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Solving word problems by adding and subtracting fractions and mixed numbers, learn how to solve fraction word problems with examples and interactive exercises.
Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
Analysis: To solve this problem, we will add two fractions with like denominators.
Answer: Rachel rode her bike for three-fifths of a mile altogether.
Analysis: To solve this problem, we will subtract two fractions with unlike denominators.
Answer: Stefanie swam one-third of a lap farther in the morning.
Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.
Answer: It took Nick three and one-fourth hours to complete his homework altogether.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.
Answer: Diego and his friends ate six pizzas in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.
Answer: The Cocozzelli family took one-half more days to drive home.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.
Answer: The warehouse has 21 and one-half meters of tape in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.
Answer: The electrician needs to cut 13 sixteenths cm of wire.
Analysis: To solve this problem, we will subtract a mixed number from a whole number.
Answer: The carpenter needs to cut four and seven-twelfths feet of wood.
Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems:
- Add fractions with like denominators.
- Subtract fractions with like denominators.
- Find the LCD.
- Add fractions with unlike denominators.
- Subtract fractions with unlike denominators.
- Add mixed numbers with like denominators.
- Subtract mixed numbers with like denominators.
- Add mixed numbers with unlike denominators.
- Subtract mixed numbers with unlike denominators.
Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.
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How to Solve Improper Fraction Math Problems
How to Do Fractions on a TI-30X IIS
Improper fractions contain a numerator that is equal to or greater than the denominator. These fractions are described as improper because a whole number can be pulled out from them, yielding a mixed number fraction. This mixed number fraction is a simplified version of the number and, therefore, is more desirable because it removes complexity in further operations that may be preformed. Performing operations on improper fractions is a pre-algebra exercise that allows students to become familiar with the concept of rational numbers.
Complete all operations indicated on an improper fraction as normal. For example, (3/2 ) * ( 5/2) = 15/4.
Divide the top number by the bottom number. If there is a remainder write it down for later use. In our example, 4 divides into 15 three times. This yields 3 with a remainder of 3.
Write down the whole number.
Create a fraction beside the whole number with the original denominator value. Continuing from above, 3 ( /4).
Place the remainder from above into the blank numerator. In conclusion, 15 / 4 = 3 3/4.
Check your work by multiplying the denominator by the whole number portion of the mixed number and adding the product to the numerator. Checking the above yields ((4 * 3) + 3)) / 4 = 15 / 4. This check proves the operation was a success and that the improper fraction was simplified properly.
How to convert a fraction to a ratio, how to turn improper fractions into whole numbers, how to square a fraction with a variable, how to type a mixed fraction in a ti-83 plus, how to add fractions with mixed numbers, how to calculate a percentage and solve percent problems, how to get rid of cubed power, how to multiply fractions by percentages, how to write the remainder as a whole number, multiplying fractions, how to convert mixed fractions to ratios, how to subtract, add & simplify fractions, how to integrate the cube root of x, how to divide ratios, how to divide radicals, how to get rid of a variable that is cubed, how to simplify algebraic expressions, how to write an equivalent fraction with a given denominator, what is the identity property of multiplication.
- "Introductory and Intermediate Algebra"; Marvin L. Bittinger and Judith A. Beecher; 2007
- Purplemath; Fractions Review - Mixed Numbers and Improper Fractions; Elizabeth Stapel; 2000
About the Author
Gabriel Dockery began writing in 2009, with his work published on various websites. He is working toward a Bachelor of Science in neuroscience in a transfer program between Ivy Tech College and Indiana State University.
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Adding Fractions With Like Denominators
As I said earlier, this is really easy. With like denominators, we add the numerators, carry the denominator and that’s it. I think that the best way to show this is through examples.
We'll be separating the following examples in two parts.
First we’re dealing with the most simple version with numerator being one, and denominator being the same. Then we’re going to use numerators greater than 1, keeping the denominators alike, of course.
First case of Adding Fractions with Like Denominators
- Numerators = 1
- Like Denominators
As you can see – we had two halves, so it’s even visually obvious that we’re going to get 1 whole (number) once we add them (or "sew" them up).
Now what about this one:
Even by saying what we see on the left hand side: two thirds – we got the answer. :-)
This one has little simplifying at the end. Two fourths = one half.
Now let’s finally look at fifths and sixths.
Same story here, adding numerators…
Again a little reducing of fractions from sixths to thirds.
