A modern deck of cards contains fifty-two cards. (a) How many hearts are there in a deck of cards? (b) What fraction of a deck is hearts?
The Correct Answer and Explanation is:
) How many hearts are there in a deck of cards?
In a standard deck of 52 playing cards, there are four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards, which are the numbers 2 through 10, the jack, the queen, the king, and the ace. Therefore, the number of hearts in the deck is 13.
Answer: There are 13 hearts in a deck of cards.
(b) What fraction of a deck is hearts?
To determine the fraction of a deck that is hearts, we take the number of hearts (13) and divide it by the total number of cards in the deck (52). This gives us the fraction of the deck that is made up of hearts.
Fraction of hearts = 13/52
Simplifying this fraction, we divide both the numerator (13) and the denominator (52) by their greatest common divisor, which is 13:
13 ÷ 13 = 1
52 ÷ 13 = 4
Thus, the simplified fraction is:
1/4
Answer: The fraction of hearts in a deck of cards is 1/4.
Explanation
A deck of 52 playing cards is evenly divided into four suits, with each suit containing 13 cards. Since there are 4 suits, and one of them is hearts, 13 out of the 52 cards belong to the hearts suit. When we calculate the fraction, we express this as 13/52, which simplifies to 1/4. This means that 1/4 of the deck consists of hearts. The concept is quite simple: by dividing the number of hearts by the total number of cards in the deck, we find the proportion of hearts in the deck.
