Math

QuestionMultiply and simplify: 24356924 \cdot \frac{3}{5} \cdot \frac{6}{9}. What is the answer as a whole or mixed number?

Studdy Solution

STEP 1

Assumptions1. We are multiplying three numbers24, 35\frac{3}{5}, and 69\frac{6}{9}. . We need to simplify the result to the lowest terms.
3. If possible, the result should be written as a whole or mixed number.

STEP 2

First, we will multiply the three numbers together. The order of multiplication does not matter due to the commutative property of multiplication.
2456924 \cdot \frac{}{5} \cdot \frac{6}{9}

STEP 3

We can simplify the multiplication by first multiplying the fractions and then multiplying the result with24.
24(3569)24 \cdot \left(\frac{3}{5} \cdot \frac{6}{9}\right)

STEP 4

Now, we multiply the fractions.
369=369=1845\frac{3}{} \cdot \frac{6}{9} = \frac{3 \cdot6}{ \cdot9} = \frac{18}{45}

STEP 5

We can simplify the fraction 1845\frac{18}{45} by dividing the numerator and the denominator by their greatest common divisor, which is9.
1845=18÷945÷9=25\frac{18}{45} = \frac{18 \div9}{45 \div9} = \frac{2}{5}

STEP 6

Now, we multiply the simplified fraction with24.
2425=2425=48524 \cdot \frac{2}{5} = \frac{24 \cdot2}{5} = \frac{48}{5}

STEP 7

The fraction 485\frac{48}{5} is an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator.
485=935\frac{48}{5} =9 \frac{3}{5}So, 243569=93524 \cdot \frac{3}{5} \cdot \frac{6}{9} =9 \frac{3}{5}.

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