What is 3\times (1 2/3+1/2) ?

The solution to 3\times (1 2/3+1/2) is 6 1/2

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Popular >

3\times (1 2/3+1/2)

Solution

3 \cdot (1 \frac{2}{3} + \frac{1}{2})

Solution

6 \frac{1}{2}

Solution steps

3 \cdot (1 \frac{2}{3} + \frac{1}{2})

Convert mixed numbers to improper fractions:

1 \frac{2}{3} = \frac{5}{3}

1 \frac{2}{3}

Convert mixed numbers to improper fraction:

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

1 \frac{2}{3} = \frac{1 \cdot 3 + 2}{3}

= \frac{5}{3}

= 3 \cdot (\frac{5}{3} + \frac{1}{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{5}{3} + \frac{1}{2}) : \frac{13}{6}

\frac{5}{3} + \frac{1}{2}

\frac{5}{3} + \frac{1}{2} = \frac{13}{6}

\frac{5}{3} + \frac{1}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

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

6

For

\frac{5}{3} :

multiply the denominator and numerator by

2

\frac{5}{3} = \frac{5 \cdot 2}{3 \cdot 2} = \frac{10}{6}

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= \frac{10}{6} + \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{10 + 3}{6}

Add the numbers:

10 + 3 = 13

= \frac{13}{6}

= \frac{13}{6}

= 3 \cdot \frac{13}{6}

Multiply and divide (left to right)

3 \cdot \frac{13}{6} : \frac{13}{2}

3 \cdot \frac{13}{6}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \cdot \frac{13}{6}

Apply the fraction rule:

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

= \frac{3 \cdot 13}{1 \cdot 6}

\frac{3 \cdot 13}{1 \cdot 6} = \frac{13}{2}

\frac{3 \cdot 13}{1 \cdot 6}

Multiply the numbers:

1 \cdot 6 = 6

= \frac{3 \cdot 13}{6}

Factor the number:

6 = 3 \cdot 2

= \frac{3 \cdot 13}{3 \cdot 2}

Cancel the common factor:

3

= \frac{13}{2}

= \frac{13}{2}

= \frac{13}{2}

Convert improper fractions to mixed numbers:

\frac{13}{2} = 6 \frac{1}{2}

\frac{13}{2} = 6

Remainder

1

\frac{13}{2}

Write the problem in long division format

2 \overline{∣ 13}

Divide

13

2

to get

6

Divide

13

2

to get

6

6 2 \overline{∣ 13}

Multiply the quotient digit

(6)

by the divisor

2

6 2 \overline{∣ 13} \underline{12}

Subtract

12

from

13

6 2 \overline{∣ 13} \underline{12} 1

6 2 \overline{∣ 13} \underline{12} 1

The solution for Long Division of

\frac{13}{2}

6

with remainder of

1

6 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{13}{2} = 6 \frac{1}{2}

= 6 \frac{1}{2}

= 6 \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is 3\times (1 2/3+1/2) ?
The solution to 3\times (1 2/3+1/2) is 6 1/2