Second case of Adding Fractions with Like Denominators
- Numerators > 1
As you can see we have an option to write down our solution as 5/2, which is an improper fraction format, or we can write down 2 and 1/2 which is a mixed fraction format (see types of fractions for more info).
Now let’s try some thirds.
In this case we can simplify our solution from 6/3 (improper fraction) to 2 wholes (meaning 2 whole numbers).
Now let's see some 4ths.
I guess you’re starting to see a pattern here – with our denominators being alike, we add the numerators, see if our sum "crossed over" for 1 or more whole numbers, plus the proper fraction "leftovers" (in this case 1/4) – and that’s it.
These were the fifths, now let’s finish with sixths.
This visual combination of fractions represented by pizza pies and numbers should be very useful. You can keep picturing this "duality" even when we remove the pizzas from the picture. It is important that you don’t mix up a numerator with a denominator.
Continue to Adding fractions with unlike denominators .
How to solve Math Word Problems With Fractions
Adding fractions word problems | fraction word problems, sharing buttons:.
00:00 welcome to math with mr. J in this video
00:05 we're going to take a look at adding
00:07 fractions word problems and we're going
00:11 to go through two problems or situations
00:13 where we'll use adding in order to get
00:17 us to our answer so let's jump right in
00:19 the number one here where we have Jose
00:22 spent two-fifths of his money on new
00:25 shirts and one-half of his money on new
00:29 shoes what fraction of his money has
00:32 been spent and what fraction is still
00:35 left so let's take the information from
00:39 the problem here we have two-fifths on
00:42 shirts and we're combining that with how
00:45 much he spent on shoes which would be
00:48 adding together whenever we have
00:49 combining of things it's going to be
00:53 addition so two-fifths plus one-half now
00:59 we do not have a common denominator so
01:03 we need to find one four five and ten so
01:06 the common denominator is going to be
01:09 ten four five minute - so I'm going to
01:11 rewrite the problem to the right here
01:14 and we have a common denominator of 10
01:19 well two-fifths I know five times two
01:22 gives me that denominator of 10 so I
01:25 need to do that to the top in order to
01:28 get an equivalent fraction and 2 times 2
01:31 is 4 so 2/5 is 4/10 equivalent to 4
01:37 tenths now we need to rename 1/2 well 2
01:42 times 5 is 10
01:43 let's do that to the top to get our
01:46 equivalent fraction 1 times 5 is 5 now
01:52 we're ready to add because we have a
01:54 common denominator 4 plus 5 is 9 and we
02:00 keep our denominator of 10 the same so
02:03 this is how much he spent he has spent
02:07 tenths of his money so 9/10 has been
02:11 spent so now we need to figure out what
02:15 fraction of his money is left how do we
02:18 get to the full one whole or ten out of
02:21 ten so what's left so if you spent nine
02:24 tenths that means one tenth is left
02:28 that's what will get us to the full hole
02:31 of ten out of ten or a hundred percent
02:34 of his money so nine tenths has been
02:37 spent and again one tenth is left let's
02:43 take a look at number two
02:45 Quinn red two-fifths of her book over
02:48 the weekend and one sixth on Monday what
02:53 fraction of the book has she read what
02:56 fraction is left so again we're
02:59 combining two-fifths from the weekend
03:02 and then one sixth from Monday so that's
03:06 going to be two-fifths plus 1/6 we do
03:14 not have a common denominator so we need
03:16 to rename with a common denominator in
03:19 order to add five and six the common
03:23 denominator is going to be 30 so let's
03:28 rename I know 5 times 6 is 30 so let's
03:32 do it to the top 2 times 6 is 12 6 times
03:39 5 will give me my denominator of 30 so I
03:43 need to do 1 times 5 is 5 so here we
03:50 have 12 plus 5 is 17 keep our
03:54 denominator of 30 so she read a total of
04:00 17 thirtieths this is how much she has
04:04 read so we need to figure out what
04:08 fraction is left how do we get to 30 out
04:11 of 30 or 100% of the book what's
04:14 remaining well 13 thirtieths would get
04:18 us to that 30
04:19 over 30 or the a hundred percent of the
04:22 book so we have thirteen thirtieths left
04:28 and think about it seventeen plus that
04:32 thirteen gets us to again the 30 out of
04:36 30 which is one whole or 100 percent of
04:39 the book so there you have it there's a
04:42 couple of situations or word problems
04:44 where we had to add fractions in order
04:47 to find the solution thanks so much for
04:51 watching until next time peace
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