( 16 frac{1}{4} ) to an improper fraction:

[

16 frac{1}{4} = frac{65}{4}

]

– Now, we need a common denominator to add ( -frac{26}{3} ) and ( frac{65}{4} ). The least common multiple of 3 and 4 is 12.
– Convert both fractions:

[

-frac{26}{3} = -frac{104}{12}, quad frac{65}{4} = frac{195}{12}

]

– Add them together:

[

-frac