Multiply.
$-\frac{3}{5} \cdot(-7)$
Write your answer in simplest form.
Answer (2)
Multiply the two numbers: − 5 3 × − 7 .
Rewrite − 7 as − 1 7 .
Multiply the numerators and the denominators: 5 − 3 × 1 − 7 = 5 × 1 ( − 3 ) × ( − 7 ) .
Simplify the fraction to its simplest form: 5 21 .
Explanation
Understanding the problem We are asked to multiply − 5 3 by − 7 and express the result in simplest form.
Multiplying the numbers To multiply two numbers, we simply multiply them together. In this case, we have a negative fraction multiplied by a negative integer. Recall that the product of two negative numbers is a positive number.
Rewriting and multiplying We can rewrite − 7 as − 1 7 . Now we multiply the two fractions: − 5 3 ⋅ ( − 7 ) = − 5 3 ⋅ ( − 1 7 ) To multiply fractions, we multiply the numerators together and the denominators together: 5 ⋅ 1 ( − 3 ) ⋅ ( − 7 ) = 5 21 Since both numbers were negative, the result is positive.
Simplifying the fraction The fraction 5 21 is already in simplest form because 21 and 5 have no common factors other than 1. We can also express this as a mixed number: 4 5 1 , but the question asks for the answer in simplest form, which usually implies an improper fraction.
Final Answer Therefore, the product of − 5 3 and − 7 in simplest form is 5 21 .
Examples
Understanding how to multiply fractions, especially negative ones, is useful in many real-life situations. For example, if you are calculating discounts or figuring out proportions in recipes, you might need to multiply fractions. Suppose you want to calculate a discount of 5 3 off an item that costs $7. This is equivalent to calculating − 5 3 × − 7 , where the negative signs indicate a reduction in price. The result, 5 21 or $4.20, represents the amount of the discount.
The product of − 5 3 and − 7 is 5 21 in simplest form. This is achieved by converting the integer to a fraction and multiplying the two fractions together, noting that the product of two negatives is positive. The final result can be left as an improper fraction or converted to a mixed number if desired.
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