Calculate [tex]$4 \div \frac{5}{7}$[/tex]
Give your answer as a fraction in its lowest terms.
Answer (2)
Rewrite the division as a multiplication by the reciprocal: 4 d i v 7 5 = 4 t im es 5 7 .
Multiply the fractions: 1 4 t im es 5 7 = 1 t im es 5 4 t im es 7 .
Calculate the numerator and denominator: 5 28 .
The fraction 5 28 is already in its lowest terms, so the final answer is 5 28 .
Explanation
Understanding the Problem We need to calculate 4 d i v 7 5 and express the answer as a fraction in its lowest terms.
Rewriting the Division as Multiplication To divide by a fraction, we multiply by its reciprocal. The reciprocal of 7 5 is 5 7 . So, we have:
4 d i v 7 5 = 4 t im es 5 7
Multiplying the Fractions Now, we multiply the whole number 4 by the fraction 5 7 . We can write 4 as a fraction 1 4 :
1 4 t im es 5 7 = 1 t im es 5 4 t im es 7
Calculating the Result Next, we perform the multiplication in the numerator and the denominator:
1 t im es 5 4 t im es 7 = 5 28
Checking for Simplification Finally, we check if the fraction 5 28 can be simplified. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 5 are 1 and 5. The only common factor is 1, so the fraction is already in its lowest terms.
Therefore, the answer is 5 28 .
Examples
Imagine you are baking a cake and the recipe calls for dividing 4 cups of flour into portions of 7 5 cup each. Calculating 4 d i v 7 5 helps you determine how many portions you can make. This type of calculation is useful in various real-life scenarios, such as dividing ingredients, measuring quantities, or splitting resources into equal parts. Understanding fractions and division is essential for accurate measurements and fair distributions.
To solve 4 ÷ 7 5 , rewrite it as 4 × 5 7 and simplify the multiplication to get 5 28 , which is already in its lowest terms.
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