What is (5/8+3/10)\times 4 ?

The solution to (5/8+3/10)\times 4 is 3 7/10

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Popular >

(5/8+3/10)\times 4

Solution

(\frac{5}{8} + \frac{3}{10}) \cdot 4

Solution

3 \frac{7}{10}

Solution steps

(\frac{5}{8} + \frac{3}{10}) \cdot 4

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{5}{8} + \frac{3}{10}) : \frac{37}{40}

\frac{5}{8} + \frac{3}{10}

\frac{5}{8} + \frac{3}{10} = \frac{37}{40}

\frac{5}{8} + \frac{3}{10}

Least Common Multiplier of

8, 10 : 40

8, 10

Least Common Multiplier (LCM)

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

8

10

= 2 \cdot 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 5 = 40

= 40

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

40

For

\frac{5}{8} :

multiply the denominator and numerator by

5

\frac{5}{8} = \frac{5 \cdot 5}{8 \cdot 5} = \frac{25}{40}

For

\frac{3}{10} :

multiply the denominator and numerator by

4

\frac{3}{10} = \frac{3 \cdot 4}{10 \cdot 4} = \frac{12}{40}

= \frac{25}{40} + \frac{12}{40}

Since the denominators are equal, combine the fractions:

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

= \frac{25 + 12}{40}

Add the numbers:

25 + 12 = 37

= \frac{37}{40}

= \frac{37}{40}

= \frac{37}{40} \cdot 4

Multiply and divide (left to right)

\frac{37}{40} \cdot 4 : \frac{37}{10}

\frac{37}{40} \cdot 4

Convert element to fraction:

4 = \frac{4}{1}

= \frac{37}{40} \cdot \frac{4}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{37 \cdot 4}{40 \cdot 1}

\frac{37 \cdot 4}{40 \cdot 1} = \frac{37}{10}

\frac{37 \cdot 4}{40 \cdot 1}

Multiply the numbers:

40 \cdot 1 = 40

= \frac{37 \cdot 4}{40}

Factor the number:

40 = 4 \cdot 10

= \frac{37 \cdot 4}{4 \cdot 10}

Cancel the common factor:

4

= \frac{37}{10}

= \frac{37}{10}

= \frac{37}{10}

Convert improper fractions to mixed numbers:

\frac{37}{10} = 3 \frac{7}{10}

\frac{37}{10} = 3

Remainder

7

\frac{37}{10}

Write the problem in long division format

10 \overline{∣ 37}

Divide

37

10

to get

3

Divide

37

10

to get

3

3 10 \overline{∣ 37}

Multiply the quotient digit

(3)

by the divisor

10

3 10 \overline{∣ 37} \underline{30}

Subtract

30

from

37

3 10 \overline{∣ 37} \underline{30} 7

3 10 \overline{∣ 37} \underline{30} 7

The solution for Long Division of

\frac{37}{10}

3

with remainder of

7

3 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{37}{10} = 3 \frac{7}{10}

= 3 \frac{7}{10}

= 3 \frac{7}{10}

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6 \div 3 + 3^{2} \times 4 - 2

23-(15+0*6)

23 - (15 + 0 \cdot 6)

2*6^4

2 \cdot 6^{4}

Frequently Asked Questions (FAQ)

What is (5/8+3/10)\times 4 ?
The solution to (5/8+3/10)\times 4 is 3 7/10