What is (10/7)(5/4+4/5) ?

The solution to (10/7)(5/4+4/5) is (411 3/7)/(20)

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Popular Pre Algebra >

(10/7)(5/4+4/5)

Solution

(\frac{10}{7}) (\frac{5}{4} + \frac{4}{5})

Solution

\frac{411 \frac{3}{7}}{20}

Decimal

8.80714 \dots

Solution steps

(\frac{10}{7}) (\frac{5}{4} + \frac{4}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{10}{7}) : 1 \frac{3}{7}

\frac{10}{7}

Convert improper fractions to mixed numbers:

\frac{10}{7} = 1 \frac{3}{7}

\frac{10}{7} = 1

Remainder

3

\frac{10}{7}

Write the problem in long division format

7 \overline{∣ 10}

Divide

10

7

to get

1

Divide

10

7

to get

1

1 7 \overline{∣ 10}

Multiply the quotient digit

(1)

by the divisor

7

1 7 \overline{∣ 10} \underline{7}

Subtract

7

from

10

1 7 \overline{∣ 10} \underline{7} 3

1 7 \overline{∣ 10} \underline{7} 3

The solution for Long Division of

\frac{10}{7}

1

with remainder of

3

1 Remainder 3

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{10}{7} = 1 \frac{3}{7}

= 1 \frac{3}{7}

= 1 \frac{3}{7}

= 1 \frac{3}{7} (\frac{5}{4} + \frac{4}{5})

Calculate within parentheses

(\frac{5}{4} + \frac{4}{5}) : \frac{41}{20}

\frac{5}{4} + \frac{4}{5}

\frac{5}{4} + \frac{4}{5} = \frac{41}{20}

\frac{5}{4} + \frac{4}{5}

Least Common Multiplier of

4, 5 : 20

4, 5

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Multiply each factor the greatest number of times it occurs in either

4

5

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

20

For

\frac{5}{4} :

multiply the denominator and numerator by

5

\frac{5}{4} = \frac{5 \cdot 5}{4 \cdot 5} = \frac{25}{20}

For

\frac{4}{5} :

multiply the denominator and numerator by

4

\frac{4}{5} = \frac{4 \cdot 4}{5 \cdot 4} = \frac{16}{20}

= \frac{25}{20} + \frac{16}{20}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{25 + 16}{20}

Add the numbers:

25 + 16 = 41

= \frac{41}{20}

= \frac{41}{20}

= 1 \frac{3}{7} \frac{41}{20}

Multiply and divide (left to right)

1 \frac{3}{7} \frac{41}{20} : \frac{411 \frac{3}{7}}{20}

1 \frac{3}{7} \frac{41}{20}

1 \frac{3}{7} \frac{41}{20} = \frac{411 \frac{3}{7}}{20}

= \frac{411 \frac{3}{7}}{20}

= \frac{411 \frac{3}{7}}{20}

Popular Examples

(+8-3-2-1)^3(+12-3-4)^2

Frequently Asked Questions (FAQ)

What is (10/7)(5/4+4/5) ?
The solution to (10/7)(5/4+4/5) is (411 3/7)/(20)

(10/7)(5/4+4/5)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is (10/7)(5/4+4/5) ?

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