Operations & Expressions
Evaluate: 118 × (2/3 + 2/6) − 6 × 4
2/3 + 2/6 = 4/6 + 2/6 = 6/6 = 1.
118×1 = 118.
6×4 = 24.
118 − 24 = 94.
Final: 94.
Find 2/3 + 1/4.
Common denominator 12: 8/12 + 3/12 = 11/12. Final: 11/12.
50 lb ÷ 8 groups — write as a fraction
(50/8 (pounds per group).
Simplifies to 6 2/8 = 6 1/4 lb.
Value of 4 in 5,472 and in 624; how many times greater?
5,472 → 400. 624 → 4. 400 ÷ 4 = 100 times greater.
3500 mL into each of 6 pitchers. How many liters total? (choices)
3500 mL = 3.5 L. 3.5×6=21 L. Final: 21 L
Write an expression for "12 times the difference between 57 and 24
12(57 − 24).
Explanation: take the difference then multiply by 12.
3/5 + 3/4 = 12/20 + / = ___/20. Fill blanks.
3/4 = 15/20. So 12/20 + 15/20 = 27/20 = 1 7/20.
Estimate 50 ÷ 8 — between which two whole numbers?
6.25 → between 6 and 7.
7500 ÷ 100 = ?
Move decimal two left or remove two zeros: 75.
Convert 5 cm to meters; 10 ribbons of 5 cm → how many meters?
5 cm = 0.05 m. 10×0.05 = 0.5 m
Evaluate: (18 + 9) ÷ 3.
(18+9)=27;
27÷3=9.
Final: 9.
Compute 3 5/8 − 2 6/8 (show work).
Rename: 3 5/8 = 2 13/8. 2 13/8 − 2 6/8 = 7/8. Final: 7/8.
Sherika used 2/3, 1/4, and 2/6 lb. Total?
2/6 = 1/3. 2/3 + 1/3 = 1. 1 + 1/4 = 1 1/4 lb.
Which number has 9 valued 10× its value in 19? (960, 689, 498, 302)
In 19, 9 = 9. Ten times = 90 → 498 (9 in tens place = 90).
1/4 + 3/8; rest = ?
1/4 = 2/8 → 2/8 + 3/8 = 5/8. Remaining = 3/8.
Compare 6 + (14 ÷ 2) and (6 + 14) ÷ 2; compute both.
6 + (14 ÷ 2) = 6 + 7 = 13.
(6 + 14) ÷ 2 = 20 ÷ 2 = 10.
Parentheses change order.
2/3 − 1/4. Show subtraction and common mistake.
2/3 = 8/12; 1/4 = 3/12; 8/12 − 3/12 = 5/12. Mistake: changing denominators but not numerators.
If she needs 2 × 1/4 more and started with 2 lb, does she have enough?
Additional = 1/2. Total = 1 1/4 + 1/2 = 1 3/4. 1 3/4 < 2 → Yes.
Pattern of zeros when multiplying by powers of 10. Two examples.
×10 adds one zero (37×10=370). ×100 adds two zeros (37×100=3700).
Two-step metric problem (example).
Example: 2.75 L = 2750 mL. 2750 ÷ 500 mL = 5 jars, remainder 250 mL.
Explain why 3 × (18932 + 921) is 3× as large as (18932 + 921).
Multiplication by 3 creates three equal copies: 3×(sum) = sum + sum + sum. So it's 3 times larger.
Explain subtracting mixed numbers when fractional part of minuend is smaller; give example.
Unbundle one whole from minuend to increase fraction numerator. Example: 5 1/6 − 2 4/6 → 4 7/6 − 2 4/6 = 2 1/2.
50 lb shared by 9 people = ?
50 ÷ 9 = 50/9 = 5 5/9 lb. Between 5 and 6.
Why does 3.4×10 shift decimal? Example with whole numbers.
×10 multiplies by 10, shifting decimal right one place: 3.4×10=34 (10× larger). Example: 56×100=5600 (100× larger).
2.75 L × 6 = ? Convert total to mL.
2.75×6 = 16.5 L → 16,500 mL.