Johnny spent 4 2/3 for his exams studying for his math exams. He spent 3/4 of the time studying for math. How many hours did Johnny spend stydying for his exam? How do I show the number sentence?
3/4 x = 4 2/3
x = (4 2/3)/(3/4)
= 14/3 * 4/3
...
To find out how many hours Johnny spent studying for his math exams, we can follow these steps:
1. Convert the mixed number 4 2/3 into an improper fraction. To do this, multiply the whole number (4) by the denominator (3) and add the numerator (2). Then, place the result over the original denominator. In this case, it will be (4 * 3 + 2) / 3 = 14/3.
2. Multiply the fraction 14/3 by the fraction representing the time spent studying for math, which is 3/4. To multiply fractions, multiply the numerators together and multiply the denominators together. The result is (14/3) * (3/4) = (14 * 3) / (3 * 4) = 42/12.
3. Simplify the fraction if possible. In this case, both the numerator and the denominator are divisible by 6, so we can divide them both by 6 to simplify the fraction. The simplified fraction is 7/2.
Therefore, Johnny spent 7/2 hours studying for his math exams. To represent this as a number sentence, you can write:
4 2/3 * 3/4 = 7/2