To add two like fractions, add the numerators of the fractions and keep the denominator.
81+ 83= 84
To add two unlike fractions, find common denominators and then add the numerators.
41+ 61= 132+ 122= 152
To subtract like fractions, subtract the numerator of the second fraction from the numerator of the first and keep the denominator.
To subtract unlike fractions, find common denominators, subtract the numerator of the second fraction from the numerator of the first, and keep the denominator.
53– 83= 4240– 4150= 490
To multiply two fractions, like or unlike, multiply the numerators and mul- tiply the denominators.
25≈ 37= 365
To divide two fractions, like or unlike, multiply the first fraction by the reciprocal of the second fraction.
6543= 65≈ 43= 2180
To convert an improper fraction into a mixed number, divide the numerator of the fraction by the denominator. The whole number part of that division is the whole number part of the mixed number. The remain- der, if any, becomes the numerator of the fraction, and the denominator remains the same.
2180= 1182
To reduce or simplify a fraction, find the greatest common factor of the numerator and denominator and divide the numerator and denominator by that number.
1125= = 132 45
135
FUEL FOR THOUGHT LIKE FRACTIONS HAVE the same denominator; 56and 46are like fractions. Unlike fractions have different denominators; 56and 19are unlike fractions. A proper fraction a value between 0 and 1 or between –1 and 0. The number in the numerator is usually less than the number in the denominator of the fraction. An improper fraction has a value greater than or equal to 1, or less than or equal to –1. A
mixed numbercontains both an integer and a fraction. The greatest
common factorof two numbers is the largest integer that both num- bers can be divided by with no remainder.
Now that we’ve reviewed how to work with fractions, let’s look at some fraction word problems. We can use any of the strategies we’ve learned to answer these questions.
Example
DeDe pours 1 cup of cereal into a bowl. She adds 21cup of milk from a container that contains 243cups of milk. How many cups of milk are left in the container?
Let’s use the eight-step process to answer this question.
Read the entire word problem.
We are given the amount of milk in the container and the amount that DeDe pours into her cereal bowl.
Identify the question being asked.
We are looking for how much milk is left in the container.
Underline the keywords.
The keyword left signals subtraction.
Cross out extra information and translate words into numbers.
We do not need to know that there is 1 cup of cereal in the bowl. That information will not help us solve this problem, so cross it out.
To find how much milk is left in the container, we have to subtract the original amount in the container from the amount that DeDe poured out.
Write number sentences for each operation.
243– 21
Solve the number sentences and decide which answer is reasonable.
Convert one-half to fourths and subtract: 243– 42= 241
Since DeDe used only half a cup of milk, this answer seems reasonable.
Check your work.
We solved this problem using subtraction, so we must use addition to check our work. Add the number of cups of milk DeDe put in her cereal to the new amount of milk in the container. The sum should equal the original volume of milk in the container: 241+ 42= 243. Our answer is correct.
Example
Tatiana spends an hour and a half at the gym four days a week. How many hours does she spend at the gym each week?
Let’s solve this problem by drawing a picture. Draw a full circle and a half circle for each of the four days Tatiana goes to the gym. The full circle rep- resents a full hour, and the half circle represents half an hour:
There are four full circles and four half circles. Each pair of half circles makes a whole circle, so we have six whole circles. Tatiana spends six hours in the gym each week.
Example
Mark buys 381pounds of turkey and 2110 pounds of bologna. He uses
45pounds to make a sandwich. How many pounds of meat does he have left?
Read the entire word problem.
We are given the number of pounds of turkey and bologna that Mark buys and the number of pounds of meat he uses to make a sandwich.
Identify the question being asked.
We are looking for how much meat he has left.
Underline the keywords.
The keyword add signals addition, and the keyword left signals subtraction.
Cross out extra information and translate words into numbers.
There is no extra information in this word problem.
List the possible operations.
First, we need to find how much meat Mark bought by adding the weight of the turkey to the weight of the bologna. Then, we will sub- tract the weight of the meat used to make the sandwich from this total.
Write number sentences for each operation.
381+ 2110
Solve the number sentences and decide which answer is reasonable.
Convert eighths and tenths to fortieths and add: 381+ 2110= 3450+ 2440= 5490
Write number sentences for each operation.
Now that we have the total weight of the meat Mark bought, we can subtract the weight of the meat used to make the sandwich to find how much meat is left:
5490– 43
Solve the number sentences and decide which answer is reasonable.
Convert fourths to fortieths and subtract:
Check your work.
We solved this problem using subtraction and addition, so we must use addition and subtraction to check our work. Add the number of pounds of meat Mark used for his sandwich to the number of pounds of meat he had left: 44190+ 3040= 5490. Subtract from that total the number of pounds of bologna Mark bought, 2110, and we should be left with the number of pounds of turkey Mark bought, 381: 5490– 2110
= 5490– 2440 = 3450= 381pounds of meat.
PRACTICE L AP
1.When Zoe’s birthday party is over, 58of the cake remains. If Mor- gan eats 18of the cake, how much of the cake will be left?
2.Sue has 35ounces of almond extract. If she divides it equally over four batches of fudge, how many ounces of almond extract are in each batch of fudge?
3.Yves uses 23yards of string to tie a bundle of magazines. If he has six bundles to tie, how many yards of string does he need?
4. Every student in Sayda’s class must bring in 87square feet of fab- ric for an art project. If there are 24 students in the class, and her teacher brings in an additional 347square feet of fabric, how many total square feet of fabric will be used for the project?
5. Patrick spends three-fourths of an hour studying for his math test and half an hour studying for his science test. How many total minutes did Patrick spend studying?
PACE YOURSELF
HOPE BUYS WATERby the case. One water company sells a case of 24 bottles, each filled with 59liters of water. A second company sells a case of 20 bottles, each filled with 57liters of water. Which case contains more water? How did you figure that out? If you knew the price of each case, what would you do to figure out which case was the better deal?