karen decorated her mother's birthday cake. one-third of candles are pink, three-eights are yellow, one-quater are blue and the two remaining candles are white. calculate
(a). the fraction of candles that are white.
(b). the total number of candles on the cake.
a. Add the fractions:
1/3 + 3/8 + 1/4 =
8/24 + 9/24 + 6/24 = 23/24
24/24 - 23/24 = 1/24
To calculate the fraction of candles that are white, first, we need to find the fraction of candles that are not white, and then subtract that from 1.
Given:
Pink candles: 1/3
Yellow candles: 3/8
Blue candles: 1/4
To find the fraction of candles that are not white, we add up the fractions of each color candle:
1/3 (pink) + 3/8 (yellow) + 1/4 (blue) = 8/24 + 9/24 + 6/24
Now, let's find the common denominator (24):
(8 + 9 + 6) / 24 = 23/24
The fraction of candles that are not white is 23/24.
To find the fraction of candles that are white, we subtract the fraction of candles that are not white from 1:
1 - 23/24 = 1/24
Therefore, the fraction of candles that are white is 1/24.
To calculate the total number of candles on the cake, we need to know the number of candles in each color category.
Given:
Pink candles: 1/3
Yellow candles: 3/8
Blue candles: 1/4
White candles: 2
To find the total number of candles, we add the number of candles in each color category:
Pink candles: 1/3 * Total number of candles = 1/3 * Total number of candles
Yellow candles: 3/8 * Total number of candles = 3/8 * Total number of candles
Blue candles: 1/4 * Total number of candles = 1/4 * Total number of candles
White candles: 2
Since we know that the sum of all the candles equals the total number of candles, we can write the equation:
1/3 * Total number of candles + 3/8 * Total number of candles + 1/4 * Total number of candles + 2 = Total number of candles
To solve for the total number of candles, let's find a common denominator:
[(8 + 9 + 6)/24] * Total number of candles + 2 = Total number of candles
[23/24] * Total number of candles + 2 = Total number of candles
Multiply both sides by 24 to remove the denominator:
23 * Total number of candles + 48 = 24 * Total number of candles
48 = 24 * Total number of candles - 23 * Total number of candles
48 = Total number of candles
Therefore, the total number of candles on the cake is 48.
To solve this problem, we need to break it down step by step. Let's first calculate the fraction of candles that are white.
Step 1: Add up the fractions of the different colored candles:
1/3 (pink) + 3/8 (yellow) + 1/4 (blue)
Step 2: Find a common denominator for these three fractions. Since the denominators are all different (3, 8, and 4), we need to find the least common multiple (LCM) of these three numbers, which is 24.
Step 3: Convert each fraction to have a denominator of 24:
1/3 * 8/8 (pink) = 8/24
3/8 * 3/3 (yellow) = 9/24
1/4 * 6/6 (blue) = 6/24
Step 4: Add up the fractions:
8/24 + 9/24 + 6/24 = 23/24
Therefore, the fraction of candles that are white is 1 - 23/24, which simplifies to 1/24.
Now let's calculate the total number of candles on the cake.
Step 1: Determine the total number of candles represented by the fraction 23/24. Since the fraction 1/24 represents the white candles, we can think of the fraction 23/24 as representing the non-white candles.
Step 2: Set up a proportion to find the total number of candles:
23/24 = x/total number of candles
Step 3: Cross multiply:
23 * total number of candles = 24 * x
Step 4: Simplify:
23 * total number of candles = 24x
Step 5: Solve for x by dividing both sides by 24:
total number of candles = (24x) / 23
So, the total number of candles on the cake is (24x) / 23.