What is (9/8)(5)+(8/12)(3) ?

The solution to (9/8)(5)+(8/12)(3) is 7 5/8

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(9/8)(5)+(8/12)(3)

Solution

(\frac{9}{8}) (5) + (\frac{8}{12}) (3)

Solution

7 \frac{5}{8}

Solution steps

(\frac{9}{8}) (5) + (\frac{8}{12}) (3)

\frac{8}{12} = \frac{2}{3}

Cancel the common factor:

4

\frac{2}{3}

= \frac{9}{8} \cdot 5 + \frac{2}{3} \cdot 3

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{9}{8} \cdot 5 : \frac{45}{8}

\frac{9}{8} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{9}{8} \cdot \frac{5}{1}

Apply the fraction rule:

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

= \frac{9 \cdot 5}{8 \cdot 1}

Multiply the numbers:

9 \cdot 5 = 45

= \frac{45}{8 \cdot 1}

Multiply the numbers:

8 \cdot 1 = 8

= \frac{45}{8}

= \frac{45}{8} + \frac{2}{3} \cdot 3

Multiply and divide (left to right)

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

\frac{2}{3} \cdot 3

Convert element to fraction:

3 = \frac{3}{1}

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

Cross-cancel common factor:

3

= \frac{2}{1}

Divide the numbers:

\frac{2}{1} = 2

= 2

= \frac{45}{8} + 2

Add and subtract (left to right)

\frac{45}{8} + 2 : \frac{61}{8}

\frac{45}{8} + 2

\frac{45}{8} + 2 = \frac{61}{8}

\frac{45}{8} + 2

Convert element to fraction:

2 = \frac{2 \cdot 8}{8}

= \frac{2 \cdot 8}{8} + \frac{45}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 8 + 45}{8}

2 \cdot 8 + 45 = 61

2 \cdot 8 + 45

Multiply the numbers:

2 \cdot 8 = 16

= 16 + 45

Add the numbers:

16 + 45 = 61

= 61

= \frac{61}{8}

= \frac{61}{8}

= \frac{61}{8}

Convert improper fractions to mixed numbers:

\frac{61}{8} = 7 \frac{5}{8}

\frac{61}{8} = 7

Remainder

5

\frac{61}{8}

Write the problem in long division format

8 \overline{∣ 61}

Divide

61

8

to get

7

Divide

61

8

to get

7

7 8 \overline{∣ 61}

Multiply the quotient digit

(7)

by the divisor

8

7 8 \overline{∣ 61} \underline{56}

Subtract

56

from

61

7 8 \overline{∣ 61} \underline{56} 5

7 8 \overline{∣ 61} \underline{56} 5

The solution for Long Division of

\frac{61}{8}

7

with remainder of

5

7 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{61}{8} = 7 \frac{5}{8}

= 7 \frac{5}{8}

= 7 \frac{5}{8}

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Frequently Asked Questions (FAQ)

What is (9/8)(5)+(8/12)(3) ?
The solution to (9/8)(5)+(8/12)(3) is 7 5/8