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Unit 1 Math

Vocabulary

Question: What do you call a fraction that has a whole number part and a fraction part?
Answer: A mixed number

Question: What do you call fractions that have only 1's in the numerator portion of the fraction?
Answer: Unit fractions

Question: 2/5 and 5/6 do NOT have common ______________?
Answer: Denominators

Question: What do you call a fraction that has been rewritten with a common denominator?
Answer: An equivalent fraction

Question: What do you call a fraction that has a larger number in the numerator portion than in the denominator? (hint:  the bunk bed could collapse if the heavier person is on the top) AND What do you use to avoid having to simplify a fraction?
Answer: An improper fraction/LCD or LCM (least common denominator/least common multiple)

Equal Rights!!!

Question: Give an equivalent fraction for 5/6.
Answer: Possible answers:  10/12; 15/18

Question: Give an equivalent fraction to 9/15.
Answer: Possible answers:  3/5; 18/30

Question: Give an equivalent fraction to 2/10.
Answer: Possible answers:  1/5; 20/100

Question: Are 3/4 and 6/8 equivalent fractions?  Why?
Answer: Yes, they are.  If you multiply the numerator and denominator in 3/4 by 2, you will get 6/8.

Question: Name a fraction and an equivalent fraction for it.  Explain.
Answer: Answers will vary.

Compare Me

Question: 3/10 vs. 3/11  
Answer: 3/10 > 3/11

Question: 5/9 vs. 7/12
Answer: 5/9 < 7/12

Question: 1/3 vs. 3/8
Answer: 1/3 < 3/8

Question: If two fractions have the same numerator, such as 4/5 and 4/6, which one is bigger?  Why?
Answer: 4/5 is bigger, because the smaller the denominator, the bigger the "pieces" there are.

Question: If two fractions have the same denominator, such as 6/7 and 3/7, which one is bigger.  Explain your answer.  AND Which benchmark fraction is 6/7 closer to, 0, 1/2, or 1?  Explain.
Answer: 6/7 is bigger.  When two fractions have the same denominator, which ever one has more "pieces," is the bigger fraction.  6/7 is closer to 1, because it is only 1 away from 7/7, which would be one whole.

Be Reasonable!

Question: Ms. Thames walked to school from her house in Laredo Ranch.  It is 5 1/2 miles away.  She ran the first 4  5/8 of a mile, but she had to walk the last 7/10 of a mile.  How far is it from Ms. Thames' house to Ellsworth Elementary?  Check to make sure your answer is reasonable.
Answer: 5  13/40 miles

Question: Mr. Olsen has 2  3/4 cups of raisins.  He wants to make his famous raisin bread recipe that calls for 4  1/3 cups of raisins.  How many more cup(s) of raisins does he need?  Is 7 cups a reasonable answer?
Answer: 1  7/12 cups of raisins/no

Question: Mrs. Gutierrez  bought 5  1/4 yards of blue bulletin board paper and 3  2/3 yards of red bulletin board paper for her back wall in her classroom.  She gave 2  3/4 yards to Mrs. Bencomo.  How much bulletin board paper does she now have left?  EXPLAIN how you know your answer is reasonable.
Answer: 6  1/6 yards of bulletin board paper; 5  1/4 yards rounds to 5, & 3  2/3 rounds to 4.  2  3/4 rounds to 3, so she had about 9 yards and gave away about 3 yards, leaving her with about 6 yards.

Question: Puzzled Penguin did the math problem 7  1/5 -  1  2/3 on his whiteboard.  His answer was 6  8/15.  Did he get the problem right?  Does he EVER? :)  Why or why not?  Give the correct answer if he is wrong and explain.
Answer: No, he didn't.  The correct answer is 5  8/15.  He forgot to make the whole number 7 a 6 when he ungrouped so that he could subtract the numerators in the fractions.

Question: Explain how you know that the sum in this problem is NOT REASONABLE WITHOUT figuring out the actual sum.  
8/9 + 1/7 = 35/63

Answer: Possible response:  8/9 is almost one whole.  How could adding another fraction to that equal out to be barely more than 1/2?!  35 is barely more than 1/2 of 63.

He Giveth and Taketh Away

Question: Add or Subtract:  2/9 + 2/3
Answer: 8/9

Question: Add or Subtract:  5/8 - 3/10
Answer: 13/40

Question: Add or Subtract:  6/7 + 2  5/6
Answer: 3  29/42

Question: Add or Subtract:  4  1/5 -  3  7/10
Answer: 1/2

Question: Add or Subtract:  1  5/8 + 2  1/2
Answer: 4  1/8