I'm teaching myself maths from a text book. I have spent several hours over this simple question, but I cannot solve it. A jug contains 1 3/4 litres of milk. Mrs Jones makes a rice pudding with 1 1/3 litres of the milk in the jug. What fraction of the milk in the jug does Mrs Jones use to make a rice pudding? I have tried working it out like this: 1 1/3 x 1 3/4, which I think is 1 1/3 of 1 3/4, but my answer is 7/3, when the correct anwer is 16/21. I have also tried subtracting thus: 1 3/4 - 1 1/3, which is 5/12, and think that leaves 7/12, which is still not 16/21. Would be so grateful if anyone could explain what I am doing wrong?
puzzle with fractions
- Thread starter Yvonne
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D
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What fraction of the milk in the jug does Mrs Jones use
= \(\displaystyle \dfrac{(milk used)}{(available milk)}\)
= \(\displaystyle \ \dfrac{\frac{4}{3}}{\frac{7}{4}}\)
= \(\displaystyle \ \frac{4}{3} * \frac{4}{7}\)
= \(\displaystyle \dfrac{16}{21}\)
Do not understand the symbols
Thank you so much, but I do not know what the symbols mean. I am totally non mathematical.
Thank you so much, but I do not know what the symbols mean. I am totally non mathematical.
D
Deleted member 4993
Guest
Thank you so much, but I do not know what the symbols mean. I am totally non mathematical.
* means multiply
other than that - which symbols?
Don't worry. Fractions seem to be non-intuitive for people who are first learning about them. Let's start at the VERY beginning to make sure there are no questions along the way.
A fraction consists of two parts written as 3/4 or \(\displaystyle \dfrac{3}{4}.\)
The part to the left of the / or above the bar is called the numerator, and the part to the right of the / or below the bar is called the denominator. These names actually do explain what a fraction means.
What is 3/4 of a liter? The denominator (4 in this case) says not to think about a liter as our unit any more, but to name (or denominate) as our counting unit the volume that results from dividing a liter into exactly 4 exactly equal parts. The numerator (which is Latin for a person who counts) tells us how many of those units that we have.
\(\displaystyle \dfrac{3}{4} = \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4} = 3 * \dfrac{1}{4}.\)
I know; you already knew all that, but I wanted to make absolutely sure because math is cumulative.
What does 1 3/4 mean? It means 1 + 3/4. This is called a mixed fraction because it mixes up two different units. We have 1 liter and 3 quarter liters. It is really more convenient to use just one unit. How many quarter liters are there in one liter? Obviously four. So
\(\displaystyle 1\ 3/4 = 1 + \dfrac{3}{4} = 1 + \left(3 * \dfrac{1}{4}\right) = \left(4 * \dfrac{1}{4}\right) + \left(3 * \dfrac{1}{4}\right) = \(4 + 3) * \dfrac{1}{4} = 7 * \dfrac{1}{4} = \dfrac{7}{4}.\)
We are not counting in two different units any longer, but just one. 7/4 of a liter means to count in terms of the unit that is equal to dividing a liter into four equal parts and to count out 7 of those units. With me so far?
Now we have dealt in whole numbers so far, but we can get fancy. Let's go to your problem.
We have a jar that holds 1 3/4 liters or 7 quarters of a liter. We could name a new unit called a "jug" that is equal to 7/4ths of a liter.
Now our recipe calls for 1 1/3 liter or 4 thirds of a liter. We could name a unit called a "pudding" that is equal to 4/3rds of a liter.
What is one pudding equal to in terms of jugs?
Mathematically what = \(\displaystyle \dfrac{1\ pudding}{1\ jug}?\)
We know what each of those is in liters so \(\displaystyle \dfrac{1\ pudding}{1\ jug} = \dfrac{\frac{4}{3}\ liters}{\frac{7}{4}\ liters}.\)
In other words, by a long road, we have reached the same point Subhotosh Khan did.
BUT WHAT IN THE WORLD DOES THAT MESS SIMPLIFY TO?
There is a simple rule. To divide by a fraction, turn the fraction upside down and multiply.
\(\displaystyle \dfrac{\frac{4}{3}}{\frac{7}{4}} = \dfrac{4}{3} * \dfrac{4}{7} = \dfrac{16}{21}.\)
And what does that mean? It means if you divided a "jug" into 21 exactly equal parts, a "pudding" would equal exactly 16 times as much as one of those parts.
If you have more questions, ask away. (fixed a typo)
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Had lots of funny hieroglyphics
I did have lots of funny hieroglyphics, probably to do with differences in our symbol processing. I must have been seeing word processing symbols which must be normally hidden. Now they have gone and all is now clear. Thank you.
I did have lots of funny hieroglyphics, probably to do with differences in our symbol processing. I must have been seeing word processing symbols which must be normally hidden. Now they have gone and all is now clear. Thank you.