Chapter 7 Math Guide

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1 I can write fractions as a sum Write as unit fractions This means the fractions are broken into each individual unit/1 single piece. The fraction is /6. The model shows that pieces are shaded in. If you write /6 as a sum of unit fractions, you are adding each of those 1/6 pieces. /6 = 1/6 + 1/6 + 1/6 + 1/6 or 1/6 + 1/6 + 1/6 + 1/6 = /6 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 The fractions is 7/10. The model shows that 7 pieces are shaded in. If you write 7/10 as a sum of unit fractions, you are adding each of those 1/10 pieces. 7/10 = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 or 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 7/10 Write as a sum of fractions When you write as a sum (not specifically unit), you can use any numbers that add up to the total pieces. The fraction is /6. The model shows that pieces are shaded in. The pieces/fractions you put together must add up to total pieces. /6 = /6 + /6 or /6 = 1/6 + /6 or /6 = 1/6 + 1/6 + /6 Online Resources:

2 I can write fractions as a sum Write as a sum of fractions (continued) When you write as a sum (not specifically unit), you can use any numbers that add up to the total pieces. The fraction is 7/10. The model shows that 7 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 pieces are shaded in. The pieces/fractions you put together must add up to 7 total pieces. 7/10 = 5/10 + /10 or 7/10 = /10 + /10 or 7/10 = 1/10 + 6/10 or 7/10 = /10 + /10 + /10 Or 7/10 = /10 + /10 + 1/10 or 7/10 = /10 + /10 + /10 + 1/10 etc. There are more correct answers. They must just add up to the 7 total pieces. You can group them in any way; just make sure you get all 7 pieces and don t have less/extras.

3 I can write mixed numbers and improper fractions Mixed Numbers Mixed numbers are used when there is more than 1 whole. It is a mix of whole numbers and fractions. The whole number is listed first. It is written bigger. The fraction is written after and the complete fraction should be the same size as the whole number. 1 whole 1 whole 1 whole 1/ 1 Improper Fractions Improper fractions are used when there is more than one whole. They are not proper because the numerator is bigger than the denominator. You count up all of the individual pieces. The denominator is the same because the size of the pieces is the same no matter how many you have. 1 / / / 1/ Example Mixed Number 6 Improper Fraction whole 1 whole /6 6/6 6/6 /6 Online Resources:

4 I can rename mixed numbers and improper fractions Change mixed numbers to improper fractions / / + / + / + / + / = 1/ = 1/ 1. Break the whole number into the individual whole numbers as an addition problem.. Change each whole number into the fraction form of it. You have to look at the denominator because this will change each time. In order to have a whole, the numerator and denominator will be the same. You have all of those certain sized pieces. The denominator for this one is, so you would need of (/) to be a whole.. Use what you know about adding fractions to add them all up. You will add the numerators because you have that many pieces. The denominator will stay the same because the size of the pieces is staying the same. The numerator will be bigger than the denominator. This is an improper fraction /7 7/7 + 7/ /7 + 7/7 + /7 = 8/7 5 = 8/7 7 Online Resources: 1. Break the whole number into the individual whole numbers as an addition problem.. Change each whole number into the fraction form of it. You have to look at the denominator because this will change each time. In order to have a whole, the numerator and denominator will be the same. You have all of those certain sized pieces. The denominator for this one is 7, so you would need 7 of 7 (7/7) to be a whole.. Use what you know about adding fractions to add them all up. You will add the numerators because you have that many pieces. The denominator will stay the same because the size of the pieces is staying the same. The numerator will be bigger than the denominator. This is an improper fraction.

5 I can rename mixed numbers and improper fractions Change improper fractions to mixed numbers 1/ Strategy 1 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ = 1/ 1. Break the fraction into a sum of unit fractions. Remember, this means it is broken into each individual piece with a 1 as the numerator.. Look at the denominator to see how you make a whole for this problem. The denominator in this problem is a, so out of pieces (/) will create one whole. Group together as many (/) as you can to create 1 wholes. This problem has wholes with of the 1/ pieces left over.. Add these wholes up and put it next to the fraction still left. The mixed number will have a whole number and the unit fractions left added back together as one fraction. = 1 7/5 Strategy 5/5 + 5/5 + 5/5+ 5/5+ 5/5+ 5/5 +5/5 + / /5 7/5 = Break the fraction into a sum of fractions. Look at the denominator to see how you make a whole for this problem. The denominator in this problem is a 5, so 5 out fo 5 (5/5) will create one whole. Think about how many of these 5/5 will add up to the 7/5. There can be 7 of them because those 7 will add up to 5/5. You need 7/5, so you add on /5 to get the full 7/5.. Add these wholes up and put it next to the fraction still left. The mixed number will have a whole number and the fraction. 7 = 7 5 5

6 I can rename mixed numbers and improper fractions Change mixed numbers to improper fractions x = 1 1. Multiply the whole number by the denominator. For this problem, you have of the / pieces. When you multiply by, you now have 1 of those pieces (1/) 1 + = 1 = 1. Add the numerator to the 1/ because the / means you also have of those 1/ size pieces.. The 1 is your numerator, you have 1 total 1/ size pieces. The denominator stays. Change improper fractions to mixed numbers. 1 R ) Divide the numerator by the denominator to find out how many whole pieces are in the fraction. The answer is, so you have as the whole number. You have a remainder of, which means of those 1/ size pieces are left. This becomes your fraction of /. 1 =. Put the whole number and fraction together to create your mixed number.

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