Divide $7 / 24$ by $35 / 48$ and reduce the quotient to the lowest fraction.
A. $4 / 10$
B. $245 / 1152$
C. $2 / 5$
D. $42 / 48$
Answer (1)
Rewrite the division as multiplication by the reciprocal: 24 7 ÷ 48 35 = 24 7 × 35 48 .
Simplify the fractions before multiplying: 24 7 × 35 48 = 1 1 × 5 2 .
Multiply the simplified fractions: 1 × 5 1 × 2 = 5 2 .
The quotient in its lowest terms is: 5 2 .
Explanation
Problem Analysis We are asked to divide 24 7 by 48 35 and reduce the result to the lowest fraction. This means we need to perform the division and simplify the resulting fraction.
Division as Multiplication To divide 24 7 by 48 35 , we multiply 24 7 by the reciprocal of 48 35 , which is 35 48 . So, we have: 24 7 ÷ 48 35 = 24 7 × 35 48
Simplifying Fractions Now, we simplify the fractions before multiplying. We can simplify 35 7 to 5 1 and 24 48 to 1 2 . So we have: 24 7 × 35 48 = 1 1 × 1 1 × 5 2 = 1 × 5 1 × 2 = 5 2
Final Result The resulting fraction is 5 2 , which is already in its lowest terms. Therefore, the answer is 5 2 .
Examples
Understanding fractions and how to divide them is essential in many real-life situations. For example, if you are baking a cake and need to halve a recipe that calls for 24 7 of a cup of flour, you would divide 24 7 by 2. This is the same as multiplying 24 7 by 2 1 , which gives you 48 7 of a cup. Similarly, if you are sharing 24 7 of a pizza equally among 48 35 of your friends, you would perform the same division to find out how much pizza each friend gets.
