Freddy has 40 cupcakes. 20 of the cupcakes are chocolate. 10 of the cupcakes are lemon. 8 of the cupcakes are strawberry. The rest of the cupcakes of vanilla.
(a) What fraction of the cupcakes are chocolate? Give the fraction in its simplest form.
(b) What fraction of the cupcakes are lemon? Give the fraction in its simplest form.
(c) What fraction of the cupcakes are strawberry? Give the fraction in its simplest form.
(d) What fraction of the cupcakes are vanilla? Give the fraction in its simplest form.
a) 20/40 = ?
b) 10/40 = ?
c) 8/40 = ?
d) (40-20-10-8)/40 = ?
(a) To find the fraction of cupcakes that are chocolate, we need to divide the number of chocolate cupcakes (20) by the total number of cupcakes (40).
Fraction of chocolate cupcakes = 20/40
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 20.
20 ÷ 20 = 1
40 ÷ 20 = 2
So, the simplified fraction of chocolate cupcakes is:
1/2
(b) To find the fraction of cupcakes that are lemon, we need to divide the number of lemon cupcakes (10) by the total number of cupcakes (40).
Fraction of lemon cupcakes = 10/40
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 10.
10 ÷ 10 = 1
40 ÷ 10 = 4
So, the simplified fraction of lemon cupcakes is:
1/4
(c) To find the fraction of cupcakes that are strawberry, we need to divide the number of strawberry cupcakes (8) by the total number of cupcakes (40).
Fraction of strawberry cupcakes = 8/40
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8.
8 ÷ 8 = 1
40 ÷ 8 = 5
So, the simplified fraction of strawberry cupcakes is:
1/5
(d) To find the fraction of cupcakes that are vanilla, we need to subtract the fractions of chocolate, lemon, and strawberry cupcakes from 1 (since these are the only flavors mentioned).
Fraction of vanilla cupcakes = 1 - (Fraction of chocolate cupcakes + Fraction of lemon cupcakes + Fraction of strawberry cupcakes)
Fraction of vanilla cupcakes = 1 - (1/2 + 1/4 + 1/5)
To combine the fractions with different denominators, we need to find a common denominator. A common denominator for 2, 4, and 5 is 20.
Fraction of vanilla cupcakes = 1 - (10/20 + 5/20 + 4/20)
Now, we can subtract the fractions:
Fraction of vanilla cupcakes = 1 - (19/20)
To simplify this, we can subtract the fractions:
Fraction of vanilla cupcakes = (20/20) - (19/20)
This gives us:
Fraction of vanilla cupcakes = 1/20
So, the simplified fraction of vanilla cupcakes is:
1/20
To find the answers to these questions, we need to compare the number of cupcakes of each flavor to the total number of cupcakes.
(a) To find the fraction of cupcakes that are chocolate, we divide the number of chocolate cupcakes (20) by the total number of cupcakes (40).
Fraction of chocolate cupcakes = 20/40 = 1/2
So, the fraction of cupcakes that are chocolate is 1/2.
(b) To find the fraction of cupcakes that are lemon, we divide the number of lemon cupcakes (10) by the total number of cupcakes (40).
Fraction of lemon cupcakes = 10/40 = 1/4
So, the fraction of cupcakes that are lemon is 1/4.
(c) To find the fraction of cupcakes that are strawberry, we divide the number of strawberry cupcakes (8) by the total number of cupcakes (40).
Fraction of strawberry cupcakes = 8/40 = 1/5
So, the fraction of cupcakes that are strawberry is 1/5.
(d) To find the fraction of cupcakes that are vanilla, we need to subtract the sum of the fractions of the other flavors from 1 since the remaining cupcakes are vanilla.
Fraction of vanilla cupcakes = 1 - (1/2 + 1/4 + 1/5)
To simplify this fraction, we need to find the least common denominator (LCD) of 2, 4, and 5, which is 20.
Fraction of vanilla cupcakes = 1 - (10/20 + 5/20 + 4/20)
= 1 - (19/20)
= 1/20
So, the fraction of cupcakes that are vanilla is 1/20.