A loaf of bread was shared by four people. The amounts they each received were in the ratio of 2/3 : 1/2 : 1/3 : 1/4. What fraction of the loaf of bread did each person receive?
recipe for bread and butter pudding 6 slices of bread,2eggs,1pint of milk,150g raisins,10g margarine this recipe is enough for 4 people work each one out for 9 people
To find out the fraction of the loaf of bread that each person received, we need to add the ratios and then divide the whole loaf into equal parts based on each person's share.
The given ratios are:
2/3 : 1/2 : 1/3 : 1/4
To add the fractions, we need to find the common denominator. The least common multiple (LCM) of 3, 2, 3, and 4 is 12.
Converting the fractions to have a denominator of 12:
(2/3) * (4/4) = 8/12
(1/2) * (6/6) = 6/12
(1/3) * (4/4) = 4/12
(1/4) * (3/3) = 3/12
Now we can sum up the fractions:
8/12 + 6/12 + 4/12 + 3/12 = 21/12
To distribute the loaf of bread equally, we need to divide it by the total fraction of 21/12.
To calculate each person's share, we divide the fraction 21/12 by 4 (the number of people), which gives us:
(21/12) รท 4 = 21/48
So, each person received 21/48 of the loaf of bread.
To find out the fraction of the loaf of bread each person received, we first need to determine the common denominator of the ratios. In this case, the common denominator would be 12 because it is the least common multiple of the denominators (3, 2, 3, and 4).
Next, we need to convert the ratios to have a denominator of 12. To do this, we multiply the numerator and the denominator of each ratio by the same value that makes the denominator equal to 12.
For the first person, the ratio is 2/3. To make the denominator 12, we multiply the numerator and denominator by 4. So, 2/3 * 4/4 = 8/12.
For the second person, the ratio is 1/2. To make the denominator 12, we multiply the numerator and denominator by 6. So, 1/2 * 6/6 = 6/12.
For the third person, the ratio is 1/3. To make the denominator 12, we multiply the numerator and denominator by 4. So, 1/3 * 4/4 = 4/12.
For the fourth person, the ratio is 1/4. To make the denominator 12, we multiply the numerator and denominator by 3. So, 1/4 * 3/3 = 3/12.
Now that we have all the fractions with a common denominator of 12, we can see that the four people received the following fractions of the loaf:
- Person 1 received 8/12 of the loaf.
- Person 2 received 6/12 of the loaf.
- Person 3 received 4/12 of the loaf.
- Person 4 received 3/12 of the loaf.
We can simplify these fractions if needed. In this case, we can simplify the fractions by dividing the numerator and denominator by their greatest common divisor, which is 4.
- Person 1 received 8/12 = 2/3 of the loaf.
- Person 2 received 6/12 = 1/2 of the loaf.
- Person 3 received 4/12 = 1/3 of the loaf.
- Person 4 received 3/12 = 1/4 of the loaf.
So, each person received 2/3, 1/2, 1/3, and 1/4 of the loaf, respectively.
simplify the ratios
(multiply by 12)
2/3 : 1/2 : 1/3 : 1/4
= 8 : 6 : 4 : 3
So there are 21 parts and the fractions each one gets is
8/21, 6/21, etc
(some fractions can be reduced)