Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
Add and subtract like fractions. Add and subtract unlike fractions. Multiply and divide fractions. Place fractions in simplest form. Read word problems to determine the appropriate operation (+, -, x, ) needed to solve a problem.
Use visuals, such as fraction bars, to help your child see fraction relationships and operations. You can draw these yourself or buy a set at a teacher supply store. To create your own you simply draw two empty rectangles (they must be the same size and work best if you draw one beneath the other). Next, split the first bar into the number of pieces determined by the denominator (bottom number) of the first fraction. For example, if I have ¾ + ½ , my first rectangle would be split into four parts because the denominator of the first fraction is 4. Next, I would color in 3 of the sections to represent the numerator. After that, I’d repeat these steps on the next rectangle to represent ½. Finally, use the both bars to combine the result. You’ll need to draw some new lines make them into the same number of pieces for both bars. So, for the ½ fraction bar you’ll draw 2 more lines to split it into fourths. Now just count the colored squares. That’s your new numerator (top number). Count all the squares colored and uncolored. That your new denominator. So, you new fraction is 5/4 or 1 ¼.
Most standardized tests require students to place fraction answers in simplest form. Remind your child to simplify fractions by dividing to put them in the lowest form. For example, if I subtract two fractions and get 7/14, I need to simplify. There are two quick checks you can do to determine if a fraction needs to be reduced. The first is to determine if the larger number of the fraction is divisible by the smaller number. For my fraction, 14 is divisible by 7 because 7x2=14. So, I simply divided both numbers by 7 and I get 77=1 (new numerator) and 147=2 (new denominator). The simplified fraction is ½. The second quick check is to determine if the numerator and denominator have a factor or factors in common. If they do, you choose the greatest common factor and divide both the numerator and denominator by it. So, if I have 6/8 and I know that 6 does not go into 8 evenly, I think about any other factors that both 6 and 8 are divisible by. I know that since they’re both even that they are divisible by 2. I divide each term by two and get ¾, my simplified fraction.
Sometimes when computing fractions you’ll get an answer that is improper. This means the number on the numerator is larger than the denominator (ex. 10/3). These fractions need to be simplified and written as a mixed number. To simplify any improper fraction you divide the numerator by the denominator (103) and write the answer showing the remainder (3 r 1). The first number is the whole number, the remainder is the numerator and the denominator stays the same. So, 10/3 = 3-1/3 in simplest form.
When adding or subtracting fractions the denominators must be the same. Once all denominators are the same we keep them and use them in the final answer. We never add or subtract denominators. Hence,
1/3 + 1/3 = 2/3, we keep the 3.
When adding and subtracting fractions you will either have like terms or unlike terms. Like terms have the same denominator and can be solved immediately by simply adding the two numerators, keeping the denominator and simplifying, if possible. However, if you have two unlike terms you need to make them like before you can begin to solve them. So, if you have 7/8 – ¾ you need to find the LCD (least common denominator) to make the fractions like. The LCD of the denominators of 8 and 4 is 8. That’s because 8 is the least (smallest) multiple of 4 and 8. Now you need to change ¾ so that it has a denominator of 8. To do this remember, "whatever you do to the bottom, you do to the top". To change the denominator from a 4 to and 8 you needed to multiply by 2. So you must do the same to the top (numerator) and multiply 3 by 2. Your new fraction will be 6/8. The problem would be re-written 7/8-6/8. To complete the problem you subtract the numerators and keep the denominator. The answer you get is 1/8.
To multiply fractions you have two choices. First, you can multiply both numerators and both denominators and then simplify your answer. However, sometimes this will leave you with very large fractions to simplify. You can take a shortcut and cross cancel before multiplying across the numerators and denominators.
To divide fractions you need to always multiply by the reciprocal of the second fraction. So, ½ ¾ becomes ½ x 4/3.
Use key words to help you determine the operation needed to solve a word problem. Words such as altogether, total, combined suggest that you should add to solve. If something is being taken away, removed, eaten, lost, etc… it would be subtracted. You multiply when you are combining or totaling groups coming together. When you want to split things into equal parts you divide.
To add or subtract mixed numbers simply follow steps to add or subtract the fractions first. Then add or subtract the whole numbers.
To multiply or divide mixed numbers you must convert them into improper fractions. You can convert a mixed number like 1-2/5 into an improper fraction by multiplying the denominator by the whole number, then adding the numerator to that product. The sum becomes your new numerator. So, 5x1=5 and 5+2=7, keep the denominator and the improper fraction is 7/5.