Addition
Compute:
5/12 + 4/12
Answer:
9/12 = 3/4
Compute:
7/9 − 1/9
Answer:
6/9 = 2/3
Compute:
1/2 x 10/11
Answer:
10/22 OR 5/11
What do we have to do when we divide by a fraction?
Keep, Change, Flip
What grade and subject will Mr. Brady be teaching this fall, and in which borough?
Answer:
9th grade Geometry, in the Bronx
T/F: You MUST change the mixed numbers in an addition problem to improper fractions before adding them.
FALSE! You can, but it can be MORE work! Who wants more work? Just make sure the fraction pieces have the same denominator. If not, you must find equivalent fractions with common denominators.
Which of these problems requires you to borrow (regroup)?
a) 8 3/4 − 2 1/4
b) 5 1/6 − 3 5/6
c) 9 7/8 − 4 3/8
d) 6 2/3 − 1 1/3
Answer: b — 1/6 is smaller than 5/6, so you have to borrow from the 5.
Compute:
2 3/4 x 16/33
11/4 x 16/33
1/1 x 4/3
Answer: 4/3 OR 1 1/3
OR 176/132
Compute:
5/8 ÷ 3/4
Answer:
5/8 × 4/3 = 20/24 = 5/6
Where did Mr. Brady go to college?
a) Fordham University
b) Cornell University
c) University of Connecticut
d) Mr. Brady was too good for college
e) Mr. Brady joined the peace corps
b) Cornell University
Give three different strategies for finding common denominators
1. Multiply the denominators together
2. The larger denominator is the common denominator (only change one fraction)
3. List the multiples of each denominator and select the first one they have in common
Explain in your own words what "borrowing" means when you subtract mixed numbers. Then show it using 5 1/4 − 2 3/4.
Answer:
You trade one whole for a fraction equal to 1 with the same denominator. 5 1/4 becomes 4 5/4 → 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2
T/F: You have to cross cancel in this problem to get the right answer:
4/7 x 21/10
You don't HAVE to! You should, though! You will get equivalent fractions either way.
Non-cross-cancelling: 4/7 x 21/10 = 84/70 = 6/5
Cross-cancelling: 2/1 x 3/5 = 6/5
T/F:
Dividing always makes a number smaller, so 3/4 ÷ 1/2 must be less than 3/4. Explain your reasoning.
Answer:
FALSE. 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1 1/2. Ask "how many halves fit into 3/4?" — since 1/2 is smaller than 3/4, more than one fits.
What is the name of Mr. Brady's Co-Fellow? The other bearded teacher in the same program as Mr. Brady that is often in the room?
Mr. Kaufman!
Compute:
7 5/8 + 4 3/10
Answer:
Least Common Denominator = 40
7 25/40 + 4 12/40 = 11 37/40
Compute:
12 1/6 − 8 3/4
Answer:
LCD 12 → 12 2/12 − 8 9/12 → borrow → 11 14/12 − 8 9/12 = 3 5/12
Compute:
4 3/8 x 1 2/14
Answer to 4 3/8 x 1 2/14:
35/8 x 16/14 = 5/1 x 2/2 = 5 x 1 = 5
Compute:
7 1/2 ÷ 2 1/4
Answer:
15/2 ÷ 9/4 = 15/2 × 4/9, cross-cancel → 5/3 × 2/1 = 10/3 = 3 1/3
What is Mr. Brady's other job when he isn't teaching?
a) Barista
b) Software engineer
c) Dog walker
d) Professional soccer player
e) All of the above
Answer: b
A student solved 2 3/4 + 1 5/6 and got 3 8/10. Find the mistake, explain what they did wrong, and give the correct answer.
Answer: They added numerators and denominators straight across instead of finding a common denominator. Correct: 9/12 + 10/12 = 19/12 = 1 7/12, so 4 7/12
Mr. Brady ran 8 1/4 miles on Saturday and 5 5/6 miles on Sunday.
(a) How many more miles did he run on Saturday than Sunday?
(b) His goal was 20 miles for the whole weekend. How many more miles does he need?
Answer:
(a) 2 5/12 miles
(b) total = 14 1/12, so he needs 5 11/12 miles
Mr. Brady and Allendy are on the same soccer team. Mr. Brady scored 6 goals in the soccer game. If Allendy scored 2/3 of the goals that Mr. Brady did in his soccer game and they are the only ones who scored, how many goals did Allendy and Mr. Brady score together?
6 + (6 x 2/3) = 6 + 4 = 10
Allendy and Mr. Brady scored 10 goals in total.
Mr. Brady's garden bed is 7 1/2 feet long. He wants to split it into plots that are each 5/6 of a foot wide.
(a) How many plots does he get?
(b) If he plants 27 seedlings spread evenly across those plots, how many go in each plot?
Answer:
(a) 15/2 × 6/5 = 9 plots
(b) 3 seedlings per plot
Mr. Brady co-founded a nonprofit (charity) in high school. What did it do?
Answer: A student-run community garden that grew food for people facing food insecurity.