Grade 7 Math notes Unit Operations with Fractions name: Using Models to Add Fractions We can use pattern blocks to model fractions. A hexagon is whole A trapezoid is of the whole. A parallelogram is of the whole A triangle is of the whole We can use these blocks to find equivalent fractions. Equivalent Fractions: two or more fractions of equal value represented by different numerators and denominators. 00 0 Ex: 00 00 0 0 0 Ex. : Find as many equivalent fractions for as possible using pattern blocks. 0 We could model as Or 9 as
Example : Add the following First model each fraction. Find a common shape that can be used to make up both fractions = Fractions can also be modeled and added using fraction circles. 7 Ex. Add Step Model each fraction 7 Step Find a common denominator 7
Step Add So the sum is whole PRACTICE PROBLEMS. Use Pattern Blocks to show each sum. Sketch the Pattern Blocks. Write an addition equation for each picture. a) + b) + c) +. Use fraction circles to show each sum. Sketch the fraction circles. Write an addition equation for each picture. a) + b) + 0 c) +
Using Symbols to Add Fractions To add fractions we need to rewrite each as equivalent fractions with a common denominator. Ex. Step : Find a common denominator. The smallest number both and will go into evenly is 0. So 0 will be our common denominator. Step : Re-write each fraction as an equivalent fraction of the common denominator. X X 0 Since X = 0 We multiply the old numerator () by to get the new numerator 0 X X X X 0 Since X = 0 We multiply the old numerator () by to get the new numerator 0 X X Step : Add the new numerators 0 0 0 0 (this is our final answer!)
This same problem could have been similarly done using fractions circles to find a common denominator. Then divide into tenths So when we combine the pieces we get 0 0 0 0 The good news is that subtraction follows almost all the same patterns as addition! See the next page for details!
Subtracting Fractions using Models When subtracting fractions we must also have a common denominator as when adding. Ex. st - we model nd we remove Ex. st model nd remove which is the same as THIS LEAVES US WITH Our final answer!!!
We can also use fraction strips to subtract fractions Ex. 9 7 st - draw a number line divided into 9 th s and shade /9 th s 0 0 nd remove which is the same as 9 0 So our final equation and answer is 9 9 Practice Problems. Subtract. a) b) c) 9 0 7 0 d) 7. Subtract. Use fraction circles or strips. Sketch pictures to show each difference. a) 7 b) 9 c) 0 d)
. Brandy spent of her summer vacation reading, 0 watching her favorite movies, visiting her grandparents, and twice the reading time playing with her friends. a) What is the difference in the fractions Brandy spent with her grandparents and playing with her friends? b) Did she spend more time reading or watching movies? Explain your thinking. c) Did Brandy have time to do anything else beside these activities? Explain your thinking.. Glenn has of a cup of walnuts. He needs of a cup of walnuts to make a loaf of banana bread. Does Glenn have enough? If your answer is yes, explain why it is enough. If your answer is no, how much more does Glenn need?
Adding with Mixed Numbers 9 When adding mixed number it is always important to first estimate the sum to make sure your answer is reasonable. Ex. is a little lass than and is a little less than a half so the sum is a bit more than To find the actual sum we can model each addend. + Split the thirds into sixth s Use a sixth to make a whole We can also use fraction strips to add mixed numbers Ex.
0 The first addend is a little less than The second is a little more than So the sum should be a little less than To find the sum first draw the number line required. 0 Model the st fraction 0 Add the second fraction = 0 Subtracting Mixed Numbers We can use fraction circles to subtract mixed numbers in the same way we used to them to add. Ex. Model the first mixed number
Divide each circle into eighths (because is a common denominator for &!!!) Remove three eighths FINAL ANSWER: We have 7 remaining We can also subtract mixed numbers on a number line. Ex. First model 0 Split each whole into sixths by dividing each half into thirds. (Because is a common denominator for &!!!) 0 Remove the wholes - 0
Remove 0 So or simplified to lowest terms our final answer is. Adding and Subtracting Mixed Numbers without models The following steps will work 00% of the time for adding and subtracting mixed numbers!!! STEP : Change your mixed numbers into improper fractions! STEP : Make sure your fractions have a common denominator (they have to have the same number on the bottom!) STEP : Add your numerators!!! STEP : Write your answer as a mixed numbers and in lowest terms!