Multiply.
[tex]\frac{2}{-7} \cdot \frac{-5}{-9} \cdot 3[/tex]
Write your answer in simplest form.
Answer (2)
Rewrite the expression: − 7 2 ⋅ − 9 − 5 ⋅ 3 = − 7 2 ⋅ 9 5 ⋅ 3 .
Multiply the numerators and denominators: ( − 7 ) ⋅ 9 2 ⋅ 5 ⋅ 3 = − 63 30 .
Simplify the fraction by dividing by the GCD (3): − 63 ÷ 3 30 ÷ 3 = − 21 10 .
Write the final simplified fraction: − 21 10 .
Explanation
Understanding the Problem We are asked to multiply three numbers: − 7 2 , − 9 − 5 , and 3 . Our goal is to simplify the result to its simplest form.
Rewriting the Expression First, let's rewrite the expression to make it easier to work with: − 7 2 ⋅ − 9 − 5 ⋅ 3 = − 7 2 ⋅ 9 5 ⋅ 3
Multiplying Numerators and Denominators Now, we multiply the numerators and the denominators: ( − 7 ) ⋅ 9 2 ⋅ 5 ⋅ 3 = − 63 30
Simplifying the Fraction Next, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 30 and 63 is 3. We divide both the numerator and the denominator by 3: − 63 ÷ 3 30 ÷ 3 = − 21 10
Final Answer Finally, we can write the fraction as: − 21 10 = − 21 10 So, the simplified form of the given expression is − 21 10 .
Examples
In real life, multiplying fractions is useful when calculating proportions or sharing quantities. For example, if you have 7 2 of a pizza and you want to give 9 5 of your share to a friend, and then multiply the result by 3 to account for three such friends, you would perform this calculation to determine how much of the whole pizza each friend receives. This type of calculation is also fundamental in various fields like cooking, construction, and finance, where proportional relationships are frequently encountered.
The multiplication of the given fractions and the whole number results in a simplified fraction of − 21 10 . This involves rewriting the expression, multiplying the numerators and denominators, and then simplifying the resulting fraction. The final answer is represented with the negative sign in the standard conventional form.
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