QuestionCalculate $\left(1 \frac{17}{25} \cdot 2 \frac{1}{7}-2 \frac{4}{7} \cdot 1 \frac{2}{5}\right) \cdot 2 \frac{7}{9}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(1 \frac{17}{25} \cdot \frac{1}{7}- \frac{4}{7} \cdot1 \frac{}{5}\right) \cdot \frac{7}{9}$ . . We need to simplify this expression following the order of operations, which is parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to convert the mixed numbers into improper fractions.For $1 \frac{17}{25}$ , the improper fraction is obtained by multiplying the whole number part by the denominator of the fractional part and adding the numerator of the fractional part. This gives the numerator of the improper fraction. The denominator of the improper fraction is the same as the denominator of the fractional part.
$1 \frac{17}{25} = \frac{1 \times25 +17}{25} = \frac{42}{25}$

STEP 3

Similarly, convert the other mixed numbers to improper fractions.
$2 \frac{1}{7} = \frac{2 \times7 +1}{7} = \frac{15}{7}$ $2 \frac{}{7} = \frac{2 \times7 +}{7} = \frac{18}{7}$ $1 \frac{2}{5} = \frac{1 \times5 +2}{5} = \frac{7}{5}$ $2 \frac{7}{9} = \frac{2 \times9 +7}{9} = \frac{25}{9}$

STEP 4

Substitute these improper fractions back into the original expression.
$\left(\frac{42}{25} \cdot \frac{15}{7}-\frac{18}{7} \cdot \frac{7}{}\right) \cdot \frac{25}{9}$

STEP 5

Now, perform the multiplication inside the parentheses. $\frac{42}{25} \cdot \frac{15}{7} = \frac{42 \times15}{25 \times7} = \frac{630}{175}$ $\frac{18}{7} \cdot \frac{7}{5} = \frac{18 \times7}{7 \times5} = \frac{126}{35}$

STEP 6

Subtract the second product from the first inside the parentheses.
$\frac{630}{175} - \frac{126}{35} = \frac{630 \times35 -126 \times175}{175 \times35} = \frac{22050 -22050}{6125} =0$

STEP 7

Now, multiply the result inside the parentheses by $\frac{25}{9}$ .
$0 \cdot \frac{25}{9} =0$ The result of the given expression is0.

Was this helpful?

QuestionCalculate $\left(1 \frac{17}{25} \cdot 2 \frac{1}{7}-2 \frac{4}{7} \cdot 1 \frac{2}{5}\right) \cdot 2 \frac{7}{9}$ .

Studdy Solution

STEP 1

STEP 2

STEP 3

Similarly, convert the other mixed numbers to improper fractions.
$2 \frac{1}{7} = \frac{2 \times7 +1}{7} = \frac{15}{7}$ $2 \frac{}{7} = \frac{2 \times7 +}{7} = \frac{18}{7}$ $1 \frac{2}{5} = \frac{1 \times5 +2}{5} = \frac{7}{5}$ $2 \frac{7}{9} = \frac{2 \times9 +7}{9} = \frac{25}{9}$

STEP 4

Substitute these improper fractions back into the original expression.
$\left(\frac{42}{25} \cdot \frac{15}{7}-\frac{18}{7} \cdot \frac{7}{}\right) \cdot \frac{25}{9}$

STEP 5

Now, perform the multiplication inside the parentheses. $\frac{42}{25} \cdot \frac{15}{7} = \frac{42 \times15}{25 \times7} = \frac{630}{175}$ $\frac{18}{7} \cdot \frac{7}{5} = \frac{18 \times7}{7 \times5} = \frac{126}{35}$

STEP 6

Subtract the second product from the first inside the parentheses.
$\frac{630}{175} - \frac{126}{35} = \frac{630 \times35 -126 \times175}{175 \times35} = \frac{22050 -22050}{6125} =0$

STEP 7

Now, multiply the result inside the parentheses by $\frac{25}{9}$ .
$0 \cdot \frac{25}{9} =0$ The result of the given expression is0.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCalculate (11725⋅217−247⋅125)⋅279\left(1 \frac{17}{25} \cdot 2 \frac{1}{7}-2 \frac{4}{7} \cdot 1 \frac{2}{5}\right) \cdot 2 \frac{7}{9}(12517​⋅271​−274​⋅152​)⋅297​.

Studdy Solution

STEP 1

STEP 2

STEP 3

STEP 4

Substitute these improper fractions back into the original expression.(4225⋅157−187⋅7)⋅259\left(\frac{42}{25} \cdot \frac{15}{7}-\frac{18}{7} \cdot \frac{7}{}\right) \cdot \frac{25}{9}(2542​⋅715​−718​⋅7​)⋅925​

STEP 5

STEP 6

STEP 7

Now, multiply the result inside the parentheses by 259\frac{25}{9}925​.0⋅259=00 \cdot \frac{25}{9} =00⋅925​=0The result of the given expression is0.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCalculate $\left(1 \frac{17}{25} \cdot 2 \frac{1}{7}-2 \frac{4}{7} \cdot 1 \frac{2}{5}\right) \cdot 2 \frac{7}{9}$ .

Substitute these improper fractions back into the original expression.
$\left(\frac{42}{25} \cdot \frac{15}{7}-\frac{18}{7} \cdot \frac{7}{}\right) \cdot \frac{25}{9}$

Now, multiply the result inside the parentheses by $\frac{25}{9}$ .
$0 \cdot \frac{25}{9} =0$ The result of the given expression is0.