UNIT 2 BRIDGES MATH

Adding/Subtracting Fractions

100

Add: 1/5+1/3

• Common denominator 15: 
• 3/15+ 5/15 =8/15

200

Add: 2/5 + 1/8=

• Common denominator 40: 
• 16/40+5/40=21/40

300

3/4-1/8=

Common denominator 8:

 6/8−1/8=5/8

400

1 2/5-6/10=

Convert to improper & common denom:

1 2/ 5=7/5

convert 6/10=3/5

• Subtract: 7/5−3/5=4/5

500

2 3/8-7/24=

Be sure to simplify

2 3/8−7/24=

2 3/8−7/24

• Convert: 2 3/8=19/8. 
• Common denominator 24: 19/8=57/24.
• Subtract: 57/24−7/24=50/24
• GCF:2  so 50/24=25/12
• Answer: 25/12= 2 1/12
  
  

Equivalent Denominators

100

Rewrite with common denominators and add: 

1/3 + 1/8=

 SHOW EQUIVALENT FRACTIONS FIRST

• Common denominator 24: 
• 8/24+3/24=11/24
• Answer: 11/24

200

Rewrite with common denominators and add:

4 2/14 + 2 4/7=

SHOW EQUIVALENT FRACTIONS FIRST

CONVERT TO MIXED NUMBERS IF NECESSARY

• Simplify mixed pieces first: 4 2/14
• note 2/14=1/7 so 4 1/7
• Second: 2 4/7 already with sevenths.
• Convert to improper:  4 1/7=29/7   
• 2 4/7=18/7
• Add: 29/7+18/7= 47/7
• Answer: 6 5/7

300

2/3-3/6=

SHOW EQUIVALENT FRACTIONS FIRST

• Convert: 3/6=1/2
• Common denominator 6: 4/6−3/6=1/6
• Answer: 1/6

400

8 1/2 - 3 1/8=

• Convert to improper: 8 1/2=17/2                 3 1/8=25/8
• Common denominator 8: 
• 17/2=68/8
• Subtract: 68/8−25/8=43/8=
• 43/8= 5 3/8
• Answer: 5 3/8

500

Convert to improper fractions, use common denominators, then add: 3 1/4+2 5/6=

• Improper: 3 1/4=13/4                                    2 5/ 6=17/6
• Common denominator 12: 13/4=39/124 17/6=34/12
• Add: 39/12+34/12= 73/12
• Answer: 6 1/12

Multiplication & Of

100

1/3 X 24=

8

200

1/12 of 72

6

300

2/5 X 15=

6

400

3/4 of 28

21

500

Sasha ran 2/3 of a 27 km race. How many km did she run? Show work using numbers or a labeled sketch.

18 K

Word Problems

100

Fill-in: Find the missing value: 2 3/8+____     = 3

5/8

200

Find the missing value: ____+ 1 1/6=2 3/4

• Convert: 1 1/6=7/6                                        2 3/4=11/4
• Convert both to twelfths: 7/6=14/12       11/4=33/12
• Subtract: 33/12−14/12=19/12
• Answer: 1 7/12

300

Connor mixed dry ingredients: 

1 1/4 + 2 2/3 + 1 1/6 cups. How many cups total?

• Convert to improper: 11/4=5/4                       2 2/3=8/3    1 1/6=7/6
• Common denominator 12:                              8/3=32/12       5/4=15/12    7/6=14/12
• Sum: 15/12+32/12+14/12=61/12
• Answer: 61/12= 5 1/12 cups

400

Ryan is 5 1/4  ft tall and John is 5 1/3 ft tall. 

a) Who is taller? b) How much taller?

• Compare: Convert to twelfths :
  • 5 1/4= 5 3/12 ft
  • 5 1/3= 5 4/12 ft
• a) Who is taller? John.
• b) Difference: 5  4/12−5 3/12
  • Use twelfths: 5 1/12  
• Answer: John is taller by 1/12 ft 

500

Combined running: Dawn ran 2/5 of the trail Monday and 1/3 Tuesday. 

a) How much of the trail in total? 

b) Which day was farther? 

c) How much farther?

• a) Total: common denominator 15: 6/15+5/15=11/15
  • Answer: 11/15of the trail
• b) Which day farther? 
• Compare 5/15-6/15= → Monday was farther.
• c) How much farther? 6/15−5/15=1/15
  • Answer: Monday by 1/15 of the trail

Better Buy & Mixed Sums

100

 Which is a better buy: 

12 cans for $7  or 

6 cans for $4? 

Explain with unit price.

• Unit price option A: $7÷12=7/12             dollars per can=$0.58
• Option B: $4÷6=4/6=                         dollars per can=$0.66
• Better buy: 12 for $7 (cheaper per can)
• Answer: 12 for $7 — unit price 7/12 ($0.58)

200

Which is a better buy: 

6 cans for $7  or 

8 cans for $9?

Explain with unit price.

• Option A: $7÷6=-$1.16
• Option B: $9÷8=$1.12
• Better buy: 8 for $9 (slightly cheaper)
• Answer: 8 for $9 — unit price $1.12
•  6 cans for $7 =$ 1.16

300

Tonya ran 2/3 of a mile and then walked 2/6 of a mile. a) Choose best estimate: 

-More than a mile 

-between 1/2 and 1 

-Less than 1/2.

b) Find exact total.

c) Is 4/9 a reasonable answer? Why or why not?

 Best precise statement: the total is exactly 1 mile.

• 
  
  • b) Exact total: 23+26=23+13=132+62=32+31=1 mile
  • c) Danny's answer 4/9 is not reasonable because sums must be at least as big as the larger addend. So 4/9 is incorrect.
  • Answer: total = 1 mile; 4/9 is not reasonable.

400

Mixed-number addition: Add and simplify: 

3 5/6 +2 7/12=

(show conversion to improper, common denom, then simplify)

• Convert: 3 5/6=23/6                                      2 7/12=31/12
• Common denom 12:
• 23/6=46/12
• Sum: 46/12+31/12=77/12
• Answer: 6 5/12

500

Mixed challenge: A recipe needs 3/8 cup of oil per batch. If you make 5 batches, how much oil total? Express as a mixed number and in cups.

Oil: 3/8 cup per batch × 5 batches

• Multiply: 3/8×5=15/8
• Answer: 1 7/8 cups