Math

QuestionWhich expressions equal the quotient of 8÷1458 \div 1 \frac{4}{5}? Choose all that apply: A. 18145\frac{1}{8} \cdot 1 \frac{4}{5}, B. 40÷940 \div 9, C. 8598 \cdot \frac{5}{9}, D. 8948 \cdot \frac{9}{4}, E. 8÷958 \div \frac{9}{5}, F. 8958 \cdot \frac{9}{5}.

Studdy Solution

STEP 1

Assumptions1. The expressions are mathematical expressions involving division and multiplication. . We are looking for expressions that have the same quotient as 8÷1458 \div1 \frac{4}{5}.

STEP 2

First, we need to simplify the expression 8÷1458 \div1 \frac{4}{5}. To do this, we need to convert the mixed number 1451 \frac{4}{5} to an improper fraction.
145=5×1+45=951 \frac{4}{5} = \frac{5 \times1 +4}{5} = \frac{9}{5}

STEP 3

Now, substitute the improper fraction back into the original expression and simplify.
8÷15=8÷958 \div1 \frac{}{5} =8 \div \frac{9}{5}

STEP 4

Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the expression as follows8÷9=898 \div \frac{9}{} =8 \cdot \frac{}{9}

STEP 5

Calculate the value of the expression.
859=4098 \cdot \frac{5}{9} = \frac{40}{9}

STEP 6

Now, we need to compare the value of 409\frac{40}{9} with each of the given options.

STEP 7

First, compare with option A.1145=195=940\frac{1}{} \cdot1 \frac{4}{5} = \frac{1}{} \cdot \frac{9}{5} = \frac{9}{40}This is not equal to 409\frac{40}{9}, so option A is not correct.

STEP 8

Next, compare with option B.40÷=4040 \div = \frac{40}{}This is equal to 40\frac{40}{}, so option B is correct.

STEP 9

Next, compare with option C.859=4098 \cdot \frac{5}{9} = \frac{40}{9}This is equal to 409\frac{40}{9}, so option C is correct.

STEP 10

Next, compare with option D.894=724=188 \cdot \frac{9}{4} = \frac{72}{4} =18This is not equal to 409\frac{40}{9}, so option D is not correct.

STEP 11

Next, compare with option.8÷95=859=4098 \div \frac{9}{5} =8 \cdot \frac{5}{9} = \frac{40}{9}This is equal to 409\frac{40}{9}, so option is correct.

STEP 12

Finally, compare with option F.895=7258 \cdot \frac{9}{5} = \frac{72}{5}This is not equal to 409\frac{40}{9}, so option F is not correct.
The expressions that have the same quotient as 8÷458 \div \frac{4}{5} are options B, C, and.

